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+% \iffalse meta-comment
+%
+%% File: l3fparray.dtx
+%
+% Copyright (C) 2018-2024 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{l3fparray} module\\ Fast global floating point arrays^^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 2024-04-11}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% For applications requiring heavy use of floating points, this module
+% provides arrays which can be accessed in constant time (contrast
+% \pkg{l3seq}, where access time is linear). The interface is very
+% close to that of \pkg{l3intarray}. The size of the array is fixed and
+% must be given at point of initialisation
+%
+% \section{Creating and initialising floating point array variables}
+%
+% \begin{function}[added = 2018-05-05]{\fparray_new:Nn, \fparray_new:cn}
+% \begin{syntax}
+% \cs{fparray_new:Nn} \meta{fparray~var} \Arg{size}
+% \end{syntax}
+% Evaluates the integer expression \meta{size} and allocates an
+% \meta{floating point array variable} with that number of (zero)
+% entries. The variable name should start with |\g_| because
+% assignments are always global.
+% \end{function}
+%
+% \begin{function}[added = 2018-05-05]{\fparray_gzero:N, \fparray_gzero:c}
+% \begin{syntax}
+% \cs{fparray_gzero:N} \meta{fparray~var}
+% \end{syntax}
+% Sets all entries of the \meta{floating point array variable} to
+% $+0$. Assignments are always global.
+% \end{function}
+%
+% \section{Adding data to floating point arrays}
+%
+% \begin{function}[added = 2018-05-05]{\fparray_gset:Nnn, \fparray_gset:cnn}
+% \begin{syntax}
+% \cs{fparray_gset:Nnn} \meta{fparray~var} \Arg{position} \Arg{value}
+% \end{syntax}
+% Stores the result of evaluating the floating point expression
+% \meta{value} into the \meta{floating point array variable} at the
+% (integer expression) \meta{position}. If the \meta{position} is not
+% between $1$ and the \cs{fparray_count:N}, an error occurs.
+% Assignments are always global.
+% \end{function}
+%
+% \section{Couting entries in floating point arrays}
+%
+% \begin{function}[EXP, added = 2018-05-05]{\fparray_count:N, \fparray_count:c}
+% \begin{syntax}
+% \cs{fparray_count:N} \meta{fparray~var}
+% \end{syntax}
+% Expands to the number of entries in the \meta{floating point array
+% variable}. This is performed in constant time.
+% \end{function}
+%
+% \section{Using a single entry}
+%
+% \begin{function}[EXP, added = 2018-05-05]
+% {
+% \fparray_item:Nn, \fparray_item:cn,
+% \fparray_item_to_tl:Nn, \fparray_item_to_tl:cn
+% }
+% \begin{syntax}
+% \cs{fparray_item:Nn} \meta{fparray~var} \Arg{position}
+% \end{syntax}
+% Applies \cs{fp_use:N} or \cs{fp_to_tl:N} (respectively) to the
+% floating point entry stored at the (integer expression)
+% \meta{position} in the \meta{floating point array variable}. If the
+% \meta{position} is not between $1$ and the
+% \cs{fparray_count:N} \meta{fparray~var}, an error occurs.
+% \end{function}
+%
+% \section{Floating point array conditional}
+%
+% \begin{function}[pTF, added = 2024-03-31]
+% {\fparray_if_exist:N, \fparray_if_exist:c}
+% \begin{syntax}
+% \cs{fparray_if_exist_p:N} \meta{fparray~var}
+% \cs{fparray_if_exist:NTF} \meta{fparray~var} \Arg{true code} \Arg{false code}
+% \end{syntax}
+% Tests whether the \meta{fparray~var} is currently defined. This
+% does not check that the \meta{fparray~var} really is a floating
+% point array variable.
+% \end{function}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fparray} implementation}
+%
+% \begin{macrocode}
+%<*package>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<@@=fp>
+% \end{macrocode}
+%
+% In analogy to \pkg{l3intarray} it would make sense to have
+% |<@@=fparray>|, but we need direct access to \cs{@@_parse:n} from
+% \pkg{l3fp-parse}, and a few other (less crucial) internals of the
+% \pkg{l3fp} family.
+%
+% \subsection{Allocating arrays}
+%
+% There are somewhat more than $(2^{31}-1)^2$ floating point numbers so
+% we store each floating point number as three entries in integer
+% arrays. To avoid having to multiply indices by three or to add 1 etc,
+% a floating point array is just a token list consisting of three
+% tokens: integer arrays of the same size.
+%
+% \begin{variable}{\g_@@_array_int}
+% Used to generate unique names for the three integer arrays.
+% \begin{macrocode}
+\int_new:N \g_@@_array_int
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_array_loop_int}
+% Used to loop in \cs{@@_array_gzero:N}.
+% \begin{macrocode}
+\int_new:N \l_@@_array_loop_int
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\fparray_new:Nn, \fparray_new:cn}
+% \begin{macro}{\@@_array_new:nNNN}
+% Build a three-token token list, then define all three tokens to be
+% integer arrays of the same size. No need to initialize the data:
+% the integer arrays start with zeros, and three zeros denote
+% precisely \cs{c_zero_fp}, as we want.
+% \begin{macrocode}
+\cs_new_protected:Npn \fparray_new:Nn #1#2
+ {
+ \tl_new:N #1
+ \prg_replicate:nn { 3 }
+ {
+ \int_gincr:N \g_@@_array_int
+ \exp_args:NNc \tl_gput_right:Nn #1
+ { g_@@_array_ \@@_int_to_roman:w \g_@@_array_int _intarray }
+ }
+ \exp_last_unbraced:Nfo \@@_array_new:nNNNN
+ { \int_eval:n {#2} } #1 #1
+ }
+\cs_generate_variant:Nn \fparray_new:Nn { c }
+\cs_new_protected:Npn \@@_array_new:nNNNN #1#2#3#4#5
+ {
+ \int_compare:nNnTF {#1} < 0
+ {
+ \msg_error:nnn { kernel } { negative-array-size } {#1}
+ \cs_undefine:N #1
+ \int_gsub:Nn \g_@@_array_int { 3 }
+ }
+ {
+ \intarray_new:Nn #2 {#1}
+ \intarray_new:Nn #3 {#1}
+ \intarray_new:Nn #4 {#1}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\fparray_count:N, \fparray_count:c}
+% Size of any of the intarrays, here we pick the third.
+% \begin{macrocode}
+\cs_new:Npn \fparray_count:N #1
+ {
+ \exp_after:wN \use_i:nnn
+ \exp_after:wN \intarray_count:N #1
+ }
+\cs_generate_variant:Nn \fparray_count:N { c }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Array items}
+%
+% \begin{macro}[EXP]{\@@_array_bounds:NNnTF, \@@_array_bounds_error:NNn}
+% See the \pkg{l3intarray} analogue: only names change.
+% The functions \cs{fparray_gset:Nnn} and \cs{fparray_item:Nn} share
+% bounds checking. The |T| branch is used if |#3| is within bounds of
+% the array |#2|.
+% \begin{macrocode}
+\cs_new:Npn \@@_array_bounds:NNnTF #1#2#3#4#5
+ {
+ \if_int_compare:w 1 > #3 \exp_stop_f:
+ \@@_array_bounds_error:NNn #1 #2 {#3}
+ #5
+ \else:
+ \if_int_compare:w #3 > \fparray_count:N #2 \exp_stop_f:
+ \@@_array_bounds_error:NNn #1 #2 {#3}
+ #5
+ \else:
+ #4
+ \fi:
+ \fi:
+ }
+\cs_new:Npn \@@_array_bounds_error:NNn #1#2#3
+ {
+ #1 { kernel } { out-of-bounds }
+ { \token_to_str:N #2 } {#3} { \fparray_count:N #2 }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fparray_gset:Nnn, \fparray_gset:cnn}
+% \begin{macro}
+% {
+% \@@_array_gset:NNNNww, \@@_array_gset:w,
+% \@@_array_gset_recover:Nw, \@@_array_gset_special:nnNNN,
+% \@@_array_gset_normal:w
+% }
+% Evaluate, then store exponent in one intarray, sign and $8$ digits
+% of mantissa in the next, and $8$ trailing digits in the last.
+% \begin{macrocode}
+\cs_new_protected:Npn \fparray_gset:Nnn #1#2#3
+ {
+ \exp_after:wN \exp_after:wN
+ \exp_after:wN \@@_array_gset:NNNNww
+ \exp_after:wN #1
+ \exp_after:wN #1
+ \int_value:w \int_eval:n {#2} \exp_after:wN ;
+ \exp:w \exp_end_continue_f:w \@@_parse:n {#3}
+ }
+\cs_generate_variant:Nn \fparray_gset:Nnn { c }
+\cs_new_protected:Npn \@@_array_gset:NNNNww #1#2#3#4#5 ; #6 ;
+ {
+ \@@_array_bounds:NNnTF \msg_error:nneee #4 {#5}
+ {
+ \exp_after:wN \@@_change_func_type:NNN
+ \@@_use_i_until_s:nw #6 ;
+ \@@_array_gset:w
+ \@@_array_gset_recover:Nw
+ #6 ; {#5} #1 #2 #3
+ }
+ { }
+ }
+\cs_new_protected:Npn \@@_array_gset_recover:Nw #1#2 ;
+ {
+ \@@_error:nffn { unknown-type } { \tl_to_str:n { #2 ; } } { } { }
+ \exp_after:wN #1 \c_nan_fp
+ }
+\cs_new_protected:Npn \@@_array_gset:w \s_@@ \@@_chk:w #1#2
+ {
+ \if_case:w #1 \exp_stop_f:
+ \@@_case_return:nw { \@@_array_gset_special:nnNNN {#2} }
+ \or: \exp_after:wN \@@_array_gset_normal:w
+ \or: \@@_case_return:nw { \@@_array_gset_special:nnNNN { #2 3 } }
+ \or: \@@_case_return:nw { \@@_array_gset_special:nnNNN { 1 } }
+ \fi:
+ \s_@@ \@@_chk:w #1 #2
+ }
+\cs_new_protected:Npn \@@_array_gset_normal:w
+ \s_@@ \@@_chk:w 1 #1 #2 #3#4#5 ; #6#7#8#9
+ {
+ \__kernel_intarray_gset:Nnn #7 {#6} {#2}
+ \__kernel_intarray_gset:Nnn #8 {#6}
+ { \if_meaning:w 2 #1 3 \else: 1 \fi: #3#4 }
+ \__kernel_intarray_gset:Nnn #9 {#6} { 1 \use:nn #5 }
+ }
+\cs_new_protected:Npn \@@_array_gset_special:nnNNN #1#2#3#4#5
+ {
+ \__kernel_intarray_gset:Nnn #3 {#2} {#1}
+ \__kernel_intarray_gset:Nnn #4 {#2} {0}
+ \__kernel_intarray_gset:Nnn #5 {#2} {0}
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fparray_gzero:N, \fparray_gzero:c}
+% \begin{macrocode}
+\cs_new_protected:Npn \fparray_gzero:N #1
+ {
+ \int_zero:N \l_@@_array_loop_int
+ \prg_replicate:nn { \fparray_count:N #1 }
+ {
+ \int_incr:N \l_@@_array_loop_int
+ \exp_after:wN \@@_array_gset_special:nnNNN
+ \exp_after:wN 0
+ \exp_after:wN \l_@@_array_loop_int
+ #1
+ }
+ }
+\cs_generate_variant:Nn \fparray_gzero:N { c }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]
+% {
+% \fparray_item:Nn,
+% \fparray_item:cn,
+% \fparray_item_to_tl:Nn,
+% \fparray_item_to_tl:cn,
+% }
+% \begin{macro}[EXP]
+% {
+% \@@_array_item:NwN,
+% \@@_array_item:NNNnN,
+% \@@_array_item:N,
+% \@@_array_item:w,
+% \@@_array_item_special:w,
+% \@@_array_item_normal:w
+% }
+% \begin{macrocode}
+\cs_new:Npn \fparray_item:Nn #1#2
+ {
+ \exp_after:wN \@@_array_item:NwN
+ \exp_after:wN #1
+ \int_value:w \int_eval:n {#2} ;
+ \@@_to_decimal:w
+ }
+\cs_generate_variant:Nn \fparray_item:Nn { c }
+\cs_new:Npn \fparray_item_to_tl:Nn #1#2
+ {
+ \exp_after:wN \@@_array_item:NwN
+ \exp_after:wN #1
+ \int_value:w \int_eval:n {#2} ;
+ \@@_to_tl:w
+ }
+\cs_generate_variant:Nn \fparray_item_to_tl:Nn { c }
+\cs_new:Npn \@@_array_item:NwN #1#2 ; #3
+ {
+ \@@_array_bounds:NNnTF \msg_expandable_error:nnfff #1 {#2}
+ { \exp_after:wN \@@_array_item:NNNnN #1 {#2} #3 }
+ { \exp_after:wN #3 \c_nan_fp }
+ }
+\cs_new:Npn \@@_array_item:NNNnN #1#2#3#4
+ {
+ \exp_after:wN \@@_array_item:N
+ \int_value:w \__kernel_intarray_item:Nn #2 {#4} \exp_after:wN ;
+ \int_value:w \__kernel_intarray_item:Nn #3 {#4} \exp_after:wN ;
+ \int_value:w \__kernel_intarray_item:Nn #1 {#4} ;
+ }
+\cs_new:Npn \@@_array_item:N #1
+ {
+ \if_meaning:w 0 #1 \exp_after:wN \@@_array_item_special:w \fi:
+ \@@_array_item:w #1
+ }
+\cs_new:Npn \@@_array_item:w #1 #2#3#4#5 #6 ; 1 #7 ;
+ {
+ \exp_after:wN \@@_array_item_normal:w
+ \int_value:w \if_meaning:w #1 1 0 \else: 2 \fi: \exp_stop_f:
+ #7 ; {#2#3#4#5} {#6} ;
+ }
+\cs_new:Npn \@@_array_item_special:w #1 ; #2 ; #3 ; #4
+ {
+ \exp_after:wN #4
+ \exp:w \exp_end_continue_f:w
+ \if_case:w #3 \exp_stop_f:
+ \exp_after:wN \c_zero_fp
+ \or: \exp_after:wN \c_nan_fp
+ \or: \exp_after:wN \c_minus_zero_fp
+ \or: \exp_after:wN \c_inf_fp
+ \else: \exp_after:wN \c_minus_inf_fp
+ \fi:
+ }
+\cs_new:Npn \@@_array_item_normal:w #1 #2#3#4#5 #6 ; #7 ; #8 ; #9
+ { #9 \s_@@ \@@_chk:w 1 #1 {#8} #7 {#2#3#4#5} {#6} ; }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[pTF]{\fparray_if_exist:N, \fparray_if_exist:c}
+% Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
+% \begin{macrocode}
+\prg_new_eq_conditional:NNn \fparray_if_exist:N \cs_if_exist:N
+ { TF , T , F , p }
+\prg_new_eq_conditional:NNn \fparray_if_exist:c \cs_if_exist:c
+ { TF , T , F , p }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+%</package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex