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diff --git a/macros/latex/contrib/l3kernel/l3sort.dtx b/macros/latex/contrib/l3kernel/l3sort.dtx deleted file mode 100644 index 818f605e07..0000000000 --- a/macros/latex/contrib/l3kernel/l3sort.dtx +++ /dev/null @@ -1,1097 +0,0 @@ -% \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 |