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-% \iffalse
-%
-%% File l3sort.dtx
-%
-% Copyright (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{l3sort} module\\ Sorting functions^^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}
-%
-% \section{Controlling sorting}
-%
-% \label{sec:l3sort:mech}
-%
-% \LaTeX3 comes with a facility to sort list variables (sequences,
-% token lists, or comma-lists) according to some user-defined
-% comparison. For instance,
-% \begin{verbatim}
-% \clist_set:Nn \l_foo_clist { 3 , 01 , -2 , 5 , +1 }
-% \clist_sort:Nn \l_foo_clist
-% {
-% \int_compare:nNnTF { #1 } > { #2 }
-% { \sort_return_swapped: }
-% { \sort_return_same: }
-% }
-% \end{verbatim}
-% results in \cs[no-index]{l_foo_clist} holding the values
-% |{ -2 , 01 , +1 , 3 , 5 }| sorted in non-decreasing order.
-%
-% The code defining the comparison should call
-% \cs{sort_return_swapped:} if the two items given as |#1|
-% and |#2| are not in the correct order, and otherwise it
-% should call \cs{sort_return_same:} to indicate that
-% the order of this pair of items should not be changed.
-%
-% For instance, a \meta{comparison code} consisting only
-% of \cs{sort_return_same:} with no test yields a trivial
-% sort: the final order is identical to the original order.
-% Conversely, using a \meta{comparison code} consisting only
-% of \cs{sort_return_swapped:} reverses the list (in a fairly
-% inefficient way).
-%
-% \begin{texnote}
-% The current implementation is limited to sorting approximately
-% $20000$ items ($40000$ in \LuaTeX{}), depending on what other
-% packages are loaded.
-%
-% Internally, the code from \pkg{l3sort} stores items in \tn{toks}
-% registers allocated locally. Thus, the \meta{comparison code}
-% should not call \tn{newtoks} or other commands that allocate new
-% \tn{toks} registers. On the other hand, altering the value of a
-% previously allocated \tn{toks} register is not a problem.
-% \end{texnote}
-%
-% \begin{function}[added = 2017-02-06]{\sort_return_same:, \sort_return_swapped:}
-% \begin{syntax}
-% \cs{seq_sort:Nn} \meta{seq~var}
-% ~~|{| \ldots{} \cs{sort_return_same:} or \cs{sort_return_swapped:} \ldots{} |}|
-% \end{syntax}
-% Indicates whether to keep the order or swap the order of two items
-% that are compared in the sorting code. Only one of the
-% \cs[no-index]{sort_return_\ldots{}} functions should be used by the
-% code, according to the results of some tests on the items |#1| and
-% |#2| to be compared.
-% \end{function}
-%
-% \end{documentation}
-%
-% \begin{implementation}
-%
-% \section{\pkg{l3sort} implementation}
-%
-% \begin{macrocode}
-%<*package>
-% \end{macrocode}
-%
-% \begin{macrocode}
-%<@@=sort>
-% \end{macrocode}
-%
-% \subsection{Variables}
-%
-% \begin{variable}{\g_@@_internal_seq, \g_@@_internal_tl}
-% Sorting happens in a group; the result is stored in those global
-% variables before being copied outside the group to the proper
-% places. For seq and tl this is more efficient than using \cs{use:e}
-% (or some \cs{exp_args:NNNe}) to smuggle the definition outside the
-% group since \TeX{} does not need to re-read tokens. For clist we
-% don't gain anything since the result is converted from seq to clist
-% anyways.
-% \begin{macrocode}
-\seq_new:N \g_@@_internal_seq
-\tl_new:N \g_@@_internal_tl
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}
-% {
-% \l_@@_length_int, \l_@@_min_int, \l_@@_top_int, \l_@@_max_int,
-% \l_@@_true_max_int
-% }
-% The sequence has \cs{l_@@_length_int} items and is stored from
-% \cs{l_@@_min_int} to $\cs{l_@@_top_int}-1$. While reading the
-% sequence in memory, we check that \cs{l_@@_top_int} remains at most
-% \cs{l_@@_max_int}, precomputed by \cs{@@_compute_range:}. That
-% bound is such that the merge sort only uses \tn{toks} registers
-% less than \cs{l_@@_true_max_int}, namely those that have not been
-% allocated for use in other code: the user's comparison code could
-% alter these.
-% \begin{macrocode}
-\int_new:N \l_@@_length_int
-\int_new:N \l_@@_min_int
-\int_new:N \l_@@_top_int
-\int_new:N \l_@@_max_int
-\int_new:N \l_@@_true_max_int
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_@@_block_int}
-% Merge sort is done in several passes. In each pass, blocks of size
-% \cs{l_@@_block_int} are merged in pairs. The block size starts
-% at $1$, and, for a length in the range $[2^k+1,2^{k+1}]$, reaches
-% $2^{k}$ in the last pass.
-% \begin{macrocode}
-\int_new:N \l_@@_block_int
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_@@_begin_int}
-% \begin{variable}{\l_@@_end_int}
-% When merging two blocks, \cs{l_@@_begin_int} marks the lowest
-% index in the two blocks, and \cs{l_@@_end_int} marks the
-% highest index, plus $1$.
-% \begin{macrocode}
-\int_new:N \l_@@_begin_int
-\int_new:N \l_@@_end_int
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_@@_A_int}
-% \begin{variable}{\l_@@_B_int}
-% \begin{variable}{\l_@@_C_int}
-% When merging two blocks (whose end-points are \texttt{beg}
-% and \texttt{end}), $A$ starts from the high end of the low
-% block, and decreases until reaching \texttt{beg}. The index
-% $B$ starts from the top of the range and marks the register
-% in which a sorted item should be put. Finally, $C$ points
-% to the copy of the high block in the interval of registers
-% starting at \cs{l_@@_length_int}, upwards. $C$ starts
-% from the upper limit of that range.
-% \begin{macrocode}
-\int_new:N \l_@@_A_int
-\int_new:N \l_@@_B_int
-\int_new:N \l_@@_C_int
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \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}
-%
-% \subsection{Finding available \tn{toks} registers}
-%
-% \begin{macro}{\@@_shrink_range:}
-% \begin{macro}{\@@_shrink_range_loop:}
-% After \cs{@@_compute_range:} (defined below) determines that
-% \tn{toks} registers between \cs{l_@@_min_int} (included) and
-% \cs{l_@@_true_max_int} (excluded) have not yet been assigned,
-% \cs{@@_shrink_range:} computes \cs{l_@@_max_int} to reflect the need
-% for a buffer when merging blocks in the merge sort. Given
-% $2^{n}\leq A\leq 2^{n}+2^{n-1}$ registers we can sort $\lfloor
-% A/2\rfloor+2^{n-2}$ items while if we have $2^{n}+2^{n-1}\leq A\leq
-% 2^{n+1}$ registers we can sort $A-2^{n-1}$ items. We first find out
-% a power $2^{n}$ such that $2^{n}\leq A\leq 2^{n+1}$ by repeatedly
-% halving \cs{l_@@_block_int}, starting at $2^{15}$ or $2^{14}$ namely
-% half the total number of registers, then we use the formulas and set
-% \cs{l_@@_max_int}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_shrink_range:
- {
- \int_set:Nn \l_@@_A_int
- { \l_@@_true_max_int - \l_@@_min_int + 1 }
- \int_set:Nn \l_@@_block_int { \c_max_register_int / 2 }
- \@@_shrink_range_loop:
- \int_set:Nn \l_@@_max_int
- {
- \int_compare:nNnTF
- { \l_@@_block_int * 3 / 2 } > \l_@@_A_int
- {
- \l_@@_min_int
- + ( \l_@@_A_int - 1 ) / 2
- + \l_@@_block_int / 4
- - 1
- }
- { \l_@@_true_max_int - \l_@@_block_int / 2 }
- }
- }
-\cs_new_protected:Npn \@@_shrink_range_loop:
- {
- \if_int_compare:w \l_@@_A_int < \l_@@_block_int
- \tex_divide:D \l_@@_block_int 2 \exp_stop_f:
- \exp_after:wN \@@_shrink_range_loop:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\@@_compute_range:, \@@_redefine_compute_range:}
-% \begin{variable}{\c_@@_max_length_int}
-% First find out what \tn{toks} have not yet been assigned. There are
-% many cases. In \LaTeXe{} with no package, available \tn{toks} range
-% from $\tn{count}15+1$ to \cs{c_max_register_int} included (this was
-% not altered despite the 2015 changes). When \tn{loctoks} is
-% defined, namely in plain (e)\TeX{}, or when the package \pkg{etex}
-% is loaded in \LaTeXe{}, redefine \cs{@@_compute_range:} to use the
-% range $\tn{count}265$ to $\tn{count}275-1$. The \pkg{elocalloc}
-% package also defines \tn{loctoks} but uses yet another number for
-% the upper bound, namely \cs{e@alloc@top} (minus one). We must check
-% for \tn{loctoks} every time a sorting function is called, as
-% \pkg{etex} or \pkg{elocalloc} could be loaded.
-%
-% In \ConTeXt{} MkIV the range is from
-% $|\c_syst_last_allocated_toks|+1$ to \cs{c_max_register_int}, and in
-% MkII it is from $|\lastallocatedtoks|+1$ to \cs{c_max_register_int}.
-% In all these cases, call \cs{@@_shrink_range:}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_compute_range:
- {
- \int_set:Nn \l_@@_min_int { \tex_count:D 15 + 1 }
- \int_set:Nn \l_@@_true_max_int { \c_max_register_int + 1 }
- \@@_shrink_range:
- \if_meaning:w \loctoks \tex_undefined:D \else:
- \if_meaning:w \loctoks \scan_stop: \else:
- \@@_redefine_compute_range:
- \@@_compute_range:
- \fi:
- \fi:
- }
-\cs_new_protected:Npn \@@_redefine_compute_range:
- {
- \cs_if_exist:cTF { ver@elocalloc.sty }
- {
- \cs_gset_protected:Npn \@@_compute_range:
- {
- \int_set:Nn \l_@@_min_int { \tex_count:D 265 }
- \int_set_eq:NN \l_@@_true_max_int \e@alloc@top
- \@@_shrink_range:
- }
- }
- {
- \cs_gset_protected:Npn \@@_compute_range:
- {
- \int_set:Nn \l_@@_min_int { \tex_count:D 265 }
- \int_set:Nn \l_@@_true_max_int { \tex_count:D 275 }
- \@@_shrink_range:
- }
- }
- }
-\cs_if_exist:NT \loctoks { \@@_redefine_compute_range: }
-\tl_map_inline:nn { \lastallocatedtoks \c_syst_last_allocated_toks }
- {
- \cs_if_exist:NT #1
- {
- \cs_gset_protected:Npn \@@_compute_range:
- {
- \int_set:Nn \l_@@_min_int { #1 + 1 }
- \int_set:Nn \l_@@_true_max_int { \c_max_register_int + 1 }
- \@@_shrink_range:
- }
- }
- }
-% \end{macrocode}
-% \end{variable}
-% \end{macro}
-%
-% \subsection{Protected user commands}
-%
-% \begin{macro}{\@@_main:NNNn}
-% Sorting happens in three steps. First store items in \tn{toks}
-% registers ranging from \cs{l_@@_min_int} to $\cs{l_@@_top_int}-1$,
-% while checking that the list is not too long. If we reach the
-% maximum length, that's an error; exit the group. Secondly, sort the
-% array of \tn{toks} registers, using the user-defined sorting
-% function: \cs{@@_level:} calls \cs{@@_compare:nn} as needed.
-% Finally, unpack the \tn{toks} registers (now sorted) into the target
-% tl, or into \cs{g_@@_internal_seq} for seq and clist. This is done
-% by \cs{@@_seq:NNNNn} and \cs{@@_tl:NNn}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_main:NNNn #1#2#3#4
- {
- \@@_disable_toksdef:
- \@@_compute_range:
- \int_set_eq:NN \l_@@_top_int \l_@@_min_int
- #1 #3
- {
- \if_int_compare:w \l_@@_top_int = \l_@@_max_int
- \@@_too_long_error:NNw #2 #3
- \fi:
- \tex_toks:D \l_@@_top_int {##1}
- \int_incr:N \l_@@_top_int
- }
- \int_set:Nn \l_@@_length_int
- { \l_@@_top_int - \l_@@_min_int }
- \cs_set:Npn \@@_compare:nn ##1 ##2 {#4}
- \int_set:Nn \l_@@_block_int { 1 }
- \@@_level:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\tl_sort:Nn, \tl_sort:cn, \tl_gsort:Nn, \tl_gsort:cn}
-% \begin{macro}{\@@_tl:NNn}
-% \begin{macro}[EXP]{\@@_tl_toks:w}
-% Call the main sorting function then unpack \tn{toks} registers
-% outside the group into the target token list. The unpacking is done
-% by \cs{@@_tl_toks:w}; registers are numbered from \cs{l_@@_min_int}
-% to $\cs{l_@@_top_int}-1$. For expansion behaviour we need a couple
-% of primitives. The \cs{tl_gclear:N} reduces memory usage. The
-% \cs{prg_break_point:} is used by \cs{@@_main:NNNn} when the list is
-% too long.
-% \begin{macrocode}
-\cs_new_protected:Npn \tl_sort:Nn { \@@_tl:NNn \tl_set_eq:NN }
-\cs_generate_variant:Nn \tl_sort:Nn { c }
-\cs_new_protected:Npn \tl_gsort:Nn { \@@_tl:NNn \tl_gset_eq:NN }
-\cs_generate_variant:Nn \tl_gsort:Nn { c }
-\cs_new_protected:Npn \@@_tl:NNn #1#2#3
- {
- \group_begin:
- \@@_main:NNNn \tl_map_inline:Nn \tl_map_break:n #2 {#3}
- \__kernel_tl_gset:Nx \g_@@_internal_tl
- { \@@_tl_toks:w \l_@@_min_int ; }
- \group_end:
- #1 #2 \g_@@_internal_tl
- \tl_gclear:N \g_@@_internal_tl
- \prg_break_point:
- }
-\cs_new:Npn \@@_tl_toks:w #1 ;
- {
- \if_int_compare:w #1 < \l_@@_top_int
- { \tex_the:D \tex_toks:D #1 }
- \exp_after:wN \@@_tl_toks:w
- \int_value:w \int_eval:n { #1 + 1 } \exp_after:wN ;
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_sort:Nn, \seq_sort:cn, \seq_gsort:Nn, \seq_gsort:cn}
-% \begin{macro}{\clist_sort:Nn, \clist_sort:cn, \clist_gsort:Nn, \clist_gsort:cn}
-% \begin{macro}{\@@_seq:NNNNn}
-% Use the same general framework for seq and clist. Apply the general
-% sorting code, then unpack \tn{toks} into \cs{g_@@_internal_seq}.
-% Outside the group copy or convert (for clist) the data to the target
-% variable. The \cs{seq_gclear:N} reduces memory usage. The
-% \cs{prg_break_point:} is used by \cs{@@_main:NNNn} when the list is
-% too long.
-% \begin{macrocode}
-\cs_new_protected:Npn \seq_sort:Nn
- { \@@_seq:NNNNn \seq_map_inline:Nn \seq_map_break:n \seq_set_eq:NN }
-\cs_generate_variant:Nn \seq_sort:Nn { c }
-\cs_new_protected:Npn \seq_gsort:Nn
- { \@@_seq:NNNNn \seq_map_inline:Nn \seq_map_break:n \seq_gset_eq:NN }
-\cs_generate_variant:Nn \seq_gsort:Nn { c }
-\cs_new_protected:Npn \clist_sort:Nn
- {
- \@@_seq:NNNNn \clist_map_inline:Nn \clist_map_break:n
- \clist_set_from_seq:NN
- }
-\cs_generate_variant:Nn \clist_sort:Nn { c }
-\cs_new_protected:Npn \clist_gsort:Nn
- {
- \@@_seq:NNNNn \clist_map_inline:Nn \clist_map_break:n
- \clist_gset_from_seq:NN
- }
-\cs_generate_variant:Nn \clist_gsort:Nn { c }
-\cs_new_protected:Npn \@@_seq:NNNNn #1#2#3#4#5
- {
- \group_begin:
- \@@_main:NNNn #1 #2 #4 {#5}
- \seq_gclear:N \g_@@_internal_seq
- \int_step_inline:nnn
- \l_@@_min_int { \l_@@_top_int - 1 }
- {
- \seq_gput_right:Ne \g_@@_internal_seq
- { \tex_the:D \tex_toks:D ##1 }
- }
- \group_end:
- #3 #4 \g_@@_internal_seq
- \seq_gclear:N \g_@@_internal_seq
- \prg_break_point:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Merge sort}
-%
-% \begin{macro}{\@@_level:}
-% This function is called once blocks of size \cs{l_@@_block_int}
-% (initially $1$) are each sorted. If the whole list fits in one
-% block, then we are done (this also takes care of the case of an
-% empty list or a list with one item). Otherwise, go through pairs
-% of blocks starting from $0$, then double the block size, and repeat.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_level:
- {
- \if_int_compare:w \l_@@_block_int < \l_@@_length_int
- \l_@@_end_int \l_@@_min_int
- \@@_merge_blocks:
- \tex_advance:D \l_@@_block_int \l_@@_block_int
- \exp_after:wN \@@_level:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_merge_blocks:}
-% This function is called to merge a pair of blocks, starting at
-% the last value of \cs{l_@@_end_int} (end-point of the previous
-% pair of blocks). If shifting by one block to the right we reach
-% the end of the list, then this pass has ended: the end of the
-% list is sorted already. Otherwise, store the result of that shift in $A$,
-% which indexes the first block starting from the top end.
-% Then locate the end-point (maximum) of the second block: shift
-% \texttt{end} upwards by one more block, but keeping it
-% $\leq\texttt{top}$. Copy this upper block of \tn{toks}
-% registers in registers above \texttt{length}, indexed by $C$:
-% this is covered by \cs{@@_copy_block:}. Once this is done we
-% are ready to do the actual merger using \cs{@@_merge_blocks_aux:},
-% after shifting $A$, $B$ and $C$ so that they point to the largest
-% index in their respective ranges rather than pointing just beyond
-% those ranges. Of course, once that pair of blocks is merged,
-% move on to the next pair.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_merge_blocks:
- {
- \l_@@_begin_int \l_@@_end_int
- \tex_advance:D \l_@@_end_int \l_@@_block_int
- \if_int_compare:w \l_@@_end_int < \l_@@_top_int
- \l_@@_A_int \l_@@_end_int
- \tex_advance:D \l_@@_end_int \l_@@_block_int
- \if_int_compare:w \l_@@_end_int > \l_@@_top_int
- \l_@@_end_int \l_@@_top_int
- \fi:
- \l_@@_B_int \l_@@_A_int
- \l_@@_C_int \l_@@_top_int
- \@@_copy_block:
- \int_decr:N \l_@@_A_int
- \int_decr:N \l_@@_B_int
- \int_decr:N \l_@@_C_int
- \exp_after:wN \@@_merge_blocks_aux:
- \exp_after:wN \@@_merge_blocks:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_copy_block:}
-% We wish to store a copy of the \enquote{upper} block of
-% \tn{toks} registers, ranging between the initial value of
-% \cs{l_@@_B_int} (included) and \cs{l_@@_end_int}
-% (excluded) into a new range starting at the initial value
-% of \cs{l_@@_C_int}, namely \cs{l_@@_top_int}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_copy_block:
- {
- \tex_toks:D \l_@@_C_int \tex_toks:D \l_@@_B_int
- \int_incr:N \l_@@_C_int
- \int_incr:N \l_@@_B_int
- \if_int_compare:w \l_@@_B_int = \l_@@_end_int
- \use_i:nn
- \fi:
- \@@_copy_block:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_merge_blocks_aux:}
-% At this stage, the first block starts at \cs{l_@@_begin_int},
-% and ends at \cs{l_@@_A_int}, and the second block starts at
-% \cs{l_@@_top_int} and ends at \cs{l_@@_C_int}. The result
-% of the merger is stored at positions indexed by \cs{l_@@_B_int},
-% which starts at $\cs{l_@@_end_int}-1$ and decreases down to
-% \cs{l_@@_begin_int}, covering the full range of the two blocks.
-% In other words, we are building the merger starting with the
-% largest values.
-% The comparison function is defined to return either
-% \texttt{swapped} or \texttt{same}. Of course, this
-% means the arguments need to be given in the order they
-% appear originally in the list.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_merge_blocks_aux:
- {
- \exp_after:wN \@@_compare:nn \exp_after:wN
- { \tex_the:D \tex_toks:D \exp_after:wN \l_@@_A_int \exp_after:wN }
- \exp_after:wN { \tex_the:D \tex_toks:D \l_@@_C_int }
- \prg_do_nothing:
- \@@_return_mark:w
- \@@_return_mark:w
- \s_@@_mark
- \@@_return_none_error:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\sort_return_same:, \sort_return_swapped:}
-% \begin{macro}{\@@_return_mark:w}
-% \begin{macro}{\@@_return_none_error:, \@@_return_two_error:}
-% Each comparison should call \cs{sort_return_same:} or
-% \cs{sort_return_swapped:} exactly once. If neither is called,
-% \cs{@@_return_none_error:} is called, since the \texttt{return_mark}
-% removes tokens until \cs{s_@@_mark}. If one is called, the
-% \texttt{return_mark} auxiliary removes everything except
-% \cs{@@_return_same:w} (or its \texttt{swapped} analogue) followed by
-% \cs{@@_return_none_error:}. Finally if two or more are called,
-% \cs{@@_return_two_error:} ends up before any \cs{@@_return_mark:w},
-% so that it produces an error.
-% \begin{macrocode}
-\cs_new_protected:Npn \sort_return_same:
- #1 \@@_return_mark:w #2 \s_@@_mark
- {
- #1
- #2
- \@@_return_two_error:
- \@@_return_mark:w
- \s_@@_mark
- \@@_return_same:w
- }
-\cs_new_protected:Npn \sort_return_swapped:
- #1 \@@_return_mark:w #2 \s_@@_mark
- {
- #1
- #2
- \@@_return_two_error:
- \@@_return_mark:w
- \s_@@_mark
- \@@_return_swapped:w
- }
-\cs_new_protected:Npn \@@_return_mark:w #1 \s_@@_mark { }
-\cs_new_protected:Npn \@@_return_none_error:
- {
- \msg_error:nnee { sort } { return-none }
- { \tex_the:D \tex_toks:D \l_@@_A_int }
- { \tex_the:D \tex_toks:D \l_@@_C_int }
- \@@_return_same:w \@@_return_none_error:
- }
-\cs_new_protected:Npn \@@_return_two_error:
- {
- \msg_error:nnee { sort } { return-two }
- { \tex_the:D \tex_toks:D \l_@@_A_int }
- { \tex_the:D \tex_toks:D \l_@@_C_int }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\@@_return_same:w}
-% If the comparison function returns \texttt{same},
-% then the second argument fed to \cs{@@_compare:nn}
-% should remain to the right of the other one. Since
-% we build the merger starting from the right, we copy
-% that \tn{toks} register into the allotted range, then
-% shift the pointers $B$ and $C$, and go on to do one
-% more step in the merger, unless the second block has
-% been exhausted: then the remainder of the first block
-% is already in the correct registers and we are done
-% with merging those two blocks.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_return_same:w #1 \@@_return_none_error:
- {
- \tex_toks:D \l_@@_B_int \tex_toks:D \l_@@_C_int
- \int_decr:N \l_@@_B_int
- \int_decr:N \l_@@_C_int
- \if_int_compare:w \l_@@_C_int < \l_@@_top_int
- \use_i:nn
- \fi:
- \@@_merge_blocks_aux:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_return_swapped:w}
-% If the comparison function returns \texttt{swapped},
-% then the next item to add to the merger is the first
-% argument, contents of the \tn{toks} register $A$.
-% Then shift the pointers $A$ and $B$ to the left, and
-% go for one more step for the merger, unless the left
-% block was exhausted ($A$ goes below the threshold).
-% In that case, all remaining \tn{toks} registers in
-% the second block, indexed by $C$, are copied
-% to the merger by \cs{@@_merge_blocks_end:}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_return_swapped:w #1 \@@_return_none_error:
- {
- \tex_toks:D \l_@@_B_int \tex_toks:D \l_@@_A_int
- \int_decr:N \l_@@_B_int
- \int_decr:N \l_@@_A_int
- \if_int_compare:w \l_@@_A_int < \l_@@_begin_int
- \@@_merge_blocks_end: \use_i:nn
- \fi:
- \@@_merge_blocks_aux:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_merge_blocks_end:}
-% This function's task is to copy the \tn{toks} registers
-% in the block indexed by $C$ to the merger indexed by $B$.
-% The end can equally be detected by checking when $B$ reaches
-% the threshold \texttt{begin}, or when $C$ reaches
-% \texttt{top}.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_merge_blocks_end:
- {
- \tex_toks:D \l_@@_B_int \tex_toks:D \l_@@_C_int
- \int_decr:N \l_@@_B_int
- \int_decr:N \l_@@_C_int
- \if_int_compare:w \l_@@_B_int < \l_@@_begin_int
- \use_i:nn
- \fi:
- \@@_merge_blocks_end:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Expandable sorting}
-%
-% Sorting expandably is very different from sorting and assigning to a
-% variable. Since tokens cannot be stored, they must remain in the
-% input stream, and be read through at every step. It is thus
-% necessarily much slower (at best $O(n^2\ln n)$) than non-expandable
-% sorting functions ($O(n\ln n)$).
-%
-% A prototypical version of expandable quicksort is as follows. If the
-% argument has no item, return nothing, otherwise partition, using the
-% first item as a pivot (argument |#4| of \cs{@@:nnNnn}). The
-% arguments of \cs{@@:nnNnn} are 1.~items less than |#4|, 2.~items
-% greater or equal to |#4|, 3.~comparison, 4.~pivot, 5.~next item to
-% test. If |#5| is the tail of the list, call \cs{tl_sort:nN} on |#1|
-% and on |#2|, placing |#4| in between; |\use:ff| expands the parts to
-% make \cs{tl_sort:nN} \texttt{f}-expandable. Otherwise, compare |#4|
-% and |#5| using |#3|. If they are ordered, place |#5| amongst the
-% \enquote{greater} items, otherwise amongst the \enquote{lesser} items,
-% and continue partitioning.
-% \begin{verbatim}
-% \cs_new:Npn \tl_sort:nN #1#2
-% {
-% \tl_if_blank:nF {#1}
-% {
-% \__sort:nnNnn { } { } #2
-% #1 \q__sort_recursion_tail \q__sort_recursion_stop
-% }
-% }
-% \cs_new:Npn \__sort:nnNnn #1#2#3#4#5
-% {
-% \quark_if_recursion_tail_stop_do:nn {#5}
-% { \use:ff { \tl_sort:nN {#1} #3 {#4} } { \tl_sort:nN {#2} #3 } }
-% #3 {#4} {#5}
-% { \__sort:nnNnn {#1} { #2 {#5} } #3 {#4} }
-% { \__sort:nnNnn { #1 {#5} } {#2} #3 {#4} }
-% }
-% \cs_generate_variant:Nn \use:nn { ff }
-% \end{verbatim}
-% There are quite a few optimizations available here: the code below is
-% less legible, but more than twice as fast.
-%
-% In the simple version of the code, \cs{@@:nnNnn} is called
-% \(O(n\ln n)\) times on average (the number of comparisons required by
-% the quicksort algorithm). Hence most of our focus is on
-% optimizing that function.
-%
-% The first speed up is to avoid testing for the end of the list at
-% every call to \cs{@@:nnNnn}. For this, the list is prepared by
-% changing each \meta{item} of the original token list into
-% \meta{command} \Arg{item}, just like sequences are stored. We arrange
-% things such that the \meta{command} is the \meta{conditional} provided
-% by the user: the loop over the \meta{prepared tokens} then looks like
-% \begin{quote}
-% \ttfamily
-% \cs{cs_new:Npn}~\cs{@@_loop:wNn}~\ldots{}~|#6#7|\\
-% ~~|{|\\
-% ~~~~|#6|~\Arg{pivot}~|{#7}|~\meta{loop big}~\meta{loop small}\\
-% ~~~~~~\meta{extra arguments}\\
-% ~~|}|\\
-% \cs{@@_loop:wNn}~\ldots{}~\meta{prepared tokens}\\
-% ~~\meta{end-loop}~|{}|~\cs{s_@@_stop}
-% \end{quote}
-% In this example, which matches the structure of
-% \cs{@@_quick_split_i:NnnnnNn} and a few other functions below, the
-% \cs{@@_loop:wNn} auxiliary normally receives the user's
-% \meta{conditional} as~|#6| and an \meta{item} as~|#7|. This is
-% compared to the \meta{pivot} (the argument~|#5|, not shown here), and
-% the \meta{conditional} leaves the \meta{loop big} or \meta{loop small}
-% auxiliary, which both have the same form as \cs{@@_loop:wNn},
-% receiving the next pair \meta{conditional} \Arg{item} as |#6|
-% and~|#7|. At the end, |#6| is the \meta{end-loop} function, which
-% terminates the loop.
-%
-% The second speed up is to minimize the duplicated tokens between the
-% \texttt{true} and \texttt{false} branches of the conditional. For
-% this, we introduce two versions of \cs{@@:nnNnn}, which receive
-% the new item as~|#1| and place it either into the list~|#2| of items
-% less than the pivot~|#4| or into the list~|#3| of items greater or
-% equal to the pivot.
-% \begin{verbatim}
-% \cs_new:Npn \__sort_i:nnnnNn #1#2#3#4#5#6
-% {
-% #5 {#4} {#6} \__sort_ii:nnnnNn \__sort_i:nnnnNn
-% {#6} { #2 {#1} } {#3} {#4}
-% }
-% \cs_new:Npn \__sort_ii:nnnnNn #1#2#3#4#5#6
-% {
-% #5 {#4} {#6} \__sort_ii:nnnnNn \__sort_i:nnnnNn
-% {#6} {#2} { #3 {#1} } {#4}
-% }
-% \end{verbatim}
-% Note that the two functions have the form of \cs{@@_loop:wNn} above,
-% receiving as~|#5| the conditional or a function to end the loop. In
-% fact, the lists~|#2| and~|#3| must be made of pairs \meta{conditional}
-% \Arg{item}, so we have to replace~|{#6}| above by |{|~|#5|~|{#6}|~|}|,
-% and |{#1}|~by~|#1|. The actual functions have one more argument, so
-% all argument numbers are shifted compared to this code.
-%
-% The third speed up is to avoid |\use:ff| using a continuation-passing
-% style: \cs{@@_quick_split:NnNn} expects a list followed by
-% \cs{s_@@_mark} \Arg{code}, and expands to \meta{code} \meta{sorted list}.
-% Sorting the two parts of the list around the pivot is done with
-% \begin{quote}
-% \ttfamily
-% \cs{@@_quick_split:NnNn} |#2| \ldots{} \cs{s_@@_mark}\\
-% ~~|{|\\
-% ~~~~\cs{@@_quick_split:NnNn} |#1| \ldots{} \cs{s_@@_mark} \Arg{code}\\
-% ~~~~\Arg{pivot}\\
-% ~~|}|
-% \end{quote}
-% Items which are larger than the \meta{pivot} are sorted, then placed
-% after code that sorts the smaller items, and after the (braced)
-% \meta{pivot}.
-%
-% The fourth speed up is avoid the recursive call to \cs{tl_sort:nN}
-% with an empty first argument. For this, we introduce functions
-% similar to the \cs{@@_i:nnnnNn} of the last example, but aware of
-% whether the list of \meta{conditional} \Arg{item} read so far that are
-% less than the pivot, and the list of those greater or equal, are empty
-% or not: see \cs{@@_quick_split:NnNn} and functions defined below.
-% Knowing whether the lists are empty or not is useless if we do not use
-% distinct ending codes as appropriate. The splitting auxiliaries
-% communicate to the \meta{end-loop} function (that is initially placed
-% after the ``prepared'' list) by placing a specific ending function,
-% ignored when looping, but useful at the end. In fact, the
-% \meta{end-loop} function does nothing but place the appropriate ending
-% function in front of all its arguments. The ending functions take
-% care of sorting non-empty sublists, placing the pivot in between, and
-% the continuation before.
-%
-% The final change in fact slows down the code a little, but is required
-% to avoid memory issues: schematically, when \TeX{} encounters
-% \begin{verbatim}
-% \use:n { \use:n { \use:n { ... } ... } ... }
-% \end{verbatim}
-% the argument of the first \cs{use:n} is not completely read by the
-% second \cs{use:n}, hence must remain in memory; then the argument of
-% the second \cs{use:n} is not completely read when grabbing the
-% argument of the third \cs{use:n}, hence must remain in memory, and so
-% on. The memory consumption grows quadratically with the number of
-% nested \cs{use:n}. In practice, this means that we must read
-% everything until a trailing \cs{s_@@_stop} once in a while, otherwise
-% sorting lists of more than a few thousand items would exhaust a
-% typical \TeX{}'s memory.
-%
-% \begin{macro}[EXP]{\tl_sort:nN}
-% \begin{macro}[EXP]
-% {
-% \@@_quick_prepare:Nnnn,
-% \@@_quick_prepare_end:NNNnw,
-% \@@_quick_cleanup:w
-% }
-% The code within the \cs{exp_not:f} sorts the list, leaving in most
-% cases a leading \cs{exp_not:f}, which stops the expansion, letting
-% the result be return within \cs{exp_not:n}. We filter out the case
-% of a list with no item, which would otherwise cause problems. Then
-% prepare the token list~|#1| by inserting the conditional~|#2| before
-% each item. The \texttt{prepare} auxiliary receives the conditional
-% as~|#1|, the prepared token list so far as~|#2|, the next prepared
-% item as~|#3|, and the item after that as~|#4|. The loop ends
-% when~|#4| contains \cs{prg_break_point:}, then the
-% \texttt{prepare_end} auxiliary finds the prepared token list
-% as~|#4|. The scene is then set up for \cs{@@_quick_split:NnNn},
-% which sorts the prepared list and perform the post action placed
-% after \cs{s_@@_mark}, namely removing the trailing \cs{s_@@_stop} and
-% \cs{s_@@_stop} and leaving \cs{exp_stop_f:} to stop
-% \texttt{f}-expansion.
-% \begin{macrocode}
-\cs_new:Npn \tl_sort:nN #1#2
- {
- \exp_not:f
- {
- \tl_if_blank:nF {#1}
- {
- \@@_quick_prepare:Nnnn #2 { } { }
- #1
- { \prg_break_point: \@@_quick_prepare_end:NNNnw }
- \s_@@_stop
- }
- }
- }
-\cs_new:Npn \@@_quick_prepare:Nnnn #1#2#3#4
- {
- \prg_break: #4 \prg_break_point:
- \@@_quick_prepare:Nnnn #1 { #2 #3 } { #1 {#4} }
- }
-\cs_new:Npn \@@_quick_prepare_end:NNNnw #1#2#3#4#5 \s_@@_stop
- {
- \@@_quick_split:NnNn #4 \@@_quick_end:nnTFNn { }
- \s_@@_mark { \@@_quick_cleanup:w \exp_stop_f: }
- \s_@@_mark \s_@@_stop
- }
-\cs_new:Npn \@@_quick_cleanup:w #1 \s_@@_mark \s_@@_stop {#1}
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]
-% {
-% \@@_quick_split:NnNn,
-% \@@_quick_only_i:NnnnnNn,
-% \@@_quick_only_ii:NnnnnNn,
-% \@@_quick_split_i:NnnnnNn,
-% \@@_quick_split_ii:NnnnnNn
-% }
-% The \texttt{only_i}, \texttt{only_ii}, \texttt{split_i} and
-% \texttt{split_ii} auxiliaries receive a useless first argument, the
-% new item~|#2| (that they append to either one of the next two
-% arguments), the list~|#3| of items less than the pivot, bigger
-% items~|#4|, the pivot~|#5|, a \meta{function}~|#6|, and an
-% item~|#7|. The \meta{function} is the user's \meta{conditional}
-% except at the end of the list where it is
-% \cs{@@_quick_end:nnTFNn}. The comparison is applied to the
-% \meta{pivot} and the \meta{item}, and calls the \texttt{only_i} or
-% \texttt{split_i} auxiliaries if the \meta{item} is smaller, and the
-% \texttt{only_ii} or \texttt{split_ii} auxiliaries otherwise. In
-% both cases, the next auxiliary goes to work right away, with no
-% intermediate expansion that would slow down operations. Note that
-% the argument~|#2| left for the next call has the form
-% \meta{conditional} \Arg{item}, so that the lists~|#3| and~|#4| keep
-% the right form to be fed to the next sorting function.
-% The \texttt{split} auxiliary differs from these in that it is
-% missing three of the arguments, which would be empty, and its first
-% argument is always the user's \meta{conditional} rather than an
-% ending function.
-% \begin{macrocode}
-\cs_new:Npn \@@_quick_split:NnNn #1#2#3#4
- {
- #3 {#2} {#4} \@@_quick_only_ii:NnnnnNn
- \@@_quick_only_i:NnnnnNn
- \@@_quick_single_end:nnnwnw
- { #3 {#4} } { } { } {#2}
- }
-\cs_new:Npn \@@_quick_only_i:NnnnnNn #1#2#3#4#5#6#7
- {
- #6 {#5} {#7} \@@_quick_split_ii:NnnnnNn
- \@@_quick_only_i:NnnnnNn
- \@@_quick_only_i_end:nnnwnw
- { #6 {#7} } { #3 #2 } { } {#5}
- }
-\cs_new:Npn \@@_quick_only_ii:NnnnnNn #1#2#3#4#5#6#7
- {
- #6 {#5} {#7} \@@_quick_only_ii:NnnnnNn
- \@@_quick_split_i:NnnnnNn
- \@@_quick_only_ii_end:nnnwnw
- { #6 {#7} } { } { #4 #2 } {#5}
- }
-\cs_new:Npn \@@_quick_split_i:NnnnnNn #1#2#3#4#5#6#7
- {
- #6 {#5} {#7} \@@_quick_split_ii:NnnnnNn
- \@@_quick_split_i:NnnnnNn
- \@@_quick_split_end:nnnwnw
- { #6 {#7} } { #3 #2 } {#4} {#5}
- }
-\cs_new:Npn \@@_quick_split_ii:NnnnnNn #1#2#3#4#5#6#7
- {
- #6 {#5} {#7} \@@_quick_split_ii:NnnnnNn
- \@@_quick_split_i:NnnnnNn
- \@@_quick_split_end:nnnwnw
- { #6 {#7} } {#3} { #4 #2 } {#5}
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]
-% {
-% \@@_quick_end:nnTFNn,
-% \@@_quick_single_end:nnnwnw,
-% \@@_quick_only_i_end:nnnwnw,
-% \@@_quick_only_ii_end:nnnwnw,
-% \@@_quick_split_end:nnnwnw,
-% }
-% The \cs{@@_quick_end:nnTFNn} appears instead of the user's
-% conditional, and receives as its arguments the pivot~|#1|, a fake
-% item~|#2|, a \texttt{true} and a \texttt{false} branches |#3|
-% and~|#4|, followed by an ending function~|#5| (one of the four
-% auxiliaries here) and another copy~|#6| of the fake item. All those
-% are discarded except the function~|#5|. This function receives
-% lists~|#1| and~|#2| of items less than or greater than the
-% pivot~|#3|, then a continuation code~|#5| just after \cs{s_@@_mark}.
-% To avoid a memory problem described earlier, all of the ending
-% functions read~|#6| until \cs{s_@@_stop} and place~|#6| back into the
-% input stream. When the lists |#1| and~|#2| are empty, the
-% \texttt{single} auxiliary simply places the continuation~|#5| before
-% the pivot~|{#3}|. When |#2|~is empty, |#1|~is sorted and placed
-% before the pivot~|{#3}|, taking care to feed the continuation~|#5|
-% as a continuation for the function sorting~|#1|. When |#1|~is
-% empty, |#2|~is sorted, and the continuation argument is used to
-% place the continuation~|#5| and the pivot~|{#3}| before the sorted
-% result. Finally, when both lists are non-empty, items larger than
-% the pivot are sorted, then items less than the pivot, and the
-% continuations are done in such a way to place the pivot in between.
-% \begin{macrocode}
-\cs_new:Npn \@@_quick_end:nnTFNn #1#2#3#4#5#6 {#5}
-\cs_new:Npn \@@_quick_single_end:nnnwnw #1#2#3#4 \s_@@_mark #5#6 \s_@@_stop
- { #5 {#3} #6 \s_@@_stop }
-\cs_new:Npn \@@_quick_only_i_end:nnnwnw #1#2#3#4 \s_@@_mark #5#6 \s_@@_stop
- {
- \@@_quick_split:NnNn #1
- \@@_quick_end:nnTFNn { } \s_@@_mark {#5}
- {#3}
- #6 \s_@@_stop
- }
-\cs_new:Npn \@@_quick_only_ii_end:nnnwnw #1#2#3#4 \s_@@_mark #5#6 \s_@@_stop
- {
- \@@_quick_split:NnNn #2
- \@@_quick_end:nnTFNn { } \s_@@_mark { #5 {#3} }
- #6 \s_@@_stop
- }
-\cs_new:Npn \@@_quick_split_end:nnnwnw #1#2#3#4 \s_@@_mark #5#6 \s_@@_stop
- {
- \@@_quick_split:NnNn #2 \@@_quick_end:nnTFNn { } \s_@@_mark
- {
- \@@_quick_split:NnNn #1
- \@@_quick_end:nnTFNn { } \s_@@_mark {#5}
- {#3}
- }
- #6 \s_@@_stop
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Messages}
-%
-% \begin{macro}{\@@_error:}
-% Bailing out of the sorting code is a bit tricky. It may not be safe
-% to use a delimited argument, so instead we redefine many
-% \pkg{l3sort} commands to be trivial, with \cs{@@_level:} jumping to
-% the break point. This error recovery won't work in a group.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_error:
- {
- \cs_set_eq:NN \@@_merge_blocks_aux: \prg_do_nothing:
- \cs_set_eq:NN \@@_merge_blocks: \prg_do_nothing:
- \cs_set_protected:Npn \@@_level: { \group_end: \prg_break: }
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_disable_toksdef:, \@@_disabled_toksdef:n}
-% While sorting, \tn{toksdef} is locally disabled to prevent users
-% from using \tn{newtoks} or similar commands in their comparison
-% code: the \tn{toks} registers that would be assigned are in use by
-% \pkg{l3sort}. In format mode, none of this is needed since there is
-% no \tn{toks} allocator.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_disable_toksdef:
- { \cs_set_eq:NN \toksdef \@@_disabled_toksdef:n }
-\cs_new_protected:Npn \@@_disabled_toksdef:n #1
- {
- \msg_error:nne { sort } { toksdef }
- { \token_to_str:N #1 }
- \@@_error:
- \tex_toksdef:D #1
- }
-\msg_new:nnnn { sort } { toksdef }
- { Allocation~of~\iow_char:N\\toks~registers~impossible~while~sorting. }
- {
- The~comparison~code~used~for~sorting~a~list~has~attempted~to~
- define~#1~as~a~new~\iow_char:N\\toks~register~using~
- \iow_char:N\\newtoks~
- or~a~similar~command.~The~list~will~not~be~sorted.
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\@@_too_long_error:NNw}
-% When there are too many items in a sequence, this is an error, and
-% we clean up properly the mapping over items in the list: break using
-% the type-specific breaking function |#1|.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_too_long_error:NNw #1#2 \fi:
- {
- \fi:
- \msg_error:nneee { sort } { too-large }
- { \token_to_str:N #2 }
- { \int_eval:n { \l_@@_true_max_int - \l_@@_min_int } }
- { \int_eval:n { \l_@@_top_int - \l_@@_min_int } }
- #1 \@@_error:
- }
-\msg_new:nnnn { sort } { too-large }
- { The~list~#1~is~too~long~to~be~sorted~by~TeX. }
- {
- TeX~has~#2~toks~registers~still~available:~
- this~only~allows~to~sort~with~up~to~#3~
- items.~The~list~will~not~be~sorted.
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macrocode}
-\msg_new:nnnn { sort } { return-none }
- { The~comparison~code~did~not~return. }
- {
- When~sorting~a~list,~the~code~to~compare~items~#1~and~#2~
- did~not~call~
- \iow_char:N\\sort_return_same: ~nor~
- \iow_char:N\\sort_return_swapped: .~
- Exactly~one~of~these~should~be~called.
- }
-\msg_new:nnnn { sort } { return-two }
- { The~comparison~code~returned~multiple~times. }
- {
- When~sorting~a~list,~the~code~to~compare~items~#1~and~#2~called~
- \iow_char:N\\sort_return_same: ~or~
- \iow_char:N\\sort_return_swapped: ~multiple~times.~
- Exactly~one~of~these~should~be~called.
- }
-\prop_gput:Nnn \g_msg_module_name_prop { sort } { LaTeX }
-\prop_gput:Nnn \g_msg_module_type_prop { sort } { }
-% \end{macrocode}
-%
-% \begin{macrocode}
-%</package>
-% \end{macrocode}
-%
-% \end{implementation}
-%
-% \PrintIndex