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|
% \iffalse
%
%% File l3sort.dtx (C) Copyright 2012-2018 The LaTeX3 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} package\\ Sorting functions^^A
% }
%
% \author{^^A
% The \LaTeX3 Project\thanks
% {^^A
% E-mail:
% \href{mailto:latex-team@latex-project.org}
% {latex-team@latex-project.org}^^A
% }^^A
% }
%
% \date{Released 2018-12-06}
%
% \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{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}
%<*initex|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:x}
% (or some \cs{exp_args:NNNx}) 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}
%
% \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:}. The \LaTeX3 format
% mode is easiest: no \tn{toks} are ever allocated so available
% \tn{toks} range from $0$ to \cs{c_max_register_int} and we
% precompute the result of \cs{@@_shrink_range:}.
% \begin{macrocode}
%<*package>
\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:
}
}
}
%</package>
%<*initex>
\int_const:Nn \c_@@_max_length_int
{ ( \c_max_register_int + 1 ) * 3 / 4 }
\cs_new_protected:Npn \@@_compute_range:
{
\int_set:Nn \l_@@_min_int { 0 }
\int_set:Nn \l_@@_true_max_int { \c_max_register_int + 1 }
\int_set:Nn \l_@@_max_int { \c_@@_max_length_int }
}
%</initex>
% \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
{
%<package> \@@_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}
\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_gset_from_inline_x:Nnn \g_@@_internal_seq
{
\int_step_function:nnN
{ \l_@@_min_int } { \l_@@_top_int - 1 }
}
{ \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:N
\@@_return_mark:N
\@@_return_none_error:
}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sort_return_same:, \sort_return_swapped:}
% \begin{macro}{\@@_return_mark:N}
% \begin{macro}{\@@_return_none_error:, \@@_return_two_error:w}
% The marker removes one token. 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.
% \begin{macrocode}
\cs_new_protected:Npn \sort_return_same: #1 \@@_return_mark:N
{
#1
\@@_return_mark:N
\@@_return_two_error:w \@@_return_same:
}
\cs_new_protected:Npn \sort_return_swapped: #1 \@@_return_mark:N
{
#1
\@@_return_mark:N
\@@_return_two_error:w \@@_return_swapped:
}
\cs_new_protected:Npn \@@_return_mark:N #1 { }
\cs_new_protected:Npn \@@_return_none_error:
{
\__kernel_msg_error:nnxx { kernel } { return-none }
{ \tex_the:D \tex_toks:D \l_@@_A_int }
{ \tex_the:D \tex_toks:D \l_@@_C_int }
\@@_return_same:
}
\cs_new_protected:Npn \@@_return_two_error:w
#1 \@@_return_none_error:
{ \__kernel_msg_error:nn { kernel } { return-two } }
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_return_same:}
% 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:
{
\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:}
% 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:
{
\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_recursion_tail \q_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}~|{}|~|\q_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{q_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{q_mark}\\
% ~~|{|\\
% ~~~~\cs{@@_quick_split:NnNn} |#1| \ldots{} \cs{q_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{q_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{q_mark}, namely removing the trailing \cs{s_stop} and
% \cs{q_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 }
\q_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 \q_stop
{
\@@_quick_split:NnNn #4 \@@_quick_end:nnTFNn { }
\q_mark { \@@_quick_cleanup:w \exp_stop_f: }
\s_stop \q_stop
}
\cs_new:Npn \@@_quick_cleanup:w #1 \s_stop \q_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{q_mark}.
% To avoid a memory problem described earlier, all of the ending
% functions read~|#6| until \cs{q_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 \q_mark #5#6 \q_stop
{ #5 {#3} #6 \q_stop }
\cs_new:Npn \@@_quick_only_i_end:nnnwnw #1#2#3#4 \q_mark #5#6 \q_stop
{
\@@_quick_split:NnNn #1
\@@_quick_end:nnTFNn { } \q_mark {#5}
{#3}
#6 \q_stop
}
\cs_new:Npn \@@_quick_only_ii_end:nnnwnw #1#2#3#4 \q_mark #5#6 \q_stop
{
\@@_quick_split:NnNn #2
\@@_quick_end:nnTFNn { } \q_mark { #5 {#3} }
#6 \q_stop
}
\cs_new:Npn \@@_quick_split_end:nnnwnw #1#2#3#4 \q_mark #5#6 \q_stop
{
\@@_quick_split:NnNn #2 \@@_quick_end:nnTFNn { } \q_mark
{
\@@_quick_split:NnNn #1
\@@_quick_end:nnTFNn { } \q_mark {#5}
{#3}
}
#6 \q_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}
%<*package>
\cs_new_protected:Npn \@@_disable_toksdef:
{ \cs_set_eq:NN \toksdef \@@_disabled_toksdef:n }
\cs_new_protected:Npn \@@_disabled_toksdef:n #1
{
\__kernel_msg_error:nnx { kernel } { toksdef }
{ \token_to_str:N #1 }
\@@_error:
\tex_toksdef:D #1
}
\__kernel_msg_new:nnnn { kernel } { 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.
}
%</package>
% \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:
\__kernel_msg_error:nnxxx { kernel } { 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:
}
\__kernel_msg_new:nnnn { kernel } { 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}
\__kernel_msg_new:nnnn { kernel } { 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.
}
\__kernel_msg_new:nnnn { kernel } { return-two }
{ The~comparison~code~returned~multiple~times. }
{
When~sorting~a~list,~the~code~to~compare~items~called~
\iow_char:N\\sort_return_same: ~or~
\iow_char:N\\sort_return_swapped: ~multiple~times.~
Exactly~one~of~these~should~be~called.
}
% \end{macrocode}
%
% \subsection{Deprecated functions}
%
% \begin{macro}[deprecated = 2018-12-31]{\sort_ordered:, \sort_reversed:}
% These functions were renamed for consistency.
% \begin{macrocode}
\__kernel_patch_deprecation:nnNNpn { 2018-12-31 } { \sort_return_same: }
\cs_new_protected:Npn \sort_ordered: { \sort_return_same: }
\__kernel_patch_deprecation:nnNNpn { 2018-12-31 } { \sort_return_swapped: }
\cs_new_protected:Npn \sort_reversed: { \sort_return_swapped: }
% \end{macrocode}
% \end{macro}
%
% \begin{macrocode}
%</initex|package>
% \end{macrocode}
%
% \end{implementation}
%
% \PrintIndex
|