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+% \iffalse meta-comment
+%
+%% File: l3intarray.dtx
+%
+% Copyright (C) 2017-2019 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 \textsf{l3intarray} package: fast global integer arrays^^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 2019-08-25}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \section{\pkg{l3intarray} documentation}
+%
+% For applications requiring heavy use of integers, this module provides
+% arrays which can be accessed in constant time (contrast \pkg{l3seq},
+% where access time is linear). These arrays have several important
+% features
+% \begin{itemize}
+% \item The size of the array is fixed and must be given at
+% point of initialisation
+% \item The absolute value of each entry has maximum $2^{30}-1$
+% (\emph{i.e.}~one power lower than the usual \cs{c_max_int}
+% ceiling of $2^{31}-1$)
+% \end{itemize}
+% The use of \texttt{intarray} data is therefore recommended for cases where
+% the need for fast access is of paramount importance.
+%
+% \begin{function}[added = 2018-03-29]{\intarray_new:Nn}
+% \begin{syntax}
+% \cs{intarray_new:Nn} \meta{intarray~var} \Arg{size}
+% \end{syntax}
+% Evaluates the integer expression \meta{size} and allocates an
+% \meta{integer array variable} with that number of (zero) entries.
+% The variable name should start with |\g_| because assignments are
+% always global.
+% \end{function}
+%
+% \begin{function}[EXP, added = 2018-03-29]{\intarray_count:N}
+% \begin{syntax}
+% \cs{intarray_count:N} \meta{intarray~var}
+% \end{syntax}
+% Expands to the number of entries in the \meta{integer array variable}.
+% Contrarily to \cs{seq_count:N} this is performed in constant time.
+% \end{function}
+%
+% \begin{function}[added = 2018-03-29]{\intarray_gset:Nnn}
+% \begin{syntax}
+% \cs{intarray_gset:Nnn} \meta{intarray~var} \Arg{position} \Arg{value}
+% \end{syntax}
+% Stores the result of evaluating the integer expression \meta{value}
+% into the \meta{integer array variable} at the (integer expression)
+% \meta{position}. If the \meta{position} is not between $1$ and the
+% \cs{intarray_count:N}, or the \meta{value}'s absolute value is
+% bigger than $2^{30}-1$, an error occurs. Assignments are always
+% global.
+% \end{function}
+%
+% \begin{function}[added = 2018-05-04]{\intarray_gzero:N}
+% \begin{syntax}
+% \cs{intarray_gzero:N} \meta{intarray~var}
+% \end{syntax}
+% Sets all entries of the \meta{integer array variable} to zero.
+% Assignments are always global.
+% \end{function}
+%
+% \begin{function}[EXP, added = 2018-03-29]{\intarray_item:Nn}
+% \begin{syntax}
+% \cs{intarray_item:Nn} \meta{intarray~var} \Arg{position}
+% \end{syntax}
+% Expands to the integer entry stored at the (integer expression)
+% \meta{position} in the \meta{integer array variable}. If the
+% \meta{position} is not between $1$ and the \cs{intarray_count:N}, an
+% error occurs.
+% \end{function}
+%
+% \begin{function}[EXP, added = 2018-05-05]{\intarray_rand_item:N}
+% \begin{syntax}
+% \cs{intarray_rand_item:N} \meta{intarray~var}
+% \end{syntax}
+% Selects a pseudo-random item of the \meta{integer array}. If the
+% \meta{integer array} is empty, produce an error.
+% \end{function}
+%
+% \subsection{Implementation notes}
+%
+% It is a wrapper around the \tn{fontdimen} primitive, used to store
+% arrays of integers (with a restricted range: absolute value at most
+% $2^{30}-1$). In contrast to \pkg{l3seq} sequences the access to
+% individual entries is done in constant time rather than linear time,
+% but only integers can be stored. More precisely, the primitive
+% \tn{fontdimen} stores dimensions but the \pkg{l3intarray} package
+% transparently converts these from/to integers. Assignments are always
+% global.
+%
+% While \LuaTeX{}'s memory is extensible, other engines can
+% \enquote{only} deal with a bit less than $4\times 10^6$ entries in all
+% \tn{fontdimen} arrays combined (with default \TeX{}Live settings).
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3intarray} implementation}
+%
+% \begin{macrocode}
+%<*initex|package>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<@@=intarray>
+% \end{macrocode}
+%
+% \subsection{Allocating arrays}
+%
+% \begin{macro}{\@@_entry:w, \@@_count:w}
+% We use these primitives quite a lot in this module.
+% \begin{macrocode}
+\cs_new_eq:NN \@@_entry:w \tex_fontdimen:D
+\cs_new_eq:NN \@@_count:w \tex_hyphenchar:D
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}{\l_@@_loop_int}
+% A loop index.
+% \begin{macrocode}
+\int_new:N \l_@@_loop_int
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_@@_sp_dim}
+% Used to convert integers to dimensions fast.
+% \begin{macrocode}
+\dim_const:Nn \c_@@_sp_dim { 1 sp }
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\g_@@_font_int}
+% Used to assign one font per array.
+% \begin{macrocode}
+\int_new:N \g_@@_font_int
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macrocode}
+\__kernel_msg_new:nnn { kernel } { negative-array-size }
+ { Size~of~array~may~not~be~negative:~#1 }
+% \end{macrocode}
+%
+% \begin{macro}{\intarray_new:Nn, \@@_new:N}
+% Declare |#1| to be a font (arbitrarily |cmr10| at a never-used
+% size). Store the array's size as the \tn{hyphenchar} of that font
+% and make sure enough \tn{fontdimen} are allocated, by setting the
+% last one. Then clear any \tn{fontdimen} that |cmr10| starts with.
+% It seems \LuaTeX{}'s |cmr10| has an extra \tn{fontdimen} parameter
+% number $8$ compared to other engines (for a math font we would
+% replace $8$ by $22$ or some such).
+% Every \texttt{intarray} must be global; it's enough to run this
+% check in \cs{intarray_new:Nn}.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_new:N #1
+ {
+ \__kernel_chk_if_free_cs:N #1
+ \int_gincr:N \g_@@_font_int
+ \tex_global:D \tex_font:D #1
+ = cmr10~at~ \g_@@_font_int \c_@@_sp_dim \scan_stop:
+ \int_step_inline:nn { 8 }
+ { \__kernel_intarray_gset:Nnn #1 {##1} \c_zero_int }
+ }
+\__kernel_patch:nnNNpn { \__kernel_chk_var_scope:NN g #1 } { }
+\cs_new_protected:Npn \intarray_new:Nn #1#2
+ {
+ \@@_new:N #1
+ \@@_count:w #1 = \int_eval:n {#2} \scan_stop:
+ \int_compare:nNnT { \intarray_count:N #1 } < 0
+ {
+ \__kernel_msg_error:nnx { kernel } { negative-array-size }
+ { \intarray_count:N #1 }
+ }
+ \int_compare:nNnT { \intarray_count:N #1 } > 0
+ { \__kernel_intarray_gset:Nnn #1 { \intarray_count:N #1 } { 0 } }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\intarray_count:N}
+% Size of an array.
+% \begin{macrocode}
+\cs_new:Npn \intarray_count:N #1 { \int_value:w \@@_count:w #1 }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Array items}
+%
+% \begin{macro}[EXP]{\@@_signed_max_dim:n}
+% Used when an item to be stored is larger than \cs{c_max_dim} in
+% absolute value; it is replaced by $\pm\cs{c_max_dim}$.
+% \begin{macrocode}
+\cs_new:Npn \@@_signed_max_dim:n #1
+ { \int_value:w \int_compare:nNnT {#1} < 0 { - } \c_max_dim }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_bounds:NNnTF, \@@_bounds_error:NNn}
+% The functions \cs{intarray_gset:Nnn} and \cs{intarray_item:Nn} share
+% bounds checking. The |T| branch is used if |#3| is within bounds of
+% the array |#2|.
+% \begin{macrocode}
+\cs_new:Npn \@@_bounds:NNnTF #1#2#3#4#5
+ {
+ \if_int_compare:w 1 > #3 \exp_stop_f:
+ \@@_bounds_error:NNn #1 #2 {#3}
+ #5
+ \else:
+ \if_int_compare:w #3 > \intarray_count:N #2 \exp_stop_f:
+ \@@_bounds_error:NNn #1 #2 {#3}
+ #5
+ \else:
+ #4
+ \fi:
+ \fi:
+ }
+\cs_new:Npn \@@_bounds_error:NNn #1#2#3
+ {
+ #1 { kernel } { out-of-bounds }
+ { \token_to_str:N #2 } {#3} { \intarray_count:N #2 }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\intarray_gset:Nnn, \__kernel_intarray_gset:Nnn}
+% \begin{macro}{\@@_gset:Nnn, \@@_gset_overflow:Nnn}
+% Set the appropriate \tn{fontdimen}. The
+% \cs{__kernel_intarray_gset:Nnn} function does not use
+% \cs{int_eval:n}, namely its arguments must be suitable for
+% \cs{int_value:w}. The user version checks the position and value
+% are within bounds.
+% \begin{macrocode}
+\cs_new_protected:Npn \__kernel_intarray_gset:Nnn #1#2#3
+ { \@@_entry:w #2 #1 #3 \c_@@_sp_dim }
+\cs_new_protected:Npn \intarray_gset:Nnn #1#2#3
+ {
+ \exp_after:wN \@@_gset:Nww
+ \exp_after:wN #1
+ \int_value:w \int_eval:n {#2} \exp_after:wN ;
+ \int_value:w \int_eval:n {#3} ;
+ }
+\cs_new_protected:Npn \@@_gset:Nww #1#2 ; #3 ;
+ {
+ \@@_bounds:NNnTF \__kernel_msg_error:nnxxx #1 {#2}
+ {
+ \@@_gset_overflow_test:nw {#3}
+ \__kernel_intarray_gset:Nnn #1 {#2} {#3}
+ }
+ { }
+ }
+\cs_if_exist:NTF \tex_ifabsnum:D
+ {
+ \cs_new_protected:Npn \@@_gset_overflow_test:nw #1
+ {
+ \tex_ifabsnum:D #1 > \c_max_dim
+ \exp_after:wN \@@_gset_overflow:NNnn
+ \fi:
+ }
+ }
+ {
+ \cs_new_protected:Npn \@@_gset_overflow_test:nw #1
+ {
+ \if_int_compare:w \int_abs:n {#1} > \c_max_dim
+ \exp_after:wN \@@_gset_overflow:NNnn
+ \fi:
+ }
+ }
+\cs_new_protected:Npn \@@_gset_overflow:NNnn #1#2#3#4
+ {
+ \__kernel_msg_error:nnxxxx { kernel } { overflow }
+ { \token_to_str:N #2 } {#3} {#4} { \@@_signed_max_dim:n {#4} }
+ #1 #2 {#3} { \@@_signed_max_dim:n {#4} }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\intarray_gzero:N}
+% Set the appropriate \tn{fontdimen} to zero. No bound checking
+% needed. The \cs{prg_replicate:nn} possibly uses quite a lot of
+% memory, but this is somewhat comparable to the size of the array,
+% and it is much faster than an \cs{int_step_inline:nn} loop.
+% \begin{macrocode}
+\cs_new_protected:Npn \intarray_gzero:N #1
+ {
+ \int_zero:N \l_@@_loop_int
+ \prg_replicate:nn { \intarray_count:N #1 }
+ {
+ \int_incr:N \l_@@_loop_int
+ \@@_entry:w \l_@@_loop_int #1 \c_zero_dim
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\intarray_item:Nn, \__kernel_intarray_item:Nn}
+% \begin{macro}{\@@_item:Nn}
+% Get the appropriate \tn{fontdimen} and perform bound checks. The
+% \cs{__kernel_intarray_item:Nn} function omits bound checks and omits
+% \cs{int_eval:n}, namely its argument must be a \TeX{} integer
+% suitable for \cs{int_value:w}.
+% \begin{macrocode}
+\cs_new:Npn \__kernel_intarray_item:Nn #1#2
+ { \int_value:w \@@_entry:w #2 #1 }
+\cs_new:Npn \intarray_item:Nn #1#2
+ {
+ \exp_after:wN \@@_item:Nw
+ \exp_after:wN #1
+ \int_value:w \int_eval:n {#2} ;
+ }
+\cs_new:Npn \@@_item:Nw #1#2 ;
+ {
+ \@@_bounds:NNnTF \__kernel_msg_expandable_error:nnfff #1 {#2}
+ { \__kernel_intarray_item:Nn #1 {#2} }
+ { 0 }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\intarray_rand_item:N}
+% Importantly, \cs{intarray_item:Nn} only evaluates its argument once.
+% \begin{macrocode}
+\cs_new:Npn \intarray_rand_item:N #1
+ { \intarray_item:Nn #1 { \int_rand:n { \intarray_count:N #1 } } }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Working with contents of integer arrays}
+%
+% At the time of writing these are candidates, but we need at least
+% \cs{intarray_const_from_clist:Nn} in \pkg{l3fp} so before
+% \pkg{l3candidates}.
+%
+% \begin{macro}{\intarray_const_from_clist:Nn, \@@_const_from_clist:nN}
+% Similar to \cs{intarray_new:Nn} (which we don't use because when
+% debugging is enabled that function checks the variable name starts
+% with |g_|). We make use of the fact that \TeX{} allows allocation
+% of successive \tn{fontdimen} as long as no other font has been
+% declared: no need to count the comma list items first. We need the
+% code in \cs{intarray_gset:Nnn} that checks the item value is not too
+% big, namely \cs{@@_gset_overflow_test:nw}, but not the code that
+% checks bounds. At the end, set the size of the intarray.
+% \begin{macrocode}
+\__kernel_patch:nnNNpn { \__kernel_chk_var_scope:NN c #1 } { }
+\cs_new_protected:Npn \intarray_const_from_clist:Nn #1#2
+ {
+ \@@_new:N #1
+ \int_zero:N \l_@@_loop_int
+ \clist_map_inline:nn {#2}
+ { \exp_args:Nf \@@_const_from_clist:nN { \int_eval:n {##1} } #1 }
+ \@@_count:w #1 \l_@@_loop_int
+ }
+\cs_new_protected:Npn \@@_const_from_clist:nN #1#2
+ {
+ \int_incr:N \l_@@_loop_int
+ \@@_gset_overflow_test:nw {#1}
+ \__kernel_intarray_gset:Nnn #2 \l_@@_loop_int {#1}
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[rEXP]{\intarray_to_clist:N, \@@_to_clist:Nn, \@@_to_clist:w}
+% Loop through the array, putting a comma before each item. Remove
+% the leading comma with |f|-expansion. We also use the auxiliary in
+% \cs{intarray_show:N} with argument comma, space.
+% \begin{macrocode}
+\cs_new:Npn \intarray_to_clist:N #1 { \@@_to_clist:Nn #1 { , } }
+\cs_new:Npn \@@_to_clist:Nn #1#2
+ {
+ \int_compare:nNnF { \intarray_count:N #1 } = \c_zero_int
+ {
+ \exp_last_unbraced:Nf \use_none:n
+ { \@@_to_clist:w 1 ; #1 {#2} \prg_break_point: }
+ }
+ }
+\cs_new:Npn \@@_to_clist:w #1 ; #2#3
+ {
+ \if_int_compare:w #1 > \@@_count:w #2
+ \prg_break:n
+ \fi:
+ #3 \__kernel_intarray_item:Nn #2 {#1}
+ \exp_after:wN \@@_to_clist:w
+ \int_value:w \int_eval:w #1 + \c_one_int ; #2 {#3}
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\intarray_show:N, \intarray_log:N}
+% Convert the list to a comma list (with spaces after each comma)
+% \begin{macrocode}
+\cs_new_protected:Npn \intarray_show:N { \@@_show:NN \msg_show:nnxxxx }
+\cs_generate_variant:Nn \intarray_show:N { c }
+\cs_new_protected:Npn \intarray_log:N { \@@_show:NN \msg_log:nnxxxx }
+\cs_generate_variant:Nn \intarray_log:N { c }
+\cs_new_protected:Npn \@@_show:NN #1#2
+ {
+ \__kernel_chk_defined:NT #2
+ {
+ #1 { LaTeX/kernel } { show-intarray }
+ { \token_to_str:N #2 }
+ { \intarray_count:N #2 }
+ { >~ \@@_to_clist:Nn #2 { , ~ } }
+ { }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Random arrays}
+%
+% \begin{macro}
+% {
+% \intarray_gset_rand:Nn,
+% \intarray_gset_rand:Nnn,
+% \@@_gset_rand:Nnn,
+% \@@_gset_rand:Nff,
+% \@@_gset_rand_auxi:Nnnn,
+% \@@_gset_rand_auxii:Nnnn,
+% \@@_gset_rand_auxiii:Nnnn,
+% \@@_gset_all_same:Nn,
+% }
+% We only perform the bounds checks once. This is done by two
+% \cs{@@_gset_overflow_test:nw}, with an appropriate empty argument to
+% avoid a spurious \enquote{at position \texttt{\#1}} part in the
+% error message. Then calculate the number of choices: this is at
+% most $(2^{30}-1)-(-(2^{30}-1))+1=2^{31}-1$, which just barely does
+% not overflow. For small ranges use \cs{__kernel_randint:n} (making
+% sure to subtract~$1$ \emph{before} adding the random number to the
+% \meta{min}, to avoid overflow when \meta{min} or \meta{max} are
+% $\pm\cs{c_max_int}$), otherwise \cs{__kernel_randint:nn}. Finally,
+% if there are no random numbers do not define any of the auxiliaries.
+% \begin{macrocode}
+\cs_new_protected:Npn \intarray_gset_rand:Nn #1
+ { \intarray_gset_rand:Nnn #1 { 1 } }
+\sys_if_rand_exist:TF
+ {
+ \cs_new_protected:Npn \intarray_gset_rand:Nnn #1#2#3
+ {
+ \@@_gset_rand:Nff #1
+ { \int_eval:n {#2} } { \int_eval:n {#3} }
+ }
+ \cs_new_protected:Npn \@@_gset_rand:Nnn #1#2#3
+ {
+ \int_compare:nNnTF {#2} > {#3}
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { kernel } { randint-backward-range } {#2} {#3}
+ \@@_gset_rand:Nnn #1 {#3} {#2}
+ }
+ {
+ \@@_gset_overflow_test:nw {#2}
+ \@@_gset_rand_auxi:Nnnn #1 { } {#2} {#3}
+ }
+ }
+ \cs_generate_variant:Nn \@@_gset_rand:Nnn { Nff }
+ \cs_new_protected:Npn \@@_gset_rand_auxi:Nnnn #1#2#3#4
+ {
+ \@@_gset_overflow_test:nw {#4}
+ \@@_gset_rand_auxii:Nnnn #1 { } {#4} {#3}
+ }
+ \cs_new_protected:Npn \@@_gset_rand_auxii:Nnnn #1#2#3#4
+ {
+ \exp_args:NNf \@@_gset_rand_auxiii:Nnnn #1
+ { \int_eval:n { #3 - #4 + 1 } } {#4} {#3}
+ }
+ \cs_new_protected:Npn \@@_gset_rand_auxiii:Nnnn #1#2#3#4
+ {
+ \exp_args:NNf \@@_gset_all_same:Nn #1
+ {
+ \int_compare:nNnTF {#2} > \c__kernel_randint_max_int
+ {
+ \exp_stop_f:
+ \int_eval:n { \__kernel_randint:nn {#3} {#4} }
+ }
+ {
+ \exp_stop_f:
+ \int_eval:n { \__kernel_randint:n {#2} - 1 + #3 }
+ }
+ }
+ }
+ \cs_new_protected:Npn \@@_gset_all_same:Nn #1#2
+ {
+ \int_zero:N \l_@@_loop_int
+ \prg_replicate:nn { \intarray_count:N #1 }
+ {
+ \int_incr:N \l_@@_loop_int
+ \__kernel_intarray_gset:Nnn #1 \l_@@_loop_int {#2}
+ }
+ }
+ }
+ {
+ \cs_new_protected:Npn \intarray_gset_rand:Nnn #1#2#3
+ {
+ \__kernel_msg_error:nnn { kernel } { fp-no-random }
+ { \intarray_gset_rand:Nnn #1 {#2} {#3} }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+%</initex|package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex