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Diffstat (limited to 'Master/texmf-dist/source/latex/siunitx/siunitx-number.dtx')
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diff --git a/Master/texmf-dist/source/latex/siunitx/siunitx-number.dtx b/Master/texmf-dist/source/latex/siunitx/siunitx-number.dtx new file mode 100644 index 00000000000..63de999adce --- /dev/null +++ b/Master/texmf-dist/source/latex/siunitx/siunitx-number.dtx @@ -0,0 +1,1862 @@ +% \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 |