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+% \iffalse meta-comment
+%
+% File: siunitx-number.dtx Copyright (C) 2014-2017 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}
+% 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-number} -- Parsing and formatting 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}
+%
+% \begin{function}{\siunitx_number_format:nN, \siunitx_number_format:VN}
+% \begin{syntax}
+% \cs{siunitx_number_format:nN} \Arg{number} \meta{tl~var}
+% \end{syntax}
+% \end{function}
+%
+% \begin{function}{\siunitx_number_format:nNN}
+% \begin{syntax}
+% \cs{siunitx_number_format:nNN} \Arg{number} \meta{tl~var} \meta{marker}
+% \end{syntax}
+% \end{function}
+%
+% \begin{function}[TF]{\siunitx_if_number:n}
+% \begin{syntax}
+% \cs{siunitx_if_number_token:NTF} \Arg{tokens}
+% \Arg{true code} \Arg{false code}
+% \end{syntax}
+% Determines if the \meta{tokens} form a valid number which can be fully
+% parsed by \pkg{siunitx}.
+% \end{function}
+%
+% \begin{function}[TF]{\siunitx_if_number_token:N}
+% \begin{syntax}
+% \cs{siunitx_if_number_token:NTF} \Arg{token}
+% \Arg{true code} \Arg{false code}
+% \end{syntax}
+% Determines if the \meta{token} is valid in a number based on those
+% tokens currently set up for detection in a number.
+% \end{function}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{siunitx-number} implementation}
+%
+% Start the \pkg{DocStrip} guards.
+% \begin{macrocode}
+%<*package>
+% \end{macrocode}
+%
+% Identify the internal prefix (\LaTeX3 \pkg{DocStrip} convention): only
+% internal material in this \emph{submodule} should be used directly.
+% \begin{macrocode}
+%<@@=siunitx_number>
+% \end{macrocode}
+%
+% \subsection{Initial set-up}
+%
+% Variants not provided by \pkg{expl3}.
+% \begin{macrocode}
+\cs_generate_variant:Nn \tl_if_blank:nTF { f }
+\cs_generate_variant:Nn \tl_if_blank_p:n { f }
+\cs_generate_variant:Nn \tl_if_in:NnTF { NV }
+% \end{macrocode}
+%
+% \begin{variable}{\l_@@_tmp_tl}
+% Scratch space.
+% \begin{macrocode}
+\tl_new:N \l_@@_tmp_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \subsection{Main formatting routine}
+%
+% \begin{variable}{\l_@@_formatted_tl}
+% A token list for the final formatted result: may or may not be generated
+% by the parser, depending on settings which are active.
+% \begin{macrocode}
+\tl_new:N \l_@@_formatted_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_tab_tl}
+% A token list for marking the position of tabular alignments in formatted
+% output.
+% \begin{macrocode}
+\tl_new:N \l_@@_tab_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\siunitx_number_format:nN, \siunitx_number_format:VN}
+% \begin{macro}{\siunitx_number_format:nNN}
+% \begin{macro}{\@@_format:nN}
+% \begin{macrocode}
+\cs_new_protected:Npn \siunitx_number_format:nN #1#2
+ {
+ \tl_clear:N \l_@@_tab_tl
+ \@@_format:nN {#1} #2
+ }
+\cs_generate_variant:Nn \siunitx_number_format:nN { V }
+\cs_new_protected:Npn \siunitx_number_format:nNN #1#2#3
+ {
+ \tl_set:Nn \l_@@_tab_tl {#3}
+ \@@_format:nN {#1} #2
+ }
+\cs_new_protected:Npn \@@_format:nN #1#2
+ {
+ \group_begin:
+ \@@_parse:n {#1}
+ \@@_format:
+ \exp_args:NNNV \group_end:
+ \tl_set:Nn #2 \l_@@_formatted_tl
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Parsing numbers}
+%
+% Before numbers can be manipulated or formatted they need to be parsed into
+% an internal form. In particular, if multiple code paths are to be avoided,
+% it is necessary to do such parsing even for relatively simple cases such
+% as converting |1e10| to |1 \times 10^{10}|.
+%
+% Storing the result of such parsing can be done in a number of ways. In the
+% first version of \pkg{siunitx} a series of separate data stores were used.
+% This is potentially quite fast (as recovery of items relies only on \TeX{}'s
+% hash table) but makes managing the various data entries somewhat tedious and
+% error-prone. For version two of the package, a single data structure
+% (property list) was used for each part of the parsed number. Whilst this is
+% easy to manage and extend, it is somewhat slower as at a \TeX{} level there
+% are repeated pack--unpack steps. In particular, the fact that there are a
+% limited number of items to track for a \enquote{number} means that a more
+% efficient approach is desirable (contrast parsing units, which is open-ended
+% and therefore fits well with using a property list).
+%
+% To allow for complex numbers, two parallel data structures are used, one for
+% the real part and one for the imaginary part. If the part is entirely absent
+% then the data structures are left empty. Within each part, the structure
+% is
+% \begin{quote}
+% \marg{comparator}\meta{sign}\marg{integer}\marg{decimal}
+% \marg{uncertainty}\\
+% \meta{exponent sign}\marg{exponent}
+% \end{quote}
+% where the two sign parts must be single tokens and all other components
+% must be given in braces. \emph{All} of the components must be present in
+% a stored number (\emph{i.e.}~at the end of parsing). The number must have
+% at least one digit for both the \meta{integer} and \meta{exponent} parts.
+%
+% \begin{variable}
+% {
+% \l_@@_expression_bool ,
+% \l_@@_input_uncert_close_tl ,
+% \l_@@_input_complex_tl ,
+% \l_@@_input_comparator_tl ,
+% \l_@@_input_decimal_tl ,
+% \l_@@_input_digit_tl ,
+% \l_@@_input_exponent_tl ,
+% \l_@@_input_ignore_tl ,
+% \l_@@_input_uncert_open_tl ,
+% \l_@@_input_sign_tl ,
+% \l_@@_input_uncert_sign_tl
+% }
+% \begin{macro}[EXP]{\@@_expression:n}
+% Options which determine the various valid parts of a parsed number.
+% \begin{macrocode}
+\keys_define:nn { siunitx }
+ {
+ evaluate-expression .bool_set:N =
+ \l_@@_expression_bool ,
+ expression .code:n =
+ \cs_set:Npn \@@_expression:n ##1 {#1} ,
+ input-close-uncertainty .tl_set:N =
+ \l_@@_input_uncert_close_tl ,
+ input-complex-roots .tl_set:N =
+ \l_@@_input_complex_tl ,
+ input-comparators .tl_set:N =
+ \l_@@_input_comparator_tl ,
+ input-decimal-markers .tl_set:N =
+ \l_@@_input_decimal_tl ,
+ input-digits .tl_set:N =
+ \l_@@_input_digit_tl ,
+ input-exponent-markers .tl_set:N =
+ \l_@@_input_exponent_tl ,
+ input-ignore .tl_set:N =
+ \l_@@_input_ignore_tl ,
+ input-open-uncertainty .tl_set:N =
+ \l_@@_input_uncert_open_tl ,
+ input-signs .tl_set:N =
+ \l_@@_input_sign_tl ,
+ input-uncertainty-signs .code:n =
+ {
+ \tl_set:Nn \l_@@_input_uncert_sign_tl {#1}
+ \tl_map_inline:nn {#1}
+ {
+ \tl_if_in:NnF \l_@@_input_sign_tl {##1}
+ { \tl_put_right:Nn \l_@@_input_sign_tl {##1} }
+ }
+ }
+ }
+\cs_new:Npn \@@_expression:n #1 { }
+% \end{macrocode}
+% \end{macro}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_arg_tl}
+% The input argument or a part thereof, depending on the position in
+% the parsing routine.
+% \begin{macrocode}
+\tl_new:N \l_@@_arg_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_@@_exponent_tl}
+% The exponent part of a parsed number. It is easiest to find this
+% relatively early in the parsing process, but as it needs to go at
+% the end of the internal format is held separately until required.
+% \begin{macrocode}
+\tl_new:N \l_@@_exponent_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_flex_tl}
+% When parsing for a separate uncertainty or complex number, the nature
+% of the grabbed part cannot be determined until the end of the number.
+% To avoid abusing the storage areas, this dedicated one is used for
+% \enquote{flexible} cases.
+% \begin{macrocode}
+\tl_new:N \l_@@_flex_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_imaginary_tl, \l_@@_real_tl}
+% Used to hold the real and imaginary parts of a number in the standardised
+% format.
+% \begin{macrocode}
+\tl_new:N \l_@@_imaginary_tl
+\tl_new:N \l_@@_real_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_@@_partial_tl}
+% To avoid needing to worry about the fact that the final data stores are
+% somewhat tricky to add to token-by-token, a simple store is used to build
+% up the parsed part of a number before transferring in one go.
+% \begin{macrocode}
+\tl_new:N \l_@@_partial_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_validate_bool}
+% Used to set up for validation with no error production.
+% \begin{macrocode}
+\bool_new:N \l_@@_validate_bool
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\@@_parse:n}
+% After some initial set up, the parser expands the input and then replaces
+% as far as possible tricky tokens with ones that can be handled using
+% delimited arguments. The parser begins with the assumption that the input
+% is a real number. To avoid multiple conditionals here, the parser is
+% set up as a chain of commands initially, with a loop only later. This
+% avoids more conditionals than are necessary.
+% \begin{macrocode}q
+\cs_new_protected:Npn \@@_parse:n #1
+ {
+ \tl_clear:N \l_@@_imaginary_tl
+ \tl_clear:N \l_@@_real_tl
+ \protected@edef \l_@@_arg_tl
+ {
+ \bool_if:NTF \l_@@_expression_bool
+ { \fp_eval:n { \@@_expression:n {#1} } }
+ {#1}
+ }
+ \tl_set_eq:NN \l_@@_input_tl \l_@@_arg_tl
+ \@@_parse_replace:
+ \tl_if_empty:NF \l_@@_arg_tl
+ { \@@_parse_comparator: }
+ \@@_parse_check:
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_check:}
+% After the loop there is one case that might need tidying up. If a
+% separated uncertainty was found it will be currently in \cs{l_@@_flex_tl}
+% and needs moving. A series of tests pick up that case, then the check is
+% made that some content was found for at least one of the real or imaginary
+% parts of the number.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_check:
+ {
+ \tl_if_empty:NF \l_@@_flex_tl
+ {
+ \bool_lazy_and:nnTF
+ {
+ \tl_if_blank_p:f
+ { \exp_after:wN \use_iv:nnnn \l_@@_real_tl }
+ }
+ {
+ \tl_if_blank_p:f
+ { \exp_after:wN \use_iv:nnnn \l_@@_flex_tl }
+ }
+ {
+ \tl_set:Nx \l_@@_tmp_tl
+ { \exp_after:wN \use_i:nnnn \l_@@_flex_tl }
+ \tl_if_in:NVTF \l_@@_input_uncert_sign_tl
+ \l_@@_tmp_tl
+ { \@@_parse_combine_uncert: }
+ { \tl_clear:N \l_@@_real_tl }
+ }
+ { \tl_clear:N \l_@@_real_tl }
+ }
+ \bool_lazy_and:nnTF
+ { \tl_if_empty_p:N \l_@@_real_tl }
+ { \tl_if_empty_p:N \l_@@_imaginary_tl }
+ {
+ \bool_if:NF \l_@@_validate_bool
+ {
+ \msg_error:nnx { siunitx } { number / invalid-input }
+ { \exp_not:V \l_@@_input_tl }
+ }
+ }
+ { \@@_parse_finalise: }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_combine_uncert:}
+% \begin{macro}{\@@_parse_combine_uncert_auxi:NnnnNnnn}
+% \begin{macro}
+% {
+% \@@_parse_combine_uncert_auxii:nnnnn,
+% \@@_parse_combine_uncert_auxii:fnnnn
+% }
+% \begin{macro}
+% {
+% \@@_parse_combine_uncert_auxiii:nnnnnn,
+% \@@_parse_combine_uncert_auxiii:fnnnnn
+% }
+% \begin{macro}{\@@_parse_combine_uncert_auxiv:nnnn}
+% \begin{macro}[EXP]{\@@_parse_combine_uncert_auxv:w}
+% \begin{macro}[EXP]{\@@_parse_combine_uncert_auxvi:w}
+% Conversion of a second numerical part to an uncertainty needs a bit of
+% work. The first step is to extract the useful information from the two
+% stores: the sign, integer and decimal parts from the real number and the
+% integer and decimal parts from the second number. That is done using the
+% input stack to avoid lots of assignments.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_combine_uncert:
+ {
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \@@_parse_combine_uncert_auxi:NnnnNnnn
+ \exp_after:wN \l_@@_real_tl \l_@@_flex_tl
+ }
+% \end{macrocode}
+% Here, |#4|, |#5| and |#8| are all junk arguments simply there to mop up
+% tokens, while |#1| will be recovered later from \cs{l_@@_real_tl} so does
+% not need to be passed about. The difference in places between the two
+% decimal parts is now found: this is done just once to avoid having to
+% parse token lists twice. The value is then used to generate a number of
+% filler |0| tokens, and these are added to the appropriate part of the
+% number. Finally, everything is recombined: the integer part only needs
+% a test to avoid an empty main number.
+% \begin{macrocode}
+\cs_new_protected:Npn
+ \@@_parse_combine_uncert_auxi:NnnnNnnn #1#2#3#4#5#6#7#8
+ {
+ \int_compare:nNnTF { \tl_count:n {#6} } > { \tl_count:n {#2} }
+ {
+ \tl_clear:N \l_@@_real_tl
+ \tl_clear:N \l_@@_flex_tl
+ }
+ {
+ \@@_parse_combine_uncert_auxii:fnnnn
+ { \int_eval:n { \tl_count:n {#3} - \tl_count:n {#7} } }
+ {#2} {#3} {#6} {#7}
+ }
+ }
+\cs_new_protected:Npn
+ \@@_parse_combine_uncert_auxii:nnnnn #1
+ {
+ \@@_parse_combine_uncert_auxiii:fnnnnn
+ { \prg_replicate:nn { \int_abs:n {#1} } { 0 } }
+ {#1}
+ }
+\cs_generate_variant:Nn \@@_parse_combine_uncert_auxii:nnnnn { f }
+\cs_new_protected:Npn
+ \@@_parse_combine_uncert_auxiii:nnnnnn #1#2#3#4#5#6
+ {
+ \int_compare:nNnTF {#2} > 0
+ {
+ \@@_parse_combine_uncert_auxiv:nnnn
+ {#3} {#4} {#5} { #6 #1 }
+ }
+ {
+ \@@_parse_combine_uncert_auxiv:nnnn
+ {#3} { #4 #1 } {#5} {#6}
+ }
+ }
+\cs_generate_variant:Nn
+ \@@_parse_combine_uncert_auxiii:nnnnnn { f }
+\cs_new_protected:Npn
+ \@@_parse_combine_uncert_auxiv:nnnn #1#2#3#4
+ {
+ \tl_set:Nx \l_@@_real_tl
+ {
+ \tl_head:V \l_@@_real_tl
+ { \exp_not:n {#1} }
+ {
+ \bool_lazy_and:nnTF
+ { \tl_if_blank_p:n {#2} }
+ { ! \tl_if_blank_p:n {#4} }
+ { 0 }
+ { \exp_not:n {#2} }
+ }
+ {
+ \@@_parse_combine_uncert_auxv:w #3#4
+ \q_recursion_tail \q_recursion_stop
+ }
+ }
+ }
+% \end{macrocode}
+% A short routine to remove any leading zeros in the uncertainty part,
+% which are not needed for the compact representation used by the module.
+% \begin{macrocode}
+\cs_new:Npn \@@_parse_combine_uncert_auxv:w #1
+ {
+ \quark_if_recursion_tail_stop:N #1
+ \str_if_eq:nnTF {#1} { 0 }
+ { \@@_parse_combine_uncert_auxv:w }
+ { \@@_parse_combine_uncert_auxvi:w #1 }
+ }
+\cs_new:Npn \@@_parse_combine_uncert_auxvi:w
+ #1 \q_recursion_tail \q_recursion_stop
+ { \exp_not:n {#1} }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_comparator:}
+% \begin{macro}{\@@_parse_comparator_aux:Nw}
+% A comparator has to be the very first token in the input. A such, the
+% test for this can be very fast: grab the first token, do a check and
+% if appropriate store the result.
+% \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_@@_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_aux:w}
+% \begin{macro}{\@@_parse_exponent_aux:nn}
+% \begin{macro}{\@@_parse_exponent_aux:Nw}
+% \begin{macro}{\@@_parse_exponent_aux:Nn}
+% \begin{macro}
+% {\@@_parse_exponent_zero_test:N, \@@_parse_exponent_check:N}
+% \begin{macro}{\@@_parse_exponent_cleanup:N}
+% An exponent part of a number has to come at the end and can only occur
+% once. Thus it is relatively easy to parse. First, there is a check that
+% an exponent part is allowed, and if so a split is made (the previous
+% part of the chain checks that there is some content in \cs{l_@@_arg_tl}
+% before calling this function). After splitting, if there is no exponent
+% then simply save a default. Otherwise, check for a sign and then store
+% either this or an assumed |+| and the digits after a check that nothing
+% else is present after the~|e|. The only slight complication to all of
+% this is allowing an arbitrary token in the input to represent the exponent:
+% this is done by setting any exponent tokens to the first of the allowed
+% list, then using that in a delimited argument set up. Once an exponent
+% part is found, there is a loop to check that each of the tokens is a digit
+% then a tidy up step to remove any leading zeros.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_exponent:
+ {
+ \tl_if_empty:NTF \l_@@_input_exponent_tl
+ { \tl_set:Nn \l_@@_exponent_tl { +0 } }
+ {
+ \tl_set:Nx \l_@@_tmp_tl
+ { \tl_head:V \l_@@_input_exponent_tl }
+ \tl_map_inline:Nn \l_@@_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_aux:w
+ ####1 \exp_not:V \l_@@_tmp_tl
+ ####2 \exp_not:V \l_@@_tmp_tl
+ ####3 \exp_not:N \q_stop
+ }
+ { \@@_parse_exponent_aux:nn {##1} {##2} }
+ \use:x
+ {
+ \@@_parse_exponent_aux: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_aux:w { }
+\cs_new_protected:Npn \@@_parse_exponent_aux:nn #1#2
+ {
+ \quark_if_nil:nTF {#2}
+ { \tl_set:Nn \l_@@_exponent_tl { +0 } }
+ {
+ \tl_set:Nn \l_@@_arg_tl {#1}
+ \tl_if_blank:nTF {#2}
+ { \tl_clear:N \l_@@_real_tl }
+ { \@@_parse_exponent_aux:Nw #2 \q_stop }
+ }
+ \tl_if_empty:NF \l_@@_real_tl
+ { \@@_parse_loop: }
+ }
+\cs_new_protected:Npn \@@_parse_exponent_aux:Nw #1#2 \q_stop
+ {
+ \tl_if_in:NnTF \l_@@_input_sign_tl {#1}
+ { \@@_parse_exponent_aux:Nn #1 {#2} }
+ { \@@_parse_exponent_aux:Nn + {#1#2} }
+ \tl_if_empty:NT \l_@@_exponent_tl
+ { \tl_clear:N \l_@@_real_tl }
+ }
+\cs_new_protected:Npn \@@_parse_exponent_aux:Nn #1#2
+ {
+ \tl_set:Nn \l_@@_exponent_tl { #1 }
+ \tl_if_blank:nTF {#2}
+ { \tl_clear:N \l_@@_real_tl }
+ {
+ \@@_parse_exponent_zero_test:N #2
+ \q_recursion_tail \q_recursion_stop
+ }
+ }
+\cs_new_protected:Npn \@@_parse_exponent_zero_test:N #1
+ {
+ \quark_if_recursion_tail_stop_do:Nn #1
+ { \tl_set:Nn \l_@@_exponent_tl { +0 } }
+ \str_if_eq:nnTF {#1} { 0 }
+ { \@@_parse_exponent_zero_test:N }
+ { \@@_parse_exponent_check:N #1 }
+ }
+\cs_new_protected:Npn \@@_parse_exponent_check:N #1
+ {
+ \quark_if_recursion_tail_stop:N #1
+ \tl_if_in:NnTF \l_@@_input_digit_tl {#1}
+ {
+ \tl_put_right:Nn \l_@@_exponent_tl {#1}
+ \@@_parse_exponent_check:N
+ }
+ { \@@_parse_exponent_cleanup:wN }
+ }
+\cs_new_protected:Npn \@@_parse_exponent_cleanup:wN
+ #1 \q_recursion_stop
+ { \tl_clear:N \l_@@_real_tl }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_replace:}
+% \begin{macro}{\@@_parse_replace_aux:nN}
+% \begin{macro}{\@@_parse_replace_sign:}
+% \begin{variable}{\c_@@_parse_sign_replacement_tl}
+% There are two parts to the replacement code. First, any active
+% hyphens signs are normalised: these can come up with some packages and
+% cause issues. Multi-token signs then are converted to the single token
+% equivalents so that everything else can work on a one token basis.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_replace:
+ {
+ \@@_parse_replace_minus:
+ \exp_last_unbraced:NV \@@_parse_replace_aux:nN
+ \c_@@_parse_sign_replacement_tl
+ { ? } \q_recursion_tail
+ \q_recursion_stop
+ }
+\cs_set_protected:Npn \@@_parse_replace_aux:nN #1#2
+ {
+ \quark_if_recursion_tail_stop:N #2
+ \tl_replace_all:Nnn \l_@@_arg_tl {#1} {#2}
+ \@@_parse_replace_aux:nN
+ }
+\tl_const:Nn \c_@@_parse_sign_replacement_tl
+ {
+ { -+ } \mp
+ { +- } \pm
+ { << } \ll
+ { <= } \le
+ { >> } \gg
+ { >= } \ge
+ }
+\group_begin:
+ \char_set_catcode_active:N \-
+ \cs_new_protected:Npx \@@_parse_replace_minus:
+ {
+ \tl_replace_all:Nnn \exp_not:N \l_@@_arg_tl
+ { \exp_not:N - } { \token_to_str:N - }
+ }
+\group_end:
+% \end{macrocode}
+% \end{variable}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_finalise:}
+% \begin{macro}{\@@_parse_finalise_aux:N}
+% \begin{macro}{\@@_parse_finalise_aux:Nw}
+% Combine all of the bits of a number together: both the real and
+% imaginary parts contain all of the data.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_finalise:
+ {
+ \@@_parse_finalise_aux:N \l_@@_real_tl
+ \@@_parse_finalise_aux:N \l_@@_imaginary_tl
+ }
+\cs_new_protected:Npn \@@_parse_finalise_aux:N #1
+ {
+ \tl_if_empty:NF #1
+ {
+ \tl_set:Nx #1
+ {
+ { \exp_not:V \l_@@_comparator_tl }
+ \exp_not:V #1
+ \exp_after:wN \@@_parse_finalise_aux:Nw
+ \l_@@_exponent_tl \q_stop
+ }
+ }
+ }
+\cs_new:Npn \@@_parse_finalise_aux:Nw #1#2 \q_stop
+ {
+ \exp_not:N #1
+ { \exp_not:n {#2} }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_parse_loop:}
+% \begin{macro}{\@@_parse_loop_first:N}
+% \begin{macro}{\@@_parse_loop_main:NNNNN}
+% \begin{macro}{\@@_parse_loop_main_end:NN}
+% \begin{macro}{\@@_parse_loop_main_digit:NNNNN}
+% \begin{macro}{\@@_parse_loop_main_decimal:NN}
+% \begin{macro}{\@@_parse_loop_main_uncert:NNN}
+% \begin{macro}{\@@_parse_loop_main_complex:N}
+% \begin{macro}{\@@_parse_loop_main_sign:NNN}
+% \begin{macro}{\@@_parse_loop_main_store:NNN}
+% \begin{macro}{\@@_parse_loop_after_decimal:NNN}
+% \begin{macro}{\@@_parse_loop_uncert:NNNNN}
+% \begin{macro}{\@@_parse_loop_after_uncert:NNN}
+% \begin{macro}{\@@_parse_loop_root_swap:NNwNN}
+% \begin{macro}{\@@_parse_loop_complex_cleanup:wN}
+% \begin{macro}{\@@_parse_loop_break:wN}
+% At this stage, the partial input \cs{l_@@_arg_tl} will contain any
+% mantissa, which may contain an uncertainty or complex part. Parsing this
+% and allowing for all of the different formats possible is best done using
+% a token-by-token approach. However, as at each stage only a subset of
+% tokens are valid, the approach take is to use a set of semi-dedicated
+% functions to parse different components along with switches to allow a
+% sensible amount of code sharing.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop:
+ {
+ \tl_clear:N \l_@@_partial_tl
+ \exp_after:wN \@@_parse_loop_first:NNN
+ \exp_after:wN \l_@@_real_tl \exp_after:wN \c_true_bool
+ \l_@@_arg_tl
+ \q_recursion_tail \q_recursion_stop
+ }
+% \end{macrocode}
+% The very first token of the input is handled with a dedicated function.
+% Valid cases here are
+% \begin{itemize}
+% \item Entirely blank if the original input was for example |+e10|:
+% simply clean up if in the integer part of issue an error if in
+% a second part (complex number, \emph{etc.}).
+% \item An integer part digit: pass through to the main collection
+% routine.
+% \item A decimal marker: store an empty integer part and move to
+% the main collection routine for a decimal part.
+% \item A complex root token: shuffle to the end of the input.
+% \end{itemize}
+% Anything else is invalid and sends the code to the abort function.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_first:NNN #1#2#3
+ {
+ \quark_if_recursion_tail_stop_do:Nn #3
+ {
+ \bool_if:NTF #2
+ { \tl_put_right:Nn #1 { { 1 } { } { } } }
+ { \@@_parse_loop_break:wN \q_recursion_stop }
+ }
+ \tl_if_in:NnTF \l_@@_input_digit_tl {#3}
+ {
+ \@@_parse_loop_main:NNNNN
+ #1 \c_true_bool \c_false_bool #2 #3
+ }
+ {
+ \tl_if_in:NnTF \l_@@_input_decimal_tl {#3}
+ {
+ \tl_put_right:Nn #1 { { 0 } }
+ \@@_parse_loop_after_decimal:NNN #1 #2
+ }
+ {
+ \tl_if_in:NnTF \l_@@_input_complex_tl {#3}
+ { \@@_parse_loop_root_swap:NNwNN #1 #3 }
+ { \@@_parse_loop_break:wN }
+ }
+ }
+ }
+% \end{macrocode}
+% A single function is used to cover the \enquote{main} part of numbers:
+% finding real, complex or separated uncertainty parts and covering both
+% the integer and decimal components. This works because these elements
+% share a lot of concepts: a small number of switches can be used to
+% differentiate between them. To keep the code at least somewhat readable,
+% this main function deals with the validity testing but hands off other
+% tasks to dedicated auxiliaries for each case.
+%
+% The possibilities are
+% \begin{itemize}
+% \item The number terminates, meaning that some digits were collected
+% and everything is simply tidied up (as far as the loop is concerned).
+% \item A digit is found: this is the common case and leads to a storage
+% auxiliary (which handles non-significant zeros).
+% \item A decimal marker is found: only valid in the integer part and
+% there leading to a store-and-switch situation.
+% \item An open-uncertainty token: switch to the dedicated collector
+% for uncertainties.
+% \item A complex root token: store the current number as an imaginary
+% part and terminate the loop.
+% \item A sign token (if allowed): stop collecting this number and
+% restart collection for the second part.
+% \end{itemize}
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main:NNNNN #1#2#3#4#5
+ {
+ \quark_if_recursion_tail_stop_do:Nn #5
+ { \@@_parse_loop_main_end:NN #1#2 }
+ \tl_if_in:NnTF \l_@@_input_digit_tl {#5}
+ { \@@_parse_loop_main_digit:NNNNN #1#2#3#4#5 }
+ {
+ \tl_if_in:NnTF \l_@@_input_decimal_tl {#5}
+ {
+ \bool_if:NTF #2
+ { \@@_parse_loop_main_decimal:NN #1 #4 }
+ { \@@_parse_loop_break:wN }
+ }
+ {
+ \tl_if_in:NnTF \l_@@_input_uncert_open_tl {#5}
+ { \@@_parse_loop_main_uncert:NNN #1#2 #4 }
+ {
+ \tl_if_in:NnTF \l_@@_input_complex_tl {#5}
+ {
+ \@@_parse_loop_main_store:NNN
+ #1 #2 \c_true_bool
+ \@@_parse_loop_main_complex:N #1
+ }
+ {
+ \bool_if:NTF #4
+ {
+ \tl_if_in:NnTF \l_@@_input_sign_tl {#5}
+ {
+ \@@_parse_loop_main_sign:NNN
+ #1#2 #5
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ }
+ }
+ }
+ }
+% \end{macrocode}
+% If the main loop finds the end marker then there is a tidy up phase.
+% The current partial number is stored either as the integer or decimal,
+% depending on the setting for the indicator switch. For the integer
+% part, if no number has been collected then one or more non-significant
+% zeros have been dropped. Exactly one zero is therefore needed to make
+% sure the parsed result is correct.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_end:NN #1#2
+ {
+ \bool_lazy_and:nnT
+ {#2} { \tl_if_empty_p:N \l_@@_partial_tl }
+ { \tl_set:Nn \l_@@_partial_tl { 0 } }
+ \tl_put_right:Nx #1
+ {
+ { \exp_not:V \l_@@_partial_tl }
+ \bool_if:NT #2 { { } }
+ { }
+ }
+ }
+% \end{macrocode}
+% The most common case for the main loop collector is to find a digit.
+% Here, in the integer part it is possible that zeros are non-significant:
+% that is handled using a combination of a switch and a string test. Other
+% than that, the situation here is simple: store the input and loop.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_digit:NNNNN #1#2#3#4#5
+ {
+ \bool_lazy_or:nnTF
+ {#3} { ! \str_if_eq_p:nn {#5} { 0 } }
+ {
+ \tl_put_right:Nn \l_@@_partial_tl {#5}
+ \@@_parse_loop_main:NNNNN #1 #2 \c_true_bool #4
+ }
+ { \@@_parse_loop_main:NNNNN #1 #2 \c_false_bool #4 }
+ }
+% \end{macrocode}
+% When a decimal marker was found, move the integer part to the
+% store and then go back to the loop with the flags set correctly.
+% There is the case of non-significant zeros to cover before that, of course.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_decimal:NN #1#2
+ {
+ \@@_parse_loop_main_store:NNN #1 \c_false_bool \c_false_bool
+ \@@_parse_loop_after_decimal:NNN #1 #2
+ }
+% \end{macrocode}
+% Starting an uncertainty part means storing the number to date as in other
+% cases, with the possibility of a blank decimal part allowed for. The
+% uncertainty itself is collected by a dedicated function as it is extremely
+% restricted.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_uncert:NNN #1#2#3
+ {
+ \@@_parse_loop_main_store:NNN #1 #2 \c_false_bool
+ \@@_parse_loop_uncert:NNNNN
+ #1 \c_true_bool \c_false_bool #3
+ }
+% \end{macrocode}
+% A complex root token has to be at the end of the input (leading ones
+% are dealt with specially). Thus after moving the data to the correct
+% place there is a hand-off to a cleanup function. The case where only the
+% complex root token was given is covered by
+% \cs{@@_parse_loop_root_swap:NNwNN}.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_complex:N #1
+ {
+ \tl_set_eq:NN \l_@@_imaginary_tl #1
+ \tl_clear:N #1
+ \@@_parse_loop_complex_cleanup:wN
+ }
+% \end{macrocode}
+% If a sign is found, terminate the current number, store the sign as the
+% first token of the second part and go back to do the dedicated first-token
+% function.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_sign:NNN #1#2#3
+ {
+ \@@_parse_loop_main_store:NNN #1 #2 \c_true_bool
+ \tl_set:Nn \l_@@_flex_tl {#3}
+ \@@_parse_loop_first:NNN
+ \l_@@_flex_tl \c_false_bool
+ }
+% \end{macrocode}
+% A common auxiliary for the various non-digit token functions: tidy up the
+% integer and decimal parts of a number. Here, the two flags are used to
+% indicate if empty decimal and uncertainty parts should be included in
+% the storage cycle.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_main_store:NNN #1#2#3
+ {
+ \tl_if_empty:NT \l_@@_partial_tl
+ { \tl_set:Nn \l_@@_partial_tl { 0 } }
+ \tl_put_right:Nx #1
+ {
+ { \exp_not:V \l_@@_partial_tl }
+ \bool_if:NT #2 { { } }
+ \bool_if:NT #3 { { } }
+ }
+ \tl_clear:N \l_@@_partial_tl
+ }
+% \end{macrocode}
+% After a decimal marker there has to be a digit if there wasn't one before
+% it. That is handled by using a dedicated function, which checks for
+% an empty integer part first then either simply hands off or looks for
+% a digit.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_after_decimal:NNN #1#2#3
+ {
+ \tl_if_blank:fTF { \exp_after:wN \use_none:n #1 }
+ {
+ \quark_if_recursion_tail_stop_do:Nn #3
+ { \@@_parse_loop_break:wN \q_recursion_stop }
+ \tl_if_in:NnTF \l_@@_input_digit_tl {#1}
+ {
+ \tl_put_right:Nn \l_@@_partial_tl {#3}
+ \@@_parse_loop_main:NNNNN
+ #1 \c_false_bool \c_true_bool #2
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ {
+ \@@_parse_loop_main:NNNNN
+ #1 \c_false_bool \c_true_bool #2 #3
+ }
+ }
+% \end{macrocode}
+% Inside the brackets for an uncertainty the range of valid choices is
+% very limited. Either the token is a digit, in which case there is a
+% test to look for non-significant zeros, or it is a closing bracket. The
+% latter is not valid for the very first token, which is handled using a
+% switch (it's a simple enough difference).
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_uncert:NNNNN #1#2#3#4#5
+ {
+ \quark_if_recursion_tail_stop_do:Nn #5
+ { \@@_parse_loop_break:wN \q_recursion_stop }
+ \tl_if_in:NnTF \l_@@_input_digit_tl {#5}
+ {
+ \bool_lazy_or:nnTF
+ {#3} { ! \str_if_eq_p:nn {#5} { 0 } }
+ {
+ \tl_put_right:Nn \l_@@_partial_tl {#5}
+ \@@_parse_loop_uncert:NNNNN
+ #1 \c_false_bool \c_true_bool #4
+ }
+ {
+ \@@_parse_loop_uncert:NNNNN
+ #1 \c_false_bool \c_false_bool #4
+ }
+ }
+ {
+ \tl_if_in:NnTF \l_@@_input_uncert_close_tl {#5}
+ {
+ \bool_if:NTF #2
+ { \@@_parse_loop_break:wN }
+ {
+ \@@_parse_loop_main_store:NNN #1
+ \c_false_bool \c_false_bool
+ \@@_parse_loop_after_uncert:NNN #1 #3
+ }
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ }
+% \end{macrocode}
+% After a bracketed uncertainty there are only a very small number of
+% valid choices. The number can end, there can be a complex root token
+% or there can be a sign. The latter is only allowed if the part being
+% parsed at the moment was the first part of the number. The case where
+% there is no root symbol but there should have been is cleared up after
+% the loop code, so at this stage there is no check.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_after_uncert:NNN #1#2#3
+ {
+ \quark_if_recursion_tail_stop:N #3
+ \tl_if_in:NnTF \l_@@_input_complex_tl {#3}
+ { \@@_parse_loop_main_complex:N #1 }
+ {
+ \bool_if:NTF #2
+ {
+ \tl_if_in:NnTF \l_@@_input_sign_tl {#3}
+ {
+ \tl_set:Nn \l_@@_flex_tl {#3}
+ \@@_parse_loop_first:NNN
+ \l_@@_flex_tl \c_false_bool
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ { \@@_parse_loop_break:wN }
+ }
+ }
+% \end{macrocode}
+% When the complex root symbol comes at the start of the number rather than
+% at the end, the easiest approach is to shuffle it to the \enquote{normal}
+% position. As the exponent has already been removed, this must be the last
+% token of the input and any duplication will be picked up. The case where
+% just a complex root token has to be covered: in that situation, there is
+% an implicit |1| to store after which the loop stops.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_root_swap:NNwNN #1#2#3
+ \q_recursion_tail \q_recursion_stop
+ {
+ \tl_if_blank:nTF {#3}
+ {
+ \tl_set:Nx \l_@@_imaginary_tl
+ {
+ \exp_not:V #1
+ { 1 } { } { }
+ }
+ \tl_clear:N #1
+ }
+ {
+ \use:x
+ {
+ \tl_clear:N \exp_not:N #1
+ \tl_set:Nn \exp_not:N \l_@@_flex_tl { \exp_not:V #1 }
+ }
+ \@@_parse_loop_first:NNN
+ \l_@@_flex_tl \c_false_bool
+ #3 #2 \q_recursion_tail \q_recursion_stop
+ }
+ }
+% \end{macrocode}
+% Nothing is allowed after a complex root token: check and if there is
+% kill the parsing.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_complex_cleanup:wN
+ #1 \q_recursion_tail \q_recursion_stop
+ {
+ \tl_if_blank:nF {#1}
+ { \@@_parse_loop_break:wN \q_recursion_stop }
+ }
+% \end{macrocode}
+% Something is not right: remove all of the remaining tokens from the
+% number and clear the storage areas as a signal for the next part of the
+% code.
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_parse_loop_break:wN
+ #1 \q_recursion_stop
+ {
+ \tl_clear:N \l_@@_imaginary_tl
+ \tl_clear:N \l_@@_flex_tl
+ \tl_clear:N \l_@@_real_tl
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \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; if there is no sign then the internal
+% format requires that |+| is used. For the number to be valid it has to be
+% more than just a sign, so the next part of the chain is only called if that
+% is the case.
+% \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:NnTF \l_@@_input_sign_tl {#1}
+ {
+ \tl_set:Nn \l_@@_arg_tl {#2}
+ \tl_set:Nn \l_@@_real_tl {#1}
+ }
+ { \tl_set:Nn \l_@@_real_tl { + } }
+ \tl_if_empty:NTF \l_@@_arg_tl
+ { \tl_clear:N \l_@@_real_tl }
+ { \@@_parse_exponent: }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Processing numbers}
+%
+% \begin{variable}
+% {
+% \l_@@_round_half_up_bool ,
+% \l_@@_round_min_tl ,
+% \l_@@_round_mode_tl ,
+% \l_@@_round_precision_int
+% }
+% \begin{macrocode}
+\keys_define:nn { siunitx }
+ {
+ round-half .choice: ,
+ round-half / even .code:n =
+ { \bool_set_false:N \l_@@_round_half_up_bool } ,
+ round-half / up .code:n =
+ { \bool_set_true:N \l_@@_round_half_up_bool } ,
+ round-minimum .tl_set:N =
+ \l_@@_round_min_tl ,
+ round-mode .choice: ,
+ round-mode / figures .code:n =
+ { \tl_set:Nn \_@@_round_mode_tl { figures } } ,
+ round-mode / none .code:n =
+ { \tl_set:Nn \_@@_round_mode_tl { none } } ,
+ round-mode / places .code:n =
+ { \tl_set:Nn \_@@_round_mode_tl { places } } ,
+ round-mode / uncertainty .code:n =
+ { \tl_set:Nn \_@@_round_mode_tl { uncertainty } } ,
+ round-precision .int_set:N =
+ \l_@@_round_precision_int ,
+ }
+\bool_new:N \l_@@_round_half_up_bool
+\tl_new:N \_@@_round_mode_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\@@_round:}
+% \begin{macro}{\@@_round:N}
+% \begin{macro}{\@@_round_none:nNnnnNn}
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_round:
+ {
+ \@@_round:N \l_@@_real_tl
+ \@@_round:N \l_@@_imaginary_tl
+ }
+\cs_new_protected:Npn \@@_round:N #1
+ {
+ \tl_if_empty:NF #1
+ {
+ \tl_set:Nx #1
+ {
+ \cs:w
+ @@_round_ \_@@_round_mode_tl :nNnnnNn
+ \exp_after:wN
+ \cs_end: #1
+ }
+ }
+ }
+\cs_new:Npn \@@_round_none:nNnnnNn #1#2#3#4#5#6#7
+ { \exp_not:n { {#1} #2 {#3} {#4} {#5} #6 {#7} } }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_round_figures:nNnnnNn}
+% \begin{macrocode}
+\cs_new:Npn \@@_round_figures:nNnnnNn #1#2#3#4#5#6#7
+ {
+ \tl_if_blank:nTF {#5}
+ {
+ \int_compare:nNnTF \l_@@_round_precision_int > 0
+ { }
+ { { } + { 0 } { } { } + { 0 } }
+ }
+ { \exp_not:n { {#1} #2 {#3} {#4} {#5} #6 {#7} } }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_round_places:nNnnnNn}
+% \begin{macro}[EXP]
+% {\@@_round_places_decimal:nNnnNn, \@@_round_places_integer:nNnnNn}
+% The first step when rounding to a fixed number of places is to establish
+% if this is in the decimal or integer parts. The two require different
+% calculations for how many digits to drop from the input.
+% \begin{macrocode}
+\cs_new:Npn \@@_round_places:nNnnnNn #1#2#3#4#5#6#7
+ {
+ \tl_if_blank:nTF {#5}
+ {
+ \int_compare:nNnTF \l_@@_round_precision_int > 0
+ { \@@_round_places_decimal:nNnnNn }
+ { \@@_round_places_integer:nNnnNn }
+ {#1} #2 {#3} {#4} #6 {#7}
+ }
+ { \exp_not:n { {#1} #2 {#3} {#4} {#5} #6 {#7} } }
+ }
+\cs_new:Npn \@@_round_places_decimal:nNnnNn #1#2#3#4#5#6
+ { }
+\cs_new:Npn \@@_round_places_integer:nNnnNn #1#2#3#4#5#6
+ { }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_round_uncertainty:nNnnnNn}
+% \begin{macrocode}
+\cs_new:Npn \@@_round_uncertainty:nNnnnNn #1#2#3#4#5#6#7
+ {
+ \tl_if_blank:nTF {#5}
+ { \exp_not:n { {#1} #2 {#3} {#4} { } #6 {#7} } }
+ { }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Formatting parsed numbers}
+%
+% \begin{variable}
+% {
+% \l_@@_bracket_negative_bool ,
+% \l_@@_bracket_close_tl ,
+% \l_@@_explicit_plus_bool ,
+% \l_@@_exponent_base_tl ,
+% \l_@@_exponent_product_tl ,
+% \l_@@_group_decimal_bool ,
+% \l_@@_group_integer_bool ,
+% \l_@@_group_minimum_int ,
+% \l_@@_group_separator_tl ,
+% \l_@@_negative_color_tl ,
+% \l_@@_bracket_open_tl ,
+% \l_@@_output_uncert_close_tl ,
+% \l_@@_output_complex_tl ,
+% \l_@@_output_decimal_tl ,
+% \l_@@_output_uncert_open_tl ,
+% \l_@@_uncert_separate_bool ,
+% \l_@@_tight_bool ,
+% \l_@@_unity_mantissa_bool ,
+% \l_@@_zero_exponent_bool
+% }
+% Keys producing tokens in the output.
+% \begin{macrocode}
+\keys_define:nn { siunitx }
+ {
+ bracket-negative .bool_set:N =
+ \l_@@_bracket_negative_bool ,
+ explicit-plus .bool_set:N =
+ \l_@@_explicit_plus_bool ,
+ exponent-base .tl_set:N =
+ \l_@@_exponent_base_tl ,
+ exponent-product .tl_set:N =
+ \l_@@_exponent_product_tl ,
+ group-digits .choice: ,
+ group-digits / all .code:n =
+ {
+ \bool_set_true:N \l_@@_group_decimal_bool
+ \bool_set_true:N \l_@@_group_integer_bool
+ } ,
+ group-digits / decimal .code:n =
+ {
+ \bool_set_true:N \l_@@_group_decimal_bool
+ \bool_set_false:N \l_@@_group_integer_bool
+ } ,
+ group-digits / integer .code:n =
+ {
+ \bool_set_false:N \l_@@_group_decimal_bool
+ \bool_set_true:N \l_@@_group_integer_bool
+ } ,
+ group-digits / none .code:n =
+ {
+ \bool_set_false:N \l_@@_group_decimal_bool
+ \bool_set_false:N \l_@@_group_integer_bool
+ } ,
+ group-digits .default:n = all ,
+ group-minimum-digits .int_set:N =
+ \l_@@_group_minimum_int ,
+ group-separator .tl_set:N =
+ \l_@@_group_separator_tl ,
+ negative-color .tl_set:N =
+ \l_@@_negative_color_tl ,
+ number-close-bracket .tl_set:N =
+ \l_@@_bracket_close_tl ,
+ number-open-bracket .tl_set:N =
+ \l_@@_bracket_open_tl ,
+ output-close-uncertainty .tl_set:N =
+ \l_@@_output_uncert_close_tl ,
+ output-complex-root .tl_set:N =
+ \l_@@_output_complex_tl ,
+ output-decimal-marker .tl_set:N =
+ \l_@@_output_decimal_tl ,
+ output-open-uncertainty .tl_set:N =
+ \l_@@_output_uncert_open_tl ,
+ separate-uncertainty .bool_set:N =
+ \l_@@_uncert_separate_bool ,
+ tight-spacing .bool_set:N =
+ \l_@@_tight_bool ,
+ unity-mantissa .bool_set:N =
+ \l_@@_unity_mantissa_bool ,
+ zero-exponent .bool_set:N =
+ \l_@@_zero_exponent_bool ,
+ }
+\bool_new:N \l_@@_group_decimal_bool
+\bool_new:N \l_@@_group_integer_bool
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\@@_format:}
+% \begin{macrocode}
+\cs_new_protected:Npn \@@_format:
+ {
+ \tl_set:Nx \l_@@_formatted_tl
+ {
+ \tl_if_empty:NTF \l_@@_real_tl
+ {
+ \tl_if_empty:NF \l_@@_imaginary_tl
+ { \@@_format:N \l_@@_imaginary_tl }
+ }
+ {
+ \tl_if_empty:NTF \l_@@_imaginary_tl
+ { \@@_format:N \l_@@_real_tl }
+ { ??? }
+ }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format:N}
+% \begin{macro}[EXP]{\@@_format:nNnnnNn}
+% \begin{macro}[EXP]{\@@_format_comparator:n}
+% \begin{macro}[EXP]{\@@_format_sign:N, \@@_format_sign_aux:N}
+% \begin{macro}[EXP]
+% {\@@_format_sign_color:w, \@@_format_sign_brackets:w}
+% \begin{macro}[EXP]{\@@_format_integer:nnn}
+% \begin{macro}[EXP]{\@@_format_decimal:n, \@@_format_decimal:f}
+% \begin{macro}[EXP]{\@@_format_digits:nn}
+% \begin{macro}[EXP]{\@@_format_integer_aux:n}
+% \begin{macro}[EXP]
+% {
+% \@@_format_integer_aux_0:n,
+% \@@_format_integer_aux_1:n,
+% \@@_format_integer_aux_2:n
+% }
+% \begin{macro}[EXP]{\@@_format_decimal_aux:n}
+% \begin{macro}[EXP]{\@@_format_decimal_loop:NNNN}
+% \begin{macro}[EXP]{\@@_format_integer_first:nnNN}
+% \begin{macro}[EXP]{\@@_format_integer_loop:NNNN}
+% \begin{macro}[EXP]{\@@_format_uncertainty:nn}
+% \begin{macro}[EXP]{\@@_format_uncertainty_unaligned:}
+% \begin{macro}[EXP]
+% {\@@_format_uncertainty_aux:nn, \@@_format_uncertainty_aux:fn}
+% \begin{macro}[EXP]
+% {\@@_format_uncertainty:nnw, \@@_format_uncertainty:fnw}
+% \begin{macro}[EXP]{\@@_format_uncertainty:nw}
+% \begin{macro}[EXP]{\@@_format_exponent:Nnn}
+% \begin{macro}[EXP]{\@@_format_end:}
+% The approach to formatting a single number is to split into
+% the constituent parts. All of the parts are assembled including
+% inserting tabular alignment markers (which may be empty) for each
+% separate unit.
+% \begin{macrocode}
+\cs_new:Npn \@@_format:N #1
+ { \exp_after:wN \@@_format:nNnnnNn #1 }
+\cs_new:Npn \@@_format:nNnnnNn #1#2#3#4#5#6#7
+ {
+ \@@_format_comparator:n {#1}
+ \@@_format_sign:N #2
+ \@@_format_integer:nnn {#3} {#4} {#7}
+ \@@_format_decimal:n {#4}
+ \@@_format_uncertainty:nn {#5} {#4}
+ \@@_format_exponent:Nnn #6 {#7} { #3 . #4 }
+ \@@_format_end:
+ }
+% \end{macrocode}
+% To get the spacing correct this needs to be an ordinary math character.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_comparator:n #1
+ {
+ \tl_if_blank:nF {#1}
+ { \exp_not:n { \mathord {#1} } }
+ \exp_not:V \l_@@_tab_tl
+ }
+% \end{macrocode}
+% Formatting signs has to deal with some additional formatting requirements
+% for negative numbers. Both making such numbers a fixed color and bracketing
+% them needs some rearrangement of the order of tokens, which is set up in
+% the main formatting macro by the dedicated do-nothing end function.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_sign:N #1
+ {
+ \str_if_eq:nnTF {#1} { + }
+ {
+ \bool_if:NT \l_@@_explicit_plus_bool
+ { \@@_format_sign_aux:N #1 }
+ }
+ {
+ \str_if_eq:nnTF {#1} { - }
+ {
+ \tl_if_empty:NF \l_@@_negative_color_tl
+ { \@@_format_sign_color:w }
+ \bool_if:NTF \l_@@_bracket_negative_bool
+ { \@@_format_sign_brackets:w }
+ { \@@_format_sign_aux:N #1 }
+ }
+ { \@@_format_sign_aux:N #1 }
+ }
+ }
+\cs_new:Npn \@@_format_sign_aux:N #1
+ {
+ \bool_if:NTF \l_@@_tight_bool
+ { \exp_not:n { \mathord {#1} } }
+ { \exp_not:n {#1} }
+ }
+\cs_new:Npn
+ \@@_format_sign_color:w #1 \@@_format_end:
+ {
+ \exp_not:N \textcolor { \exp_not:V \l_@@_negative_color_tl }
+ {
+ #1
+ \@@_format_end:
+ }
+ }
+\cs_new:Npn
+ \@@_format_sign_brackets:w #1 \@@_format_end:
+ {
+ \exp_not:V \l_@@_bracket_open_tl
+ #1
+ \exp_not:V \l_@@_bracket_close_tl
+ \@@_format_end:
+ }
+% \end{macrocode}
+% Digit formatting leads off with separate functions to allow for a few
+% \enquote{up front} items before using a common set of tests for some common
+% cases. The code then splits again as the two types of grouping need
+% different strategies.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_integer:nnn #1#2#3
+ {
+ \bool_lazy_all:nF
+ {
+ { \str_if_eq_p:nn {#1} { 1 } }
+ { \tl_if_blank_p:n {#2} }
+ { ! \str_if_eq_p:nn {#3} { 0 } }
+ { ! \l_@@_unity_mantissa_bool }
+ }
+ { \@@_format_digits:nn { integer } {#1} }
+ }
+\cs_new:Npn \@@_format_decimal:n #1
+ {
+ \exp_not:V \l_@@_tab_tl
+ \tl_if_blank:nF {#1}
+ { \exp_not:V \l_@@_output_decimal_tl }
+ \exp_not:V \l_@@_tab_tl
+ \@@_format_digits:nn { decimal } {#1}
+ }
+\cs_generate_variant:Nn \@@_format_decimal:n { f }
+\cs_new:Npn \@@_format_digits:nn #1#2
+ {
+ \bool_if:cTF { l_@@_group_ #1 _ bool }
+ {
+ \int_compare:nNnTF
+ { \tl_count:n {#2} } < \l_@@_group_minimum_int
+ { \exp_not:n {#2} }
+ { \use:c { @@_format_ #1 _aux:n } {#2} }
+ }
+ { \exp_not:n {#2} }
+ }
+% \end{macrocode}
+% For integers, we need to know how many digits there are to allow for the
+% correct insertion of separators. That is done using a two-part set up such
+% that there is no separator on the first pass.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_integer_aux:n #1
+ {
+ \use:c
+ {
+ @@_format_integer_aux_
+ \int_eval:n { \int_mod:nn { \tl_count:n {#1} } { 3 } }
+ :n
+ } {#1}
+ }
+\cs_new:cpn { @@_format_integer_aux_0:n } #1
+ { \@@_format_integer_first:nnNN #1 \q_nil }
+\cs_new:cpn { @@_format_integer_aux_1:n } #1
+ { \@@_format_integer_first:nnNN { } { } #1 \q_nil }
+\cs_new:cpn { @@_format_integer_aux_2:n } #1
+ { \@@_format_integer_first:nnNN { } #1 \q_nil }
+\cs_new:Npn \@@_format_integer_first:nnNN #1#2#3#4
+ {
+ \exp_not:n {#1#2#3}
+ \quark_if_nil:NF #4
+ { \@@_format_integer_loop:NNNN #4 }
+ }
+\cs_new:Npn \@@_format_integer_loop:NNNN #1#2#3#4
+ {
+ \exp_not:V \l_@@_group_separator_tl
+ \exp_not:n {#1#2#3}
+ \quark_if_nil:NF #4
+ { \@@_format_integer_loop:NNNN #4 }
+ }
+% \end{macrocode}
+% For decimals, no need to do any counting, just loop using enough markers to
+% find the end of the list. By passing the decimal marker, it is possible not
+% to have to use a check on the content of the rest of the number. The
+% |\use_none:n(n)| mop up the remaining |\q_nil| tokens.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_decimal_aux:n #1
+ {
+ \@@_format_decimal_loop:NNNN \c_empty_tl
+ #1 \q_nil \q_nil \q_nil
+ }
+\cs_new:Npn \@@_format_decimal_loop:NNNN #1#2#3#4
+ {
+ \quark_if_nil:NF #2
+ {
+ \exp_not:V #1
+ \exp_not:n {#2}
+ \quark_if_nil:NTF #3
+ { \use_none:n }
+ {
+ \exp_not:n {#3}
+ \quark_if_nil:NTF #4
+ { \use_none:nn }
+ {
+ \exp_not:n {#4}
+ \@@_format_decimal_loop:NNNN
+ \l_@@_group_separator_tl
+ }
+ }
+ }
+ }
+% \end{macrocode}
+% Uncertainties which are directly attached are easy to deal with. For those
+% that are separated, the first step is to find if they are entirely
+% contained within the decimal part, and to pad if they are. For the case
+% where the boundary is crossed to the integer part, the correct number of
+% digit tokens need to be removed from the start of the uncertainty and
+% the split result sent to the appropriate auxiliaries.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_uncertainty:nn #1#2
+ {
+ \tl_if_blank:nTF {#1}
+ { \@@_format_uncertainty_unaligned: }
+ {
+ \bool_if:NTF \l_@@_uncert_separate_bool
+ {
+ \exp_not:V \l_@@_tab_tl
+ \@@_format_sign_aux:N \pm
+ \exp_not:V \l_@@_tab_tl
+ \@@_format_uncertainty_aux:fn
+ { \int_eval:n { \tl_count:n {#1} - \tl_count:n {#2} } }
+ {#1}
+ }
+ {
+ \exp_not:V \l_@@_output_uncert_open_tl
+ \exp_not:n {#1}
+ \exp_not:V \l_@@_output_uncert_close_tl
+ \@@_format_uncertainty_unaligned:
+ }
+ }
+ }
+\cs_new:Npn \@@_format_uncertainty_unaligned:
+ {
+ \exp_not:V \l_@@_tab_tl
+ \exp_not:V \l_@@_tab_tl
+ \exp_not:V \l_@@_tab_tl
+ \exp_not:V \l_@@_tab_tl
+ }
+\cs_new:Npn \@@_format_uncertainty_aux:nn #1#2
+ {
+ \int_compare:nNnTF {#1} > 0
+ {
+ \@@_format_uncertainty_aux:fnw
+ { \int_eval:n { #1 - 1 } }
+ { }
+ #2 \q_nil
+ }
+ {
+ 0
+ \@@_format_decimal:f
+ {
+ \prg_replicate:nn { \int_abs:n {#1} } { 0 }
+ #2
+ }
+ }
+ }
+\cs_generate_variant:Nn \@@_format_uncertainty_aux:nn { f }
+\cs_new:Npn \@@_format_uncertainty_aux:nnw #1#2#3
+ {
+ \quark_if_nil:NF #3
+ {
+ \int_compare:nNnTF {#1} = 0
+ { \@@_format_uncertainty_aux:nw {#2#3} }
+ {
+ \@@_format_uncertainty_aux:fnw
+ { \int_eval:n { #1 - 1 } }
+ {#2#3}
+ }
+ }
+ }
+\cs_generate_variant:Nn \@@_format_uncertainty_aux:nnw { f }
+\cs_new:Npn \@@_format_uncertainty_aux:nw #1#2 \q_nil
+ {
+ \@@_format_digits:nn { integer } {#1}
+ \@@_format_decimal:n {#2}
+ }
+% \end{macrocode}
+% Setting the exponent part requires some information about the mantissa:
+% was it there or not. This means that whilst only the sign and value for
+% the exponent are typeset here, there is a need to also have access to the
+% combined mantissa part (with a decimal marker). The rest of the work is
+% about picking up the various options and getting the combinations right.
+% For signs, the auxiliary from the main sign routine can be used, but not
+% the main function: negative exponents don't have special handling.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_exponent:Nnn #1#2#3
+ {
+ \exp_not:V \l_@@_tab_tl
+ \bool_lazy_or:nnTF
+ { \l_@@_zero_exponent_bool }
+ { ! \str_if_eq_p:nn {#2} { 0 } }
+ {
+ \bool_lazy_and:nnTF
+ { \str_if_eq_p:nn {#3} { 1. } }
+ { ! \l_@@_unity_mantissa_bool }
+ { \exp_not:V \l_@@_tab_tl }
+ {
+ \bool_if:NTF \l_@@_tight_bool
+ {
+ \exp_not:N \mathord
+ { \exp_not:V \l_@@_exponent_product_tl }
+ }
+ { \exp_not:V \l_@@_exponent_product_tl }
+ \exp_not:V \l_@@_tab_tl
+ }
+ \exp_not:V \l_@@_exponent_base_tl
+ ^
+ {
+ \bool_lazy_or:nnT
+ { \l_@@_explicit_plus_bool }
+ { ! \str_if_eq_p:nn {#1} { + } }
+ { \@@_format_sign_aux:N #1 }
+ \@@_format_digits:nn { integer } {#2}
+ }
+ }
+ { \exp_not:V \l_@@_tab_tl }
+ }
+% \end{macrocode}
+% A do-nothing marker used to allow shuffling of the output and so expandable
+% operations for formatting.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_end: { }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Miscellaneous tools}
+%
+% \begin{variable}{\l_@@_valid_tl}
+% The list of valid tokens.
+% \begin{macrocode}
+\tl_new:N \l_@@_valid_tl
+% \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[TF]{\siunitx_if_number:n}
+% Test if an entire number is valid: this means parsing the number but not
+% returning anything.
+% \begin{macrocode}
+\prg_new_protected_conditional:Npnn \siunitx_if_number:n #1
+ { T , F , TF }
+ {
+ \group_begin:
+ \bool_set_true:N \l_@@_validate_bool
+ \@@_parse:n {#1}
+ \bool_lazy_and:nnTF
+ { \tl_if_empty_p:N \l_@@_real_tl }
+ { \tl_if_empty_p:N \l_@@_imaginary_tl }
+ {
+ \group_end:
+ \prg_return_false:
+ }
+ {
+ \group_end:
+ \prg_return_true:
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[TF]{\siunitx_if_number_token:N}
+% A simple conditional to answer the question of whether a specific token is
+% possibly valid in a number.
+% \begin{macrocode}
+\prg_new_protected_conditional:Npnn \siunitx_if_number_token:N #1
+ { T , F , TF }
+ {
+ \tl_set:Nx \l_@@_valid_tl
+ {
+ \exp_not:V \l_@@_input_uncert_close_tl
+ \exp_not:V \l_@@_input_complex_tl
+ \exp_not:V \l_@@_input_comparator_tl
+ \exp_not:V \l_@@_input_decimal_tl
+ \exp_not:V \l_@@_input_digit_tl
+ \exp_not:V \l_@@_input_exponent_tl
+ \exp_not:V \l_@@_input_ignore_tl
+ \exp_not:V \l_@@_input_uncert_open_tl
+ \exp_not:V \l_@@_input_sign_tl
+ \exp_not:V \l_@@_input_uncert_sign_tl
+ }
+ \tl_if_in:VnTF \l_@@_valid_tl {#1}
+ { \prg_return_true: }
+ { \prg_return_false: }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Messages}
+%
+% \begin{macrocode}
+\msg_new:nnnn { siunitx } { number / invalid-input }
+ { Invalid~number~'#1'. }
+ {
+ The~input~'#1'~could~not~be~parsed~as~a~number~following~the~
+ format~defined~in~module~documentation.
+ }
+% \end{macrocode}
+%
+% \subsection{Standard settings for module options}
+%
+% Some of these follow naturally from the point of definition
+% (\emph{e.g.}~boolean variables are always |false| to begin with),
+% but for clarity everything is set here.
+% \begin{macrocode}
+\keys_set:nn { siunitx }
+ {
+ bracket-negative = false ,
+ evaluate-expression = false ,
+ explicit-plus = false ,
+ exponent-base = 10 ,
+ exponent-product = \times ,
+ expression = #1 ,
+ group-digits = all ,
+ group-minimum-digits = 4 ,
+ group-separator = \, , % (
+ input-close-uncertainty = ) ,
+ input-complex-roots = ij ,
+ input-comparators = { <=>\approx\ge\geq\gg\le\leq\ll\sim } ,
+ input-decimal-markers = { ., } ,
+ input-digits = 0123456789 ,
+ input-exponent-markers = dDeE ,
+ input-ignore = \, ,
+ input-open-uncertainty = ( , % )
+ input-signs = +-\mp\pm ,
+ input-uncertainty-signs = \pm ,
+ negative-color = , % (
+ number-close-bracket = ) ,
+ number-open-bracket = ( , % )
+ output-close-uncertainty = ) ,
+ output-complex-root = \mathrm { i } ,
+ output-decimal-marker = . ,
+ output-open-uncertainty = ( , % )
+ round-half = up ,
+ round-minimum = 0 ,
+ round-mode = none ,
+ round-precision = 2 ,
+ separate-uncertainty = false ,
+ tight-spacing = false ,
+ unity-mantissa = false ,
+ zero-exponent = false
+ }
+% \end{macrocode}
+%
+% \begin{macrocode}
+%</package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex