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|
% \iffalse meta-comment
%
% File: siunitx-complex.dtx Copyright (C) 2021,2022 Joseph Wright
%
% 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 "siunitx bundle" (The Work in LPPL)
% and all files in that bundle must be distributed together.
%
% The released version of this bundle is available from CTAN.
%
% -----------------------------------------------------------------------
%
% The development version of the bundle can be found at
%
% https://github.com/josephwright/siunitx
%
% for those people who are interested.
%
% -----------------------------------------------------------------------
%
%<*driver>
\documentclass{l3doc}
\ProvideDocumentCommand\foreign{m}{\textit{#1}}
% The next line is needed so that \GetFileInfo will be able to pick up
% version data
\usepackage{siunitx}
\begin{document}
\DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
% \GetFileInfo{siunitx.sty}
%
% \title{^^A
% \pkg{siunitx-complex} -- Complex numbers^^A
% \thanks{This file describes \fileversion,
% last revised \filedate.}^^A
% }
%
% \author{^^A
% Joseph Wright^^A
% \thanks{^^A
% E-mail:
% \href{mailto:joseph.wright@morningstar2.co.uk}
% {joseph.wright@morningstar2.co.uk}^^A
% }^^A
% }
%
% \date{Released \filedate}
%
% \maketitle
%
% \begin{documentation}
%
% This submodule is concerned with formatting complex numbers. It augments the
% standard functions \cs{siunitx_number_format:nN} and \cs{siunitx_quantity:nn}
% by allowing parsing of numbers with a complex part. There are no additional
% assumptions concerning \LaTeXe{} commands in the submodule beyond those in the
% core number and unit submodules.
%
% \begin{function}{\siunitx_complex_number:n}
% \begin{syntax}
% \cs{siunitx_complex_number:n} \Arg{number}
% \end{syntax}
% Parses the \meta{number} and splits into real and complex parts, which are
% then formatted as described for \cs{siunitx_number_format:nN}. The results
% are combined and printed using the standard functions in the module. If
% the setting \opt{complex-mode} is set to \meta{polar}, the input is
% parsed, converted to polar form and then passed to
% \cs{siunitx_complex_number:nn}. This parsing requires that the complex root
% is given as \texttt{i} at the \emph{end} of the value.
% \end{function}
%
% \begin{function}{\siunitx_complex_number:nn}
% \begin{syntax}
% \cs{siunitx_complex_number:nn} \Arg{magnitude} \Arg{angle}
% \end{syntax}
% Parses the \meta{magnitude} and \meta{angle} and then formats each as
% described for \cs{siunitx_number_format:nN}. The two are separated by the
% angle symbol, which is treated as a numerical part. If
% \opt{complex-angle-unit} is set to \opt{degrees} then the unit symbol is
% added: this is printed as a unit in the usual way. If
% the setting \opt{complex-mode} is set to \meta{cartesian}, the input is
% parsed, converted to Cartesian form and then passed to
% \cs{siunitx_complex_number:n}.
% \end{function}
%
% \begin{function}{\siunitx_complex_quantity:nn, \siunitx_complex_quantity:nnn}
% \begin{syntax}
% \cs{siunitx_complex_quantity:nn} \Arg{number} \Arg{units}
% \cs{siunitx_complex_quantity:nnn} \Arg{magnitude} \Arg{angle} \Arg{units}
% \end{syntax}
% These functions treat their numerical argument(s) as described
% for the corresponding \texttt{number} functions. They then typeset the
% entire numerical part and the unit as described for \cs{siunitx_quantity:nn}.
% \end{function}
%
% \begin{function}{complex-angle-unit}
% \begin{syntax}
% |complex-angle-unit| = |degrees|\verb"|"|radians|
% \end{syntax}
% Sets how the unit for polar complex numbers is treated. This setting
% is used to determine how polar \emph{input} is interpreted, how
% conversion to polar form works and how output in polar form is typeset.
% The standard setting is |degrees|.
% \end{function}
%
% \begin{function}{complex-mode}
% \begin{syntax}
% |complex-mode| = |cartesian|\verb"|"|input|\verb"|"|polar|
% \end{syntax}
% Selects how complex values are formatted: a choice from the options
% |cartesian|, |input| and |polar|. The option |cartesian| means that
% complex values will always be typeset in cartesian ($x + y\mathrm{i}$)
% format, whilst |polar| means that complex are typeset as a magnitude
% and angle. Finally, |input| setting means that the input format
% (\foreign{i.e.}~difference between \cs{siunitx_complex_number:n} and
% \cs{siunitx_complex_number:nn}) is maintained. The standard setting is
% |input|.
% \end{function}
%
% \begin{function}{complex-root-position}
% \begin{syntax}
% |complex-root-position| = |after-number|\verb"|"|before-number|
% \end{syntax}
% Choice which determines where the complex root symbol is printed relative
% to the numbers. The standard setting is |after-number|.
% \end{function}
%
% \begin{function}{complex-symbol-angle}
% \begin{syntax}
% |complex-symbol-angle| = \meta{symbol}
% \end{syntax}
% Sets the symbol used before the polar angle.
% \end{function}
%
% \begin{function}{complex-symbol-degree}
% \begin{syntax}
% |complex-symbol-degree| = \meta{symbol}
% \end{syntax}
% Sets the symbol used for polar degrees.
% \end{function}
%
% \begin{function}{input-complex-root}
% \begin{syntax}
% |input-complex-root| = \meta{tokens}
% \end{syntax}
% The token(s) considered as complexes roots for number parsing.
% The standard setting is |ij|.
% \end{function}
%
% \begin{function}{output-complex-root}
% \begin{syntax}
% |output-complex-root| = \meta{tokens}
% \end{syntax}
% The token(s) used to show the complex root in output. The standard setting
% is |\mathrm{i}|.
% \end{function}
%
% \begin{function}{print-complex-unity}
% \begin{syntax}
% |print-complex-unity| = |true|\verb"|"|false|
% \end{syntax}
% Switch to determine if the number \num{1} is printed for a complex
% part which is exactly unity.
% \end{function}
%
% \end{documentation}
%
% \begin{implementation}
%
% Start the \pkg{DocStrip} guards.
% \begin{macrocode}
%<*package>
% \end{macrocode}
%
% \section{\pkg{siunitx-complex} implementation}
%
% Identify the internal prefix (\LaTeX3 \pkg{DocStrip} convention): only
% internal material in this \emph{submodule} should be used directly.
% \begin{macrocode}
%<@@=siunitx_complex>
% \end{macrocode}
%
% \subsection{General setup}
%
% \begin{variable}{\l_@@_tmp_fp, \l_@@_tmp_tl}
% \begin{macrocode}
\fp_new:N \l_@@_tmp_fp
\tl_new:N \l_@@_tmp_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_input_tl}
% The numerical input exactly as given by the user.
% \begin{macrocode}
\tl_new:N \l_@@_input_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_comparator_tl}
% A comparator, if found, is held here.
% \begin{macrocode}
\tl_new:N \l_@@_comparator_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_exp_tl}
% The exponent part of a parsed number.
% \begin{macrocode}
\tl_new:N \l_@@_exp_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_real_tl, \l_@@_img_tl}
% The real and imaginary parts of cartesian form, respectively.
% \begin{macrocode}
\tl_new:N \l_@@_real_tl
\tl_new:N \l_@@_img_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_mag_tl, \l_@@_angle_tl}
% The magnitude and angle of polar form, respectively.
% \begin{macrocode}
\tl_new:N \l_@@_mag_tl
\tl_new:N \l_@@_angle_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_join_tl, \l_@@_sign_tl}
% Staging posts for a joining and leading sign, respectively.
% \begin{macrocode}
\tl_new:N \l_@@_join_tl
\tl_new:N \l_@@_sign_tl
% \end{macrocode}
% \end{variable}
%
% \begin{variable}
% {
% \l_@@_root_after_bool ,
% \l_@@_force_cartesian_bool ,
% \l_@@_force_polar_bool ,
% \l_@@_polar_degree_bool ,
% \l_@@_symbol_angle_tl ,
% \l_@@_symbol_degree_tl ,
% \l_@@_input_root_tl ,
% \l_@@_output_root_tl
% }
% \begin{macrocode}
\bool_new:N \l_@@_root_after_bool
\bool_new:N \l_@@_force_cartesian_bool
\bool_new:N \l_@@_force_polar_bool
\bool_new:N \l_@@_polar_degree_bool
\keys_define:nn { siunitx }
{
complex-mode .choice: ,
complex-mode / cartesian .code:n =
{
\bool_set_true:N \l_@@_force_cartesian_bool
\bool_set_false:N \l_@@_force_polar_bool
} ,
complex-mode / polar .code:n =
{
\bool_set_false:N \l_@@_force_cartesian_bool
\bool_set_true:N \l_@@_force_polar_bool
} ,
complex-mode / input .code:n =
{
\bool_set_false:N \l_@@_force_cartesian_bool
\bool_set_false:N \l_@@_force_polar_bool
} ,
complex-angle-unit .choice: ,
complex-angle-unit / degrees .code:n =
{ \bool_set_true:N \l_@@_polar_degree_bool } ,
complex-angle-unit / radians .code:n =
{ \bool_set_false:N \l_@@_polar_degree_bool } ,
complex-root-position .choice: ,
complex-root-position / after-number .code:n =
{ \bool_set_true:N \l_@@_root_after_bool } ,
complex-root-position / before-number .code:n =
{ \bool_set_false:N \l_@@_root_after_bool } ,
complex-symbol-angle .tl_set:N =
\l_@@_symbol_angle_tl ,
complex-symbol-degree .tl_set:N =
\l_@@_symbol_degree_tl ,
input-complex-root .tl_set:N =
\l_@@_input_root_tl ,
output-complex-root .tl_set:N =
\l_@@_output_root_tl ,
print-complex-unity .bool_set:N =
\l_@@_print_unity_bool
}
% \end{macrocode}
% \end{variable}
%
% \subsection{Parsing}
%
% \begin{macro}{\@@_parse:nNN}
% \begin{macro}{\@@_parse_end:}
% \begin{macro}{\@@_parse_clear:}
% Parsing for complex numbers needs some of the same approaches as the
% general parser. However, as the aim here is to do only enough to split
% the real and imaginary parts before handing off the the usual code,
% it's not a full repeat. Instead, we shortcut where we can. The |clear|
% function here is not only there to make this function shorter: it
% also allows a single way to zap any stored data if a parse error occurs.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse:nNN #1#2#3
{
\group_begin:
\@@_parse_clear:
\protected@edef \l_@@_arg_tl {#1}
\tl_set_eq:NN \l_@@_input_tl \l_@@_arg_tl
\siunitx_number_normalize_symbols:N \l_@@_arg_tl
\tl_if_empty:NF \l_@@_arg_tl
{ \@@_parse_comparator: }
\@@_parse_check:
\cs_set_protected:Npx \@@_parse_end:
{
\tl_set:Nn \exp_not:N #2 { \exp_not:V \l_@@_real_tl }
\tl_set:Nn \exp_not:N #3 { \exp_not:V \l_@@_img_tl }
}
\exp_after:wN \group_end:
\@@_parse_end:
}
\cs_new_protected:Npn \@@_parse_end: { }
\cs_new_protected:Npn \@@_parse_clear:
{
\tl_clear:N \l_@@_real_tl
\tl_clear:N \l_@@_img_tl
\tl_clear:N \l_@@_exp_tl
\tl_clear:N \l_@@_sign_tl
\tl_clear:N \l_@@_join_tl
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_check:}
% \begin{macro}{\@@_parse_check:N}
% Now we tidy up and do the main work: passing to the standard formatter for
% final parsing.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_check:
{
\tl_if_empty:NTF \l_@@_img_tl
{ \@@_parse_check:N \l_@@_real_tl }
{
\tl_if_empty:NTF \l_@@_real_tl
{ \@@_parse_check:N \l_@@_img_tl }
{
\@@_parse_check:N \l_@@_real_tl
\tl_set_eq:NN \l_@@_sign_tl \l_@@_join_tl
\@@_parse_check:N \l_@@_img_tl
}
}
}
\cs_new_protected:Npn \@@_parse_check:N #1
{
\tl_set:Nx #1
{
\exp_not:V \l_@@_comparator_tl
\exp_not:V \l_@@_sign_tl
\exp_not:V #1
\exp_not:V \l_@@_exp_tl
}
\tl_clear:N \l_@@_comparator_tl
\tl_clear:N \l_@@_sign_tl
\siunitx_number_parse:VN #1 #1
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_comparator:}
% \begin{macro}{\@@_parse_comparator_aux:Nw}
% The first step is to extract any comparator: this is the same as
% for a full number parse.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_comparator:
{
\exp_after:wN \@@_parse_comparator_aux:Nw
\l_@@_arg_tl \q_stop
}
\cs_new_protected:Npn \@@_parse_comparator_aux:Nw #1#2 \q_stop
{
\tl_if_in:NnTF \l_siunitx_number_input_comparator_tl {#1}
{
\tl_set:Nn \l_@@_comparator_tl {#1}
\tl_set:Nn \l_@@_arg_tl {#2}
}
{ \tl_clear:N \l_@@_comparator_tl }
\tl_if_empty:NF \l_@@_arg_tl
{ \@@_parse_sign: }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_exponent:}
% \begin{macro}{\@@_parse_exponent_auxi:w}
% \begin{macro}{\@@_parse_exponent_auxii:nn}
% An exponent part of a number has to come at the end and can only occur
% once. Thus it is relatively easy to parse. The code here is a simplified
% version of that in \pkg{siunitx-number}: we only need to find \emph{some}
% exponent, not check on the detail. Notice that we need to retain the
% exponent marker here: that is done using the short-lived temporary
% variable.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_exponent:
{
\tl_if_empty:NTF \l_siunitx_number_input_exponent_tl
{ \@@_parse_root: }
{
\tl_set:Nx \l_@@_tmp_tl
{ \tl_head:V \l_siunitx_number_input_exponent_tl }
\tl_map_inline:Nn \l_siunitx_number_input_exponent_tl
{
\tl_replace_all:NnV \l_@@_arg_tl
{##1} \l_@@_tmp_tl
}
\use:x
{
\cs_set_protected:Npn
\exp_not:N \@@_parse_exponent_auxi:w
####1 \exp_not:V \l_@@_tmp_tl
####2 \exp_not:V \l_@@_tmp_tl
####3 \exp_not:N \q_stop
}
{ \@@_parse_exponent_auxii:nn {##1} {##2} }
\use:x
{
\@@_parse_exponent_auxi:w
\exp_not:V \l_@@_arg_tl
\exp_not:V \l_@@_tmp_tl \exp_not:N \q_nil
\exp_not:V \l_@@_tmp_tl \exp_not:N \q_stop
}
}
}
\cs_new_protected:Npn \@@_parse_exponent_auxi:w { }
\cs_new_protected:Npn \@@_parse_exponent_auxii:nn #1#2
{
\quark_if_nil:nF {#2}
{
\tl_set:Nn \l_@@_arg_tl {#1}
\tl_set:Nx \l_@@_exp_tl
{ \exp_not:V \l_@@_tmp_tl \exp_not:n {#2} }
}
\@@_parse_root:
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_root:}
% \begin{macro}{\@@_parse_root_auxi:w}
% \begin{macro}{\@@_parse_root_auxii:nn}
% Splitting at the complex root is much like splitting the exponent.
% After dealing with the case where there is no complex root allowed,
% use the first possible symbol to do the work.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_root:
{
\tl_if_empty:NTF \l_@@_input_root_tl
{ \tl_set_eq:NN \l_@@_real_tl \l_@@_arg_tl }
{
\tl_set:Nx \l_@@_tmp_tl
{ \tl_head:V \l_@@_input_root_tl }
\tl_map_inline:Nn \l_@@_input_root_tl
{
\tl_replace_all:NnV \l_@@_arg_tl
{##1} \l_@@_tmp_tl
}
\use:x
{
\cs_set_protected:Npn
\exp_not:N \@@_parse_root_auxi:w
####1 \exp_not:V \l_@@_tmp_tl
####2 \exp_not:V \l_@@_tmp_tl
####3 \exp_not:N \q_stop
}
{ \@@_parse_root_auxii:nn {##1} {##2} }
\use:x
{
\@@_parse_root_auxi:w
\exp_not:V \l_@@_arg_tl
\exp_not:V \l_@@_tmp_tl \exp_not:N \q_nil
\exp_not:V \l_@@_tmp_tl \exp_not:N \q_stop
}
}
}
\cs_new_protected:Npn \@@_parse_root_auxi:w { }
% \end{macrocode}
% This is where the business end lies. We have four possibilities:
% \begin{itemize}
% \item There was no complex root at all: |#2| will be |\q_nil|
% \item All of the number is in the complex part with a leading
% root: |#1| will be empty. This includes the case where
% the input was \emph{just} a root symbol (plus possibly sign,
% exponent): we need to cover that.
% \item All of the number was before the complex root: |#2| will
% be empty and we need to check |#1| fully to split out the two
% parts
% \item The input has a real part with the complex part starting
% with the root symbol: just the last token needs to be separated.
% \end{itemize}
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_root_auxii:nn #1#2
{
\quark_if_nil:nTF {#2}
{ \tl_set:Nn \l_@@_real_tl {#1} }
{
\tl_set:Nn \l_@@_img_tl {#2}
\tl_if_blank:nTF {#1}
{
\tl_if_blank:nT {#2}
{ \tl_set:Nn \l_@@_img_tl { 1 } }
}
{
\tl_if_blank:nTF {#2}
{ \@@_parse_split:n {#1} }
{ \@@_parse_sign_check:n {#1} }
}
}
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_sign:}
% \begin{macro}{\@@_parse_sign_aux:Nw}
% The first token of a number after a comparator could be a sign. A quick
% check is made and if found stored. There is no need to worry about the
% nature of the sign: we keep them regardless.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_sign:
{
\exp_after:wN \@@_parse_sign_aux:Nw
\l_@@_arg_tl \q_stop
}
\cs_new_protected:Npn \@@_parse_sign_aux:Nw #1#2 \q_stop
{
\tl_if_in:NnT \l_siunitx_number_input_sign_tl {#1}
{
\tl_set:Nn \l_@@_sign_tl {#1}
\tl_set:Nn \l_@@_arg_tl {#2}
}
\tl_if_empty:NF \l_@@_arg_tl
{ \@@_parse_exponent: }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_sign_check:n}
% \begin{macro}{\@@_parse_sign_check:nN}
% \begin{macro}{\@@_parse_sign_check:nNw}
% Here, we want to check that the last token in the input is a sign.
% There cannot be anything after the sign, and there has to be at one
% token before the sign: we can therefore signal a parsing error if we
% need to.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_sign_check:n #1
{
\@@_parse_sign_check:nN { } #1 \q_recursion_tail \q_recursion_stop
}
\cs_new_protected:Npn \@@_parse_sign_check:nN #1#2
{
\quark_if_recursion_tail_stop_do:Nn #2
{ \@@_parse_clear: }
\tl_if_in:NnTF \l_siunitx_number_input_sign_tl {#2}
{ \@@_parse_sign_check:nNw {#1} #2 }
{ \@@_parse_sign_check:nN {#1#2} }
}
\cs_new_protected:Npn \@@_parse_sign_check:nNw
#1#2 #3 \q_recursion_tail \q_recursion_stop
{
\tl_if_blank:nTF {#3}
{
\tl_if_blank:nTF {#1}
{ \@@_parse_clear: }
{
\tl_set:Nn \l_@@_real_tl {#1}
\tl_set:Nn \l_@@_join_tl {#2}
}
}
{ \@@_parse_clear: }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_split:n}
% \begin{macro}{\@@_parse_split:nN}
% \begin{macro}{\@@_parse_split:w}
% Checking for a sign inside the leading part of the number is a simple loop.
% There is the possibility that there is no number in the imaginary part
% needs to be allowed for. Notice that we do a check that there is some
% real part: this covers for example an original input |++1i|, which
% otherwise would not be trapped.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_split:n #1
{
\@@_parse_split:nN { } #1 \q_recursion_tail \q_recursion_stop
}
\cs_new_protected:Npn \@@_parse_split:nN #1#2
{
\quark_if_recursion_tail_stop_do:Nn #2
{ \tl_set:Nn \l_@@_img_tl {#1} }
\tl_if_in:NnTF \l_siunitx_number_input_sign_tl {#2}
{
\tl_set:Nn \l_@@_real_tl {#1}
\tl_set:Nn \l_@@_join_tl {#2}
\@@_parse_split:w
}
{ \@@_parse_split:nN {#1#2} }
}
\cs_new_protected:Npn \@@_parse_split:w #1 \q_recursion_tail \q_recursion_stop
{
\tl_set:Nx \l_@@_img_tl
{
\tl_if_blank:nTF {#1}
{ 1 }
{ \exp_not:n {#1} }
}
\tl_if_empty:NT \l_@@_real_tl
{ \@@_parse_clear: }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_parse_polar:nn}
% Almost trivial but repeated in a couple of places so worth an auxiliary.
% \begin{macrocode}
\cs_new_protected:Npn \@@_parse_polar:nn #1#2
{
\siunitx_number_parse:nN {#1} \l_@@_mag_tl
\group_begin:
\keys_set:nn { siunitx }
{
input-comparators = ,
input-exponent-markers = ,
input-open-uncertainty = ,
input-close-uncertainty =
}
\siunitx_number_format:nN {#2} \l_@@_angle_tl
\exp_args:NNNV \group_end:
\tl_set:Nn \l_@@_angle_tl \l_@@_angle_tl
}
% \end{macrocode}
% \end{macro}
%
% \section{Formatting}
%
% \begin{variable}{\l_@@_bracket_close_tl, \l_@@_bracket_open_tl}
% Purely internal for the present.
% \begin{macrocode}
\tl_new:N \l_@@_bracket_close_tl
\tl_new:N \l_@@_bracket_open_tl
\tl_set:Nn \l_@@_bracket_open_tl { ( }
\tl_set:Nn \l_@@_bracket_close_tl { ) }
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_unit_tl}
% \begin{macrocode}
\tl_new:N \l_@@_unit_tl
% \end{macrocode}
% \end{variable}
%
% \begin{macro}{\siunitx_complex_number:n}
% \begin{macro}{\siunitx_complex_number:nn, \@@_number:nn}
% \begin{macro}{\siunitx_complex_quantity:nn}
% \begin{macro}{\siunitx_complex_quantity:nnn, \@@_quantity:nnn}
% The work here is pretty trivial: only conversion between forms makes
% things a bit more intricate.
% \begin{macrocode}
\cs_new_protected:Npn \siunitx_complex_number:n #1
{
\bool_if:NTF \l_@@_force_polar_bool
{
\use:e
{
\siunitx_complex_number:nn
\@@_convert_polar:n {#1}
}
}
{
\bool_if:NTF \l_siunitx_number_parse_bool
{
\@@_parse:nNN {#1} \l_@@_real_tl \l_@@_img_tl
\@@_format_cartesian:n { }
}
{
\siunitx_number_format:nN {#1} \l_@@_tmp_tl
\siunitx_print_number:V \l_@@_tmp_tl
}
}
}
\cs_new_protected:Npn \siunitx_complex_number:nn #1#2
{
\bool_lazy_or:nnTF
{ \tl_if_blank_p:n {#1} }
{ \tl_if_blank_p:n {#2} }
{
\msg_error:nnnn { siunitx } { invalid-polar-form }
{#1} {#2}
}
{ \@@_number:nn {#1} {#2} }
}
\cs_new_protected:Npn \@@_number:nn #1#2
{
\bool_if:NTF \l_@@_force_cartesian_bool
{
\exp_args:Ne \siunitx_complex_number:n
{ \@@_convert_cartesian:nn {#1} {#2} }
}
{
\@@_parse_polar:nn {#1} {#2}
\@@_format_polar:n { }
}
}
\cs_new_protected:Npn \siunitx_complex_quantity:nn #1#2
{
\bool_if:NTF \l_@@_force_polar_bool
{
\use:e
{
\siunitx_complex_quantity:nnn
\@@_convert_polar:n {#1}
}
{#2}
}
{
\bool_if:NTF \l_siunitx_number_parse_bool
{
\@@_parse:nNN {#1} \l_@@_real_tl \l_@@_img_tl
\@@_format_cartesian:n {#2}
}
{ \siunitx_quantity:nn {#1} {#2} }
}
}
\cs_new_protected:Npn \siunitx_complex_quantity:nnn #1#2#3
{
\bool_lazy_or:nnTF
{ \tl_if_blank_p:n {#1} }
{ \tl_if_blank_p:n {#2} }
{
\msg_error:nnnn { siunitx } { invalid-polar-form }
{#1} {#2}
}
{ \@@_quantity:nnn {#1} {#2} {#3} }
}
\cs_new_protected:Npn \@@_quantity:nnn #1#2#3
{
\bool_if:NTF \l_@@_force_cartesian_bool
{
\exp_args:Ne \siunitx_complex_quantity:nn
{ \@@_convert_cartesian:nn {#1} {#2} }
{#3}
}
{
\@@_parse_polar:nn {#1} {#2}
\@@_format_polar:n {#3}
}
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_format_cartesian:n}
% \begin{macro}{\@@_format_cartesian_auxi:n}
% \begin{macro}{\@@_format_cartesian_auxii:n}
% \begin{macro}{\@@_drop_exponent:nnnnnnn}
% \begin{macro}{\@@_format_sign:nnnnnnn}
% \begin{macro}{\@@_extract_exponent:nw}
% \begin{macro}{\@@_extract_exponent_aux:w}
% \begin{macro}[EXP]{\@@_format_bracket:n}
% We start here checking that there is something to do.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_cartesian:n #1
{
\bool_lazy_and:nnF
{ \tl_if_empty_p:N \l_@@_real_tl }
{ \tl_if_empty_p:N \l_@@_img_tl }
{ \@@_format_cartesian_auxi:n {#1} }
}
% \end{macrocode}
% We split based on whether the number has a complex part at all,
% then print the result.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_cartesian_auxi:n #1
{
\tl_clear:N \l_@@_tmp_tl
\tl_if_empty:NTF \l_@@_img_tl
{
\siunitx_number_process:NN \l_@@_real_tl \l_@@_real_tl
\tl_set:Nx \l_@@_tmp_tl
{ \siunitx_number_output:N \l_@@_real_tl }
}
{ \@@_format_cartesian_auxii:n {#1} }
\tl_if_blank:nTF {#1}
{ \siunitx_print_number:V \l_@@_tmp_tl }
{ \siunitx_quantity_print:VV \l_@@_tmp_tl \l_@@_unit_tl }
}
% \end{macrocode}
% If we get to this stage we have both parts to a complex number. We
% need to process both and do some massaging, then it's just a question
% of reassembly with the right parts in the right places.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_cartesian_auxii:n #1
{
\@@_format_cartesian_units:n {#1}
\tl_if_empty:NF \l_@@_real_tl
{ \exp_after:wN \@@_drop_exponent:nnnnnnn \l_@@_real_tl }
\exp_after:wN \@@_format_sign:nnnnnnn \l_@@_img_tl
\tl_set:Nx \l_@@_tmp_tl
{ \siunitx_number_output:NN \l_@@_img_tl \q_nil }
\exp_after:wN \@@_extract_exponent:w \l_@@_tmp_tl \q_stop
\tl_set:Nx \l_@@_tmp_tl
{
\bool_lazy_or:nnTF
{
\bool_lazy_and_p:nn
{ \l_siunitx_number_bracket_ambiguous_bool }
{ ! \tl_if_empty_p:N \l_@@_exp_tl }
}
{
! \bool_lazy_any_p:n
{
{ \tl_if_blank_p:n {#1} }
{ \tl_if_empty_p:N \l_@@_real_tl }
{ \tl_if_empty_p:N \l_@@_img_tl }
}
}
{ \@@_format_bracket:n }
{ \use:n }
{
\siunitx_number_output:N \l_@@_real_tl
\exp_not:V \l_@@_sign_tl
\bool_if:NF \l_@@_root_after_bool
{ \exp_not:V \l_@@_output_root_tl }
\exp_not:V \l_@@_tmp_tl
\bool_if:NT \l_@@_root_after_bool
{ \exp_not:V \l_@@_output_root_tl }
}
\exp_not:V \l_@@_exp_tl
}
}
% \end{macrocode}
% No exponent for the real part.
% \begin{macrocode}
\cs_new_protected:Npn \@@_drop_exponent:nnnnnnn #1#2#3#4#5#6#7
{ \tl_set:Nn \l_@@_real_tl { {#1} {#2} {#3} {#4} {#5} { } { 0 } } }
% \end{macrocode}
% Ensure the imaginary part has a sign.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_sign:nnnnnnn #1#2#3#4#5#6#7
{
\tl_set:Nx \l_@@_img_tl
{
{ }
{
\tl_if_blank:nTF {#2}
{ \tl_if_empty:NF \l_@@_real_tl { + } }
{ \exp_not:n {#2} }
}
\exp_not:n { {#3} {#4} {#5} {#6} {#7} }
}
}
% \end{macrocode}
% Pull out the formatted exponent: we also need the sign.
% An imaginary part that is exactly $1$ is omitted, with only the complex
% root printed. That means checking and removing a lone $1$ here.
% \begin{macrocode}
\cs_new_protected:Npn \@@_extract_exponent:w
#1 \q_nil #2 \q_nil #3 \q_nil #4 \q_nil #5 \q_nil #6 \q_nil #7 \q_nil #8
\q_nil #9 \q_stop
{
\tl_set:Nn \l_@@_sign_tl {#1#2}
\bool_lazy_all:nTF
{
{ ! \l_@@_print_unity_bool }
{ \str_if_eq_p:nn {#3} { 1 } }
{ \tl_if_blank_p:n {#5} }
}
{ \@@_extract_exponent_aux:nw {#6#7#8} }
{ \@@_extract_exponent_aux:nw {#3#4#5#6#7#8} }
#9 \q_stop
}
\cs_new:Npn \@@_extract_exponent_aux:nw
#1#2 \q_nil #3 \q_nil #4 \q_stop
{
\tl_set:Nn \l_@@_tmp_tl {#1#2}
\tl_set:Nn \l_@@_exp_tl {#3#4}
}
\cs_new_protected:Npn \@@_format_bracket:n #1
{
\exp_not:V \l_@@_bracket_open_tl
#1
\exp_not:V \l_@@_bracket_close_tl
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@_format_cartesian_units:n}
% \begin{macro}
% {
% \@@_format_cartesian_combine-exponent:n ,
% \@@_format_cartesian_extract-exponent:n ,
% \@@_format_cartesian_input:n
% }
% \begin{macro}{\@@_format_extract-exponent:N}
% \begin{macro}[EXP]{\@@_extract_exp:nnnnnnn}
% \begin{macro}{\@@_drop_exp:N}
% \begin{macro}[EXP]{\@@_drop_exp:nnnnnnnN}
% Formatting units needs to know the settings from the main module, and
% the flow is then much the same as in \pkg{siunitx-compound}. We only
% have to watch the fact there are two numbers to format.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_cartesian_units:n #1
{
\tl_if_blank:nTF {#1}
{
\siunitx_number_process:NN \l_@@_real_tl \l_@@_real_tl
\siunitx_number_process:NN \l_@@_img_tl \l_@@_img_tl
}
{
\use:c
{ @@_format_cartesian_ \l_siunitx_quantity_prefix_mode_tl :n } {#1}
}
}
\cs_new_protected:cpn { @@_format_cartesian_combine-exponent:n } #1
{
\tl_if_empty:NF \l_@@_real_tl
{ \siunitx_number_process:NN \l_@@_real_tl \l_@@_real_tl }
\siunitx_number_process:NN \l_@@_img_tl \l_@@_img_tl
\fp_set:Nn \l_@@_tmp_fp
{ \exp_after:wN \@@_extract_exp:nnnnnnn \l_@@_img_tl }
\@@_drop_exp:N \l_@@_real_tl
\@@_drop_exp:N \l_@@_img_tl
\siunitx_unit_format_combine_exponent:nnN {#1}
\l_@@_tmp_fp \l_@@_unit_tl
}
\cs_new_protected:cpx { @@_format_cartesian_extract-exponent:n } #1
{
\exp_not:N \siunitx_unit_format_extract_prefixes:nNN {#1}
\exp_not:N \l_@@_unit_tl \exp_not:N \l_@@_tmp_fp
\exp_not:c { @@_format_extract-exponent:N }
\exp_not:N \l_@@_img_tl
\exp_not:N \tl_if_empty:NF \exp_not:N \l_@@_real_tl
{
\exp_not:c { @@_format_extract-exponent:N }
\exp_not:N \l_@@_real_tl
}
}
\cs_new_protected:Npn \@@_format_cartesian_input:n #1
{
\siunitx_number_process:NN \l_@@_real_tl \l_@@_real_tl
\siunitx_number_process:NN \l_@@_img_tl \l_@@_img_tl
\siunitx_unit_format:nN {#1} \l_@@_unit_tl
}
\cs_new_protected:cpn { @@_format_extract-exponent:N } #1
{
\tl_set:Nx #1
{ \siunitx_number_adjust_exponent:Nn #1 \l_@@_tmp_fp }
\siunitx_number_process:NN #1 #1
}
\cs_new:Npn \@@_extract_exp:nnnnnnn #1#2#3#4#5#6#7 { #6#7 }
\cs_new_protected:Npn \@@_drop_exp:N #1
{ \exp_after:wN \@@_drop_exp:nnnnnnnN #1 #1 }
\cs_new_protected:Npn \@@_drop_exp:nnnnnnnN #1#2#3#4#5#6#7#8
{ \tl_set:Nn #8 { {#1} {#2} {#3} {#4} {#5} { } { 0 } } }
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}
% {
% \@@_format_polar:n ,
% \@@_format_combine-exponent:n ,
% \@@_format_extract-exponent:n ,
% \@@_format_polar_input:n
% }
% We see similar ideas here to the Cartesian versions, but with only
% the magnitude to adjust, things are rather simpler in the exponent
% manipulations.
% \begin{macrocode}
\cs_new_protected:Npn \@@_format_polar:n #1
{
\tl_if_blank:nTF {#1}
{ \siunitx_number_process:NN \l_@@_mag_tl \l_@@_mag_tl }
{
\use:c
{ @@_format_polar_ \l_siunitx_quantity_prefix_mode_tl :n } {#1}
}
\tl_set:Nx \l_@@_tmp_tl
{
\siunitx_number_output:N \l_@@_mag_tl
\exp_not:V \l_@@_symbol_angle_tl
\mathord % TEMP
\exp_not:V \l_@@_angle_tl
}
\siunitx_print_number:V \l_@@_tmp_tl
\bool_if:NT \l_@@_polar_degree_bool
{
\exp_args:NV \siunitx_unit_format:nN \l_@@_symbol_degree_tl \l_@@_tmp_tl
\nobreak
\siunitx_print_unit:V \l_@@_tmp_tl
}
\siunitx_quantity_print:nV { } \l_@@_unit_tl
}
\cs_new_protected:cpn { @@_format_polar_combine-exponent:n } #1
{
\siunitx_number_process:NN \l_@@_mag_tl \l_@@_mag_tl
\fp_set:Nn \l_@@_tmp_fp
{ \exp_after:wN \@@_extract_exp:nnnnnnn \l_@@_mag_tl }
\@@_drop_exp:N \l_@@_mag_tl
\siunitx_unit_format_combine_exponent:nnN {#1}
\l_@@_tmp_fp \l_@@_unit_tl
}
\cs_new_protected:cpx { @@_format_polar_extract-exponent:n } #1
{
\exp_not:N \siunitx_unit_format_extract_prefixes:nNN {#1}
\exp_not:N \l_@@_unit_tl \exp_not:N \l_@@_tmp_fp
\exp_not:c { @@_format_extract-exponent:N }
\exp_not:N \l_@@_mag_tl
}
\cs_new_protected:Npn \@@_format_polar_input:n #1
{
\siunitx_number_process:NN \l_@@_mag_tl \l_@@_mag_tl
\siunitx_unit_format:nN {#1} \l_@@_unit_tl
}
% \end{macrocode}
% \end{macro}
%
% \subsection{Conversion}
%
% \begin{macro}[EXP]
% {\@@_convert_cartesian:nn, \@@_convert_cartesian_aux:nn}
% \begin{macro}[EXP]{\@@_convert_cartesian_aux:w}
% Conversion to Cartesian form is easy as we have two inputs and need to
% do no parsing here at all.
% \begin{macrocode}
\cs_new:Npn \@@_convert_cartesian:nn #1#2
{
\exp_args:Nee \@@_convert_cartesian_aux:nn
{
\fp_to_tl:n
{ (#1) * cos \bool_if:NT \l_@@_polar_degree_bool { d } (#2) }
}
{
\fp_to_tl:n
{ (#1) * sin \bool_if:NT \l_@@_polar_degree_bool { d } (#2) }
}
}
\cs_new:Npn \@@_convert_cartesian_aux:nn #1#2
{
\@@_convert_cartesian_aux:w #1 e e \q_mark #2 e e \q_stop
}
\cs_new:Npn \@@_convert_cartesian_aux:w
#1 e #2 e #3 \q_mark #4 e #5 e #6 \q_stop
{
\fp_compare:nNnF {#1} = \c_zero_fp
{#1}
\fp_compare:nNnF {#4} = \c_zero_fp
{
\fp_compare:nNnF {#4} < \c_zero_fp { + }
#4 i
}
\tl_if_blank:nF {#2}
{ e #2 }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[EXP]{\@@_convert_polar:n}
% \begin{macro}[EXP]{\@@_convert_polar_auxi:w}
% \begin{macro}[EXP]{\@@_convert_polar_auxii:nw}
% \begin{macro}[EXP]{\@@_convert_polar_auxiii:nnw}
% \begin{macro}[EXP]{\@@_convert_polar_auxiv:nnw}
% \begin{macro}[EXP]{\@@_convert_polar_auxv:nnw}
% \begin{macro}[EXP]{\@@_convert_polar_auxvi:nnn}
% \begin{macro}[EXP]{\@@_convert_polar_auxvii:nnn}
% \begin{macro}[EXP]{\@@_convert_polar_auxviii:nn}
% A simplified parser for complex numbers which works by expansion,
% then converts to polar form.
% \begin{macrocode}
\cs_new:Npn \@@_convert_polar:n #1
{ \@@_convert_polar_auxi:w #1 e e \q_stop }
\cs_new:Npn \@@_convert_polar_auxi:w #1 e #2 e #3 \q_stop
{ \@@_convert_polar_auxii:nw {#2} #1 \q_stop }
\cs_new:Npn \@@_convert_polar_auxii:nw #1#2#3 \q_stop
{
\bool_lazy_or:nnTF
{ \str_if_eq_p:nn {#2} { i } }
{ \str_if_eq_p:nn {#2#3} { +i } }
{ \@@_convert_polar_auxvi:nnn { } { 1 } {#1} }
{
\str_if_eq:nnTF {#2#3} { -i }
{ \@@_convert_polar_auxvi:nnn { } { -1 } {#1} }
{ \@@_convert_polar_auxiii:nnw {#1} {#2} #3 + + \q_stop }
}
}
\cs_new:Npn \@@_convert_polar_auxiii:nnw #1#2#3 + #4 + #5 \q_stop
{
\tl_if_blank:nTF {#4}
{ \@@_convert_polar_auxiv:nnw {#1} {#2} #3 - - \q_stop }
{
\str_if_eq:nnTF {#4} { i }
{ \@@_convert_polar_auxvi:nnn {#2#3} { 1 } {#1} }
{ \@@_convert_polar_auxv:nnw {#2#3} {#1} #4 i \q_nil i \q_stop }
}
}
\cs_new:Npn \@@_convert_polar_auxiv:nnw #1#2#3 - #4 - #5 \q_stop
{
\tl_if_blank:nTF {#4}
{ \@@_convert_polar_auxv:nnw { } {#1} #2#3 i \q_nil i \q_stop }
{
\str_if_eq:nnTF {#4} { i }
{ \@@_convert_polar_auxvi:nnn { } { -1 } {#1} }
{ \@@_convert_polar_auxv:nnw {#2#3} {#1} -#4 i \q_nil i \q_stop }
}
}
\cs_new:Npn \@@_convert_polar_auxv:nnw #1#2#3 i #4 i #5 \q_stop
{
\quark_if_nil:nTF {#4}
{ { #3 \tl_if_blank:nF {#2} { e#2 } } { 0 } }
{ \@@_convert_polar_auxvi:nnn {#1} {#3} {#2} }
}
\cs_new:Npn \@@_convert_polar_auxvi:nnn #1#2#3
{
\exp_args:Neee \@@_convert_polar_auxvii:nnn
{ \tl_if_blank:nTF {#1} { 0 } {#1} }
{ \tl_if_blank:nTF {#2} { 0 } {#2} }
{ \tl_if_blank:nF {#3} { e#3 } }
}
\cs_new:Npn \@@_convert_polar_auxvii:nnn #1#2#3
{
\exp_args:Nee \@@_format_polar_auxviii:nn
{ \fp_eval:n { sqrt ( (#1#3)^2 + (#2#3)^2 ) } }
{
\fp_eval:n
{ atan \bool_if:NT \l_@@_polar_degree_bool { d } (#2 , #1) }
}
}
\cs_new:Npn \@@_format_polar_auxviii:nn #1#2 { {#1} {#2} }
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \subsection{Messages}
%
% \begin{macrocode}
\msg_new:nnnn { siunitx } { invalid-polar-form }
{ Invalid~polar~form~"#1:#2". }
{
Complex~numbers~in~polar~form~must~have~both~a~magnitude~and~and~
angle.
}
% \end{macrocode}
%
% \subsection{Standard settings for module options}
%
% Some of these follow naturally from the point of definition
% (\foreign{e.g.}~boolean variables are always |false| to begin with),
% but for clarity everything is set here.
% \begin{macrocode}
\keys_set:nn { siunitx }
{
complex-angle-unit = degrees ,
complex-mode = input ,
complex-root-position = after-number ,
complex-symbol-angle = \angle ,
complex-symbol-degree = \degree ,
input-complex-root = ij ,
output-complex-root = \mathrm { i } ,
print-complex-unity = false
}
% \end{macrocode}
%
% \begin{macrocode}
%</package>
% \end{macrocode}
%
% \end{implementation}
%
% \PrintIndex
|