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+% \iffalse
+%
+%% File l3fp-symbolic.dtx (C) Copyright 2012-2015,2017,2018,2020,2021,2023 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
+%
+% http://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]{l3doc}
+\usepackage{amsmath}
+\begin{document}
+ \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+% The \pkg{l3fp-symbolic} package\\ Symbolic expressions^^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 2023-10-23}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-symbolic} implementation}
+%
+% \begin{macrocode}
+%<*package>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<@@=fp>
+% \end{macrocode}
+%
+% \subsection{Misc}
+%
+% \begin{variable}{\l_@@_symbolic_fp}
+% Scratch floating point.
+% \begin{macrocode}
+\fp_new:N \l_@@_symbolic_fp
+% \end{macrocode}
+% \end{variable}
+%
+% \subsection{Building blocks for expressions}
+%
+% Every symbolic expression has the form \cs{s_@@_symbolic}
+% \cs{@@_symbolic_chk:w} \meta{operation} |,| \Arg{operands} \meta{junk}
+% |;| where the \meta{operation} is a list of \texttt{N}-type tokens,
+% the \meta{operands} is an array of floating point objects, and the
+% \meta{junk} is to be discarded. If the outermost operator (last to be
+% evaluated) is unary, the expression has the form
+% \begin{quote}
+% \cs{s_@@_symbolic} \cs{@@_symbolic_chk:w} \\
+% \cs{@@_types_unary:NNw} |\__fp_|\meta{op}|_o:w| \meta{token} |,| \\
+% |{| \meta{operand} |}| \meta{junk} |;|
+% \end{quote}
+% where the \meta{op} is a unary operation (|set_sign|, |cos|,
+% \ldots{}), and the \meta{token} and \meta{operand} are used as
+% arguments for \cs{@@_\meta{op}_o:w} (or the type-specific analog of
+% this function). If the outermost operator is binary, the expression
+% has the form
+% \begin{quote}
+% \cs{s_@@_symbolic} \cs{@@_symbolic_chk:w} \\
+% \cs{@@_types_binary:Nww} |\__fp_|\meta{op}|_o:ww| |,| \\
+% |{| \meta{operand_1} \meta{operand_2} |}| \meta{junk} |;|
+% \end{quote}
+% where the \meta{op} is an operation (|+|, |&|, \ldots{}), and
+% |\__fp_|\meta{op}|_o:ww| receives the \meta{operands} as arguments.
+% If the expression consists of a single variable, it is stored as
+% \begin{quote}
+% \cs{s_@@_symbolic} \cs{@@_symbolic_chk:w} \\
+% \cs{@@_variable_o:w} \meta{identifier} |,| \\
+% |{| |}| \meta{junk} |;|
+% \end{quote}
+%
+% Symbolic expressions are stored in a prefix form. When encountering a
+% symbolic expression in a floating point computation, we attempt to
+% evaluate the operands as much as possible, and if that yields floating
+% point numbers rather than expressions, we apply the operator which
+% follows (if the function is known).
+%
+% For instance, the expression |a + b * sin(c)| is stored as
+% \begin{verbatim}
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_types_binary:Nww \__fp_+_o:ww ,
+% {
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_variable_o:w a , { } ;
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_types_binary:Nww \__fp_*_o:ww ,
+% {
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_variable_o:w b , { } ;
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_types_unary:NNw \__fp_sin_o:w \use_i:nn ,
+% {
+% \s__fp_symbolic \__fp_symbolic_chk:w
+% \__fp_variable_o:w c , { } ;
+% } ;
+% } ;
+% } ;
+% \end{verbatim}
+%
+% \begin{variable}{\s_@@_symbolic}
+% Scan mark indicating the start of a symbolic expression.
+% \begin{macrocode}
+\scan_new:N \s_@@_symbolic
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\@@_symbolic_chk:w}
+% Analog of \cs{@@_chk:w} for symbolic expressions.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_symbolic_chk:w #1,#2#3;
+ {
+ \msg_error:nne { fp } { misused-fp }
+ {
+ \@@_to_tl_dispatch:w
+ \s_@@_symbolic \@@_symbolic_chk:w #1,{#2};
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Expanding after a symbolic expression}
+%
+% \begin{macro}[EXP]
+% {\@@_if_has_symbolic:nTF, \@@_if_has_symbolic_aux:w}
+% Tests if |#1| contains \cs{s_@@_symbolic} at top-level. This test
+% should be precise enough to determine if a given an array contains a
+% symbolic expression or only consists in floating points. Used in
+% \cs{@@_exp_after_symbolic_f:nw}.
+% \begin{macrocode}
+\cs_new:Npn \@@_if_has_symbolic:nTF #1
+ {
+ \@@_if_has_symbolic_aux:w
+ #1 \s_@@_mark \use_i:nn
+ \s_@@_symbolic \s_@@_mark \use_ii:nn
+ \s_@@_stop
+ }
+\cs_new:Npn \@@_if_has_symbolic_aux:w
+ #1 \s_@@_symbolic #2 \s_@@_mark #3#4 \s_@@_stop { #3 }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_exp_after_symbolic_f:nw}
+% \begin{macro}[EXP]
+% {\@@_exp_after_symbolic_aux:w, \@@_exp_after_symbolic_loop:N}
+% This function does two things: trigger an \texttt{f}-expansion of
+% the argument~|#1| after the following symbolic expression, and
+% evaluate all pieces of the expression which can be evaluated.
+% \begin{macrocode}
+\cs_new:Npn \@@_exp_after_symbolic_f:nw
+ #1 \s_@@_symbolic \@@_symbolic_chk:w #2, #3#4;
+ {
+ \exp_after:wN \@@_exp_after_symbolic_aux:w
+ \exp:w
+ \@@_exp_after_symbolic_loop:N #2
+ { , \exp:w \use_none:nn }
+ \exp_after:wN \exp_end: \exp_after:wN
+ {
+ \exp:w \exp_end_continue_f:w
+ \@@_exp_after_array_f:w #3 \s_@@_expr_stop
+ \exp_after:wN
+ }
+ \exp_after:wN ;
+ \exp:w \exp_end_continue_f:w #1
+ }
+\cs_new:Npn \@@_exp_after_symbolic_aux:w #1, #2;
+ {
+ \@@_if_has_symbolic:nTF {#2}
+ { \s_@@_symbolic \@@_symbolic_chk:w #1, {#2} ; }
+ { #1 #2 @ \prg_do_nothing: }
+ }
+\cs_new:Npn \@@_exp_after_symbolic_loop:N #1
+ {
+ \exp_after:wN \exp_end:
+ \exp_after:wN #1
+ \exp:w
+ \@@_exp_after_symbolic_loop:N
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Applying infix operators to expressions}
+%
+% \begin{macro}[EXP]{\@@_symbolic_binary_o:Nww}
+% Used when applying infix operators to expressions.
+% \begin{macrocode}
+\cs_new:Npn \@@_symbolic_binary_o:Nww #1 #2; #3;
+ {
+ \@@_exp_after_symbolic_f:nw { \exp_after:wN \exp_stop_f: }
+ \s_@@_symbolic \@@_symbolic_chk:w
+ \@@_types_binary:Nww #1 , { #2; #3; } ;
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{@makeother}{^} %^^A Hack!
+% \begin{@makeother}{|} %^^A Hack!
+% \begin{@makeother}{&} %^^A Hack!
+% \begin{macro}[EXP]
+% {
+% \@@_symbolic_+_symbolic_o:ww,
+% \@@_symbolic_+_o:ww,
+% \@@_+_symbolic_o:ww,
+% \@@_symbolic_-_symbolic_o:ww,
+% \@@_symbolic_-_o:ww,
+% \@@_-_symbolic_o:ww,
+% \@@_symbolic_*_symbolic_o:ww,
+% \@@_symbolic_*_o:ww,
+% \@@_*_symbolic_o:ww,
+% \@@_symbolic_/_symbolic_o:ww,
+% \@@_symbolic_/_o:ww,
+% \@@_/_symbolic_o:ww,
+% \@@_symbolic_^_symbolic_o:ww,
+% \@@_symbolic_^_o:ww,
+% \@@_^_symbolic_o:ww,
+% \@@_symbolic_|_symbolic_o:ww,
+% \@@_symbolic_|_o:ww,
+% \@@_|_symbolic_o:ww,
+% \@@_symbolic_&_symbolic_o:ww,
+% \@@_symbolic_&_o:ww,
+% \@@_&_symbolic_o:ww,
+% }
+% \begin{macrocode}
+\cs_set:Npn \@@_tmp:w #1#2
+ {
+ \cs_new_nopar:cpn
+ { @@_symbolic_#2_symbolic_o:ww }
+ { \@@_symbolic_binary_o:Nww #1 }
+ \cs_new_eq:cc
+ { @@_symbolic_#2 _o:ww }
+ { @@_symbolic_#2_symbolic_o:ww }
+ \cs_new_eq:cc
+ { @@ _#2_symbolic_o:ww }
+ { @@_symbolic_#2_symbolic_o:ww }
+ }
+\tl_map_inline:nn { + - * / ^ & | }
+ { \exp_args:Nc \@@_tmp:w { @@_#1_o:ww } {#1} }
+% \end{macrocode}
+% \end{macro}
+% \end{@makeother}
+% \end{@makeother}
+% \end{@makeother}
+%
+% \subsection{Applying prefix functions to expressions}
+%
+% \begin{macro}[aux, EXP]{\@@_symbolic_unary_o:NNw}
+% Used when applying infix operators to expressions.
+% \begin{macrocode}
+\cs_new:Npn \@@_symbolic_unary_o:NNw #1#2#3; @
+ {
+ \@@_exp_after_symbolic_f:nw { \exp_after:wN \exp_stop_f: }
+ \s_@@_symbolic \@@_symbolic_chk:w
+ \@@_types_unary:NNw #1#2 , { #3; } ;
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]
+% {
+% \@@_symbolic_acos_o:w ,
+% \@@_symbolic_acsc_o:w ,
+% \@@_symbolic_asec_o:w ,
+% \@@_symbolic_asin_o:w ,
+% \@@_symbolic_cos_o:w ,
+% \@@_symbolic_cot_o:w ,
+% \@@_symbolic_csc_o:w ,
+% \@@_symbolic_exp_o:w ,
+% \@@_symbolic_ln_o:w ,
+% \@@_symbolic_not_o:w ,
+% \@@_symbolic_sec_o:w ,
+% \@@_symbolic_set_sign_o:w ,
+% \@@_symbolic_sin_o:w ,
+% \@@_symbolic_tan_o:w ,
+% }
+% \begin{macrocode}
+\tl_map_inline:nn
+ {
+ {acos} {acsc} {asec} {asin} {cos} {cot} {csc} {exp} {ln}
+ {not} {sec} {set_sign} {sin} {sqrt} {tan}
+ }
+ {
+ \cs_new_nopar:cpe { @@_symbolic_#1_o:w }
+ {
+ \exp_not:N \@@_symbolic_unary_o:NNw
+ \exp_not:c { @@_#1_o:w }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Conversions}
+%
+% \begin{macro}[EXP]
+% {
+% \@@_symbolic_to_decimal:w,
+% \@@_symbolic_to_int:w,
+% \@@_symbolic_to_scientific:w
+% }
+% \begin{macro}[EXP]{\@@_symbolic_convert:wnnN}
+% Symbolic expressions cannot be converted to decimal, integer, or
+% scientific notation unless they can be reduced to
+% \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1#2#3
+ {
+ \cs_new_nopar:cpn { @@_symbolic_to_#1:w }
+ {
+ \exp_after:wN \@@_symbolic_convert:wnnN
+ \exp:w \exp_end_continue_f:w
+ \@@_exp_after_symbolic_f:nw { { #2 } { fp_to_#1 } #3 }
+ }
+ }
+\@@_tmp:w { decimal } { 0 } \@@_to_decimal_dispatch:w
+\@@_tmp:w { int } { 0 } \@@_to_int_dispatch:w
+\@@_tmp:w { scientific } { nan } \@@_to_scientific_dispatch:w
+\cs_new:Npn \@@_symbolic_convert:wnnN #1#2; #3#4#5
+ {
+ \str_if_eq:nnTF {#1} { \s_@@_symbolic }
+ { \@@_invalid_operation:nnw {#3} {#4} #1#2; }
+ { #5 #1#2; }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]
+% {\@@_symbolic_cs_arg_to_fn:NN, \@@_symbolic_op_arg_to_fn:nN}
+% \begin{macrocode}
+\cs_new:Npn \@@_symbolic_cs_arg_to_fn:NN #1
+ {
+ \exp_args:Nf \@@_symbolic_op_arg_to_fn:nN
+ { \@@_types_cs_to_op:N #1 }
+ }
+\cs_new:Npn \@@_symbolic_op_arg_to_fn:nN #1#2
+ {
+ \str_case:nnF { #1 #2 }
+ {
+ { not ? } { ! }
+ { set_sign 0 } { abs }
+ { set_sign 2 } { - }
+ }
+ {
+ \token_if_eq_meaning:NNTF #2 \use_ii:nn
+ { #1 d } {#1}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_symbolic_to_tl:w}
+% \begin{macro}[rEXP]
+% {
+% \@@_symbolic_unary_to_tl:NNw,
+% \@@_symbolic_binary_to_tl:Nww
+% }
+% Converting a symbolic expression to a token list is possible.
+% \begin{macrocode}
+\cs_new:Npn \@@_symbolic_to_tl:w
+ \s_@@_symbolic \@@_symbolic_chk:w #1#2, #3#4;
+ {
+ \str_case:nnTF {#1}
+ {
+ { \@@_types_unary:NNw } { \@@_symbolic_unary_to_tl:NNw }
+ { \@@_types_binary:Nww } { \@@_symbolic_binary_to_tl:Nww }
+ { \@@_function_o:w } { \@@_symbolic_function_to_tl:Nw }
+ }
+ { #2, #3 @ }
+ { \tl_to_str:n {#2} }
+ }
+\cs_new:Npn \@@_symbolic_unary_to_tl:NNw #1#2 , #3 @
+ {
+ \use:e
+ {
+ \@@_symbolic_cs_arg_to_fn:NN #1#2
+ ( \@@_to_tl_dispatch:w #3 )
+ }
+ }
+\cs_new:Npn \@@_symbolic_binary_to_tl:Nww #1, #2; #3; @
+ {
+ \use:e
+ {
+ ( \@@_to_tl_dispatch:w #2; )
+ \@@_types_cs_to_op:N #1
+ ( \@@_to_tl_dispatch:w #3; )
+ }
+ }
+\cs_new:Npn \@@_symbolic_function_to_tl:Nw #1, #2@
+ {
+ \use:e
+ {
+ \@@_types_cs_to_op:N #1
+ ( \@@_array_to_clist:n {#2} )
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Identifiers}
+%
+% Functions defined here are not necessarily tied to symbolic
+% expressions.
+%
+% \begin{macro}[TF]{\@@_id_if_invalid:n}
+% \begin{macro}[EXP]{\@@_id_if_invalid_aux:N}
+% If |#1| contains a space, it is not a valid identifier. Otherwise,
+% loop through letters in |#1|: if it is not a letter, break the loop
+% and return \texttt{true}. If the end of the loop is reached
+% without finding any non-letter, return \texttt{false}.
+% \begin{macrocode}
+\prg_new_protected_conditional:Npnn
+ \@@_id_if_invalid:n #1 { T , F , TF }
+ {
+ \tl_if_empty:nTF {#1}
+ { \prg_return_true: }
+ {
+ \tl_if_in:onTF { \tl_to_str:n {#1} } { ~ }
+ { \prg_return_true: }
+ {
+ \exp_after:wN \@@_id_if_invalid_aux:N \tl_to_str:n {#1}
+ { ? \prg_break:n \prg_return_false: }
+ \prg_break_point:
+ }
+ }
+ }
+\cs_new:Npn \@@_id_if_invalid_aux:N #1
+ {
+ \use_none:n #1
+ \int_compare:nF { `a <= `#1 <= `z }
+ {
+ \int_compare:nF { `A <= `#1 <= `Z }
+ { \prg_break:n \prg_return_true: }
+ }
+ \@@_id_if_invalid_aux:N
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Declaring variables and assigning values}
+%
+% \begin{macro}[EXP]{\@@_variable_o:w}
+% We do not use \cs{exp_last_unbraced:Nv} to extract the value of
+% |\l__fp_variable_#1_fp| because in \cs{fp_set_variable:nn} we define
+% this \texttt{fp} variable to be something which \texttt{f}-expands
+% to an actual floating point, rather than a genuine floating point.
+% \begin{macrocode}
+\cs_new:Npn \@@_variable_o:w #1 @ #2
+ {
+ \fp_if_exist:cTF { l_@@_variable_#1_fp }
+ {
+ \exp_last_unbraced:Nf \@@_exp_after_array_f:w
+ { \use:c { l_@@_variable_#1_fp } } \s_@@_expr_stop
+ \exp_after:wN \exp_stop_f: #2
+ }
+ {
+ \token_if_eq_meaning:NNTF #2 \prg_do_nothing:
+ {
+ \s_@@_symbolic \@@_symbolic_chk:w
+ \@@_variable_o:w #1 , { } ;
+ }
+ {
+ \exp_after:wN \s_@@_symbolic
+ \exp_after:wN \@@_symbolic_chk:w
+ \exp_after:wN \@@_variable_o:w
+ \exp:w
+ \@@_exp_after_symbolic_loop:N #1
+ { , \exp:w \use_none:nn }
+ \exp_after:wN \exp_end:
+ \exp_after:wN { \exp_after:wN } \exp_after:wN ;
+ #2
+ }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+% {\@@_variable_set_parsing:Nn, \@@_variable_set_parsing_aux:NNn}
+% \begin{macrocode}
+\cs_new:Npn \@@_variable_set_parsing:Nn #1#2
+ {
+ \cs_set_nopar:Npn \@@_tmp:w
+ {
+ \@@_exp_after_symbolic_f:nw { \@@_parse_infix:NN }
+ \s_@@_symbolic \@@_symbolic_chk:w
+ \@@_variable_o:w #2 , { } ;
+ }
+ \exp_args:NNc \@@_variable_set_parsing_aux:NNn #1
+ { @@_parse_word_#2:N } {#2}
+ }
+\cs_new:Npn \@@_variable_set_parsing_aux:NNn #1#2#3
+ {
+ \cs_if_eq:NNF #2 \@@_tmp:w
+ {
+ \cs_if_exist:NTF #2
+ {
+ \msg_warning:nnnn
+ { fp } { id-used-elsewhere } {#3} { variable }
+ #1 #2 \@@_tmp:w
+ }
+ {
+ \cs_new_eq:NN #2 \scan_stop: % to declare the function
+ #1 #2 \@@_tmp:w
+ }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fp_clear_variable:n}
+% \begin{macro}{\@@_clear_variable:n}
+% \begin{macrocode}
+\cs_new_protected:Npn \fp_clear_variable:n #1
+ {
+ \@@_id_if_invalid:nTF {#1}
+ { \msg_error:nnn { fp } { id-invalid } {#1} }
+ { \exp_args:No \@@_clear_variable:n { \tl_to_str:n {#1} } }
+ }
+\cs_new_protected:Npn \@@_clear_variable:n #1
+ {
+ \cs_undefine:c { l_@@_variable_#1_fp }
+ \@@_variable_set_parsing:Nn \cs_set_eq:NN {#1}
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fp_new_variable:n}
+% \begin{macro}{\@@_new_variable:n}
+% Check that |#1| is a valid identifier. If the identifier is already
+% in use, complain. Then set |\__fp_parse_word_#1:N| to use
+% |\__fp_variable_o:w|.
+% \begin{macrocode}
+\cs_new_protected:Npn \fp_new_variable:n #1
+ {
+ \@@_id_if_invalid:nTF {#1}
+ { \msg_error:nnn { fp } { id-invalid } {#1} }
+ { \exp_args:No \@@_new_variable:n { \tl_to_str:n {#1} } }
+ }
+\cs_new_protected:Npn \@@_new_variable:n #1
+ {
+ \cs_if_exist:cT { @@_parse_word_#1:N }
+ {
+ \msg_error:nnn
+ { fp } { id-already-defined } {#1}
+ \cs_undefine:c { @@_parse_word_#1:N }
+ \cs_undefine:c { l_@@_variable_#1_fp }
+ }
+ \@@_variable_set_parsing:Nn \cs_gset_eq:NN {#1}
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fp_set_variable:nn}
+% \begin{macro}{\@@_set_variable:nn}
+% Refuse invalid identifiers. If the variable does not exist yet,
+% define it just as in \cs{fp_new_variable:n} (but without unnecessary
+% checks). Then evaluate~|#2|. If the result contains the
+% identifier~|#1|, we would later get a loop in cases such as
+% \begin{quote}
+% \cs{fp_set_variable:nn} |{A}| |{A}|\\
+% \cs{fp_show:n} |{A}|
+% \end{quote}
+% To detect this, define |\l__fp_variable_#1_fp| to raise an
+% internal flag and evaluate to \texttt{nan}. Then re-evaluate
+% \cs{l_@@_symbolic_fp}, and store the result in~|#1|. If the flag is
+% raised, |#1|~was present in \cs{l_@@_symbolic_fp}. In all cases,
+% the |#1|-free result ends up in |\l__fp_variable_#1_fp|.
+% \begin{macrocode}
+\flag_new:n { @@_symbolic }
+\cs_new_protected:Npn \fp_set_variable:nn #1
+ {
+ \@@_id_if_invalid:nTF {#1}
+ { \msg_error:nnn { fp } { id-invalid } {#1} }
+ { \exp_args:No \@@_set_variable:nn { \tl_to_str:n {#1} } }
+ }
+\cs_new_protected:Npn \@@_set_variable:nn #1#2
+ {
+ \@@_variable_set_parsing:Nn \cs_set_eq:NN {#1}
+ \fp_set:Nn \l_@@_symbolic_fp {#2}
+ \cs_set_nopar:cpn { l_@@_variable_#1_fp }
+ { \flag_ensure_raised:n { @@_symbolic } \c_nan_fp }
+ \flag_clear:n { @@_symbolic }
+ \fp_set:cn { l_@@_variable_#1_fp } { \l_@@_symbolic_fp }
+ \flag_if_raised:nT { @@_symbolic }
+ {
+ \msg_error:nneee { fp } { id-loop }
+ { \tl_to_str:n {#1} }
+ { \tl_to_str:n {#2} }
+ { \fp_to_tl:N \l_@@_symbolic_fp }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Messages}
+%
+% \begin{macrocode}
+\msg_new:nnnn { fp } { id-invalid }
+ { Floating~point~identifier~'#1'~invalid. }
+ {
+ LaTeX~has~been~asked~to~create~a~new~floating~point~identifier~'#1'~
+ but~this~may~only~contain~ASCII~letters.
+ }
+\msg_new:nnnn { fp } { id-already-defined }
+ { Floating~point~identifier~'#1'~already~defined. }
+ {
+ LaTeX~has~been~asked~to~create~a~new~floating~point~identifier~'#1'~
+ but~this~name~has~already~been~used~elsewhere.
+ }
+\msg_new:nnnn { fp } { id-used-elsewhere }
+ { Floating~point~identifier~'#1'~already~used~for~something~else. }
+ {
+ LaTeX~has~been~asked~to~create~a~new~floating~point~identifier~'#1'~
+ but~this~name~is~used,~and~is~not~a~user-defined~#2.
+ }
+\msg_new:nnnn { fp } { id-loop }
+ { Variable~'#1'~used~in~the~definition~of~'#1'. }
+ {
+ LaTeX~has~been~asked~to~set~the~floating~point~identifier~'#1'~
+ to~the~expression~'#2'.~Evaluating~this~expression~yields~'#3',~
+ which~contains~'#1'~itself.
+ }
+% \end{macrocode}
+%
+% \subsection{Road-map}
+%
+% The following functions are not implemented: |min|, |max|, |?:|,
+% comparisons, |round|, |atan|, |acot|.
+%
+% \begin{macrocode}
+%</package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex