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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/l3experimental/l3str-format.dtx
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+% \iffalse meta-comment
+%
+%% File: l3str-format.dtx
+%
+% Copyright (C) 2012-2019 The LaTeX3 Project
+%
+% It may be distributed and/or modified under the conditions of the
+% LaTeX Project Public License (LPPL), either version 1.3c of this
+% license or (at your option) any later version. The latest version
+% of this license is in the file
+%
+% https://www.latex-project.org/lppl.txt
+%
+% This file is part of the "l3experimental bundle" (The Work in LPPL)
+% and all files in that bundle must be distributed together.
+%
+% -----------------------------------------------------------------------
+%
+% The development version of the bundle can be found at
+%
+% https://github.com/latex3/latex3
+%
+% for those people who are interested.
+%
+%<*driver|package>
+\RequirePackage{expl3}
+%</driver|package>
+%<*driver>
+\documentclass[full]{l3doc}
+\usepackage{amsmath}
+\begin{document}
+ \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+%
+% \title{^^A
+% The \textsf{l3str-format} package: formatting strings of characters^^A
+% }
+%
+% \author{^^A
+% The \LaTeX3 Project\thanks
+% {^^A
+% E-mail:
+% \href{mailto:latex-team@latex-project.org}
+% {latex-team@latex-project.org}^^A
+% }^^A
+% }
+%
+% \date{Released 2019-08-25}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \section{Format specifications}
+%
+% In this module, we introduce the notion of a string \meta{format}.
+% The syntax follows that of Python's \texttt{format} built-in function.
+% A \meta{format specification} is a string of the form
+% \begin{equation*}
+% \meta{format specification} = [[\meta{fill}]\meta{alignment}]
+% [\meta{sign}] [\meta{width}] [.\meta{precision}] [\meta{style}]
+% \end{equation*}
+% where each $[\ldots]$ denotes an independent optional part.
+% \begin{itemize}
+% \item \meta{fill} can be any character: it is assumed to be present
+% whenever the second character of the \meta{format specification}
+% is a valid \meta{alignment} character.
+% \item \meta{alignment} can be |<|~(left alignment), |>|~(right
+% alignment), |^|~(centering), or |=|~(for numeric types only).
+% \item \meta{sign} is allowed for numeric types; it can be |+|~(show
+% a sign for positive and negative numbers), |-|~(only put a sign
+% for negative numbers), or a space~(show a space or a~|-|).
+% \item \meta{width} is the minimum number of characters of the
+% result: if the result is naturally shorter than this \meta{width},
+% then it is padded with copies of the character \meta{fill}, with a
+% position depending on the choice of \meta{alignment}. If the
+% result is naturally longer, it is not truncated.
+% \item \meta{precision}, whose presence is indicated by a period,
+% can have different meanings depending on the type.
+% \item \meta{style} is one character, which controls how the given
+% data should be formatted. The list of allowed \meta{styles}
+% depends on the type.
+% \end{itemize}
+% The choice of \meta{alignment} |=| is only valid for numeric types: in
+% this case the padding is inserted between the sign and the rest of the
+% number.
+%
+% \section{Formatting various data-types}
+%
+% \begin{function}[EXP]{\tl_format:Nn, \tl_format:cn, \tl_format:nn}
+% \begin{syntax}
+% \cs{tl_format:nn} \Arg{token list} \Arg{format specification}
+% \end{syntax}
+% Converts the \meta{token list} to a string according to the
+% \meta{format specification}. The \meta{style}, if present, must
+% be~|s|. If \meta{precision} is given, all characters of the string
+% representation of the \meta{token list} beyond the first
+% \meta{precision} characters are discarded.
+% \end{function}
+%
+% \begin{function}[EXP]{\seq_format:Nn, \seq_format:cn}
+% \begin{syntax}
+% \cs{seq_format:Nn} \Arg{sequence} \Arg{format specification}
+% \end{syntax}
+% Converts each item in the \meta{sequence} to a string according to
+% the \meta{format specification}, and concatenates the results.
+% \end{function}
+%
+% \begin{function}[EXP]{\int_format:nn}
+% \begin{syntax}
+% \cs{int_format:nn} \Arg{intexpr} \Arg{format specification}
+% \end{syntax}
+% Evaluates the \meta{integer expression} and converts the result to a
+% string according to the \meta{format specification}. The
+% \meta{precision} argument is not allowed. The \meta{style} can be
+% |b| for binary output, |d| for decimal output (this is the default),
+% |o| for octal output, |X| for hexadecimal output (using capital
+% letters).
+% \end{function}
+%
+% \begin{function}[EXP]{\fp_format:nn}
+% \begin{syntax}
+% \cs{fp_format:nn} \Arg{fpexpr} \Arg{format specification}
+% \end{syntax}
+% Evaluates the \meta{floating point expression} and converts the
+% result to a string according to the \meta{format specification}.
+% The \meta{style} can be
+% \begin{itemize}
+% \item |e| for scientific notation, with one digit before and
+% \meta{precision} digits after the decimal separator, and an
+% integer exponent, following |e|;
+% \item |f| for a fixed point notation, with \meta{precision} digits
+% after the decimal separator and no exponent;
+% \item |g| for a general format, which uses style |f| for numbers
+% in the range $[10^{-4}, 10^{\meta{precision}})$ and style |e|
+% otherwise.
+% \end{itemize}
+% When there is no \meta{style} specifier nor \meta{precision} the
+% number is displayed without rounding. Otherwise the
+% \meta{precision} defaults to~$6$.
+% \end{function}
+%
+% \section{Possibilities, and things to do}
+%
+% \begin{itemize}
+% \item Provide a token list formatting \meta{style} which keeps the
+% last \meta{precision} characters rather than the first
+% \meta{precision}.
+% \end{itemize}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3str-format} implementation}
+%
+% \begin{macrocode}
+%<*initex|package>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<@@=str>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<*package>
+\ProvidesExplPackage{l3str-format}{2019-08-25}{}
+ {L3 Experimental string formatting}
+%</package>
+% \end{macrocode}
+%
+% \subsection{Helpers}
+%
+% \begin{macro}[EXP]{\use:nf, \use:fnf}
+% A simple variant.
+% \begin{macrocode}
+\cs_generate_variant:Nn \use:nn { nf }
+\cs_generate_variant:Nn \use:nnn { fnf }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\tl_to_str:f}
+% A simple variant.
+% \begin{macrocode}
+\cs_generate_variant:Nn \tl_to_str:n { f }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_if_digit:NTF}
+% Here we expect |#1| to be a character with category other, or
+% \cs{s_stop}.
+% \begin{macrocode}
+\prg_new_conditional:Npnn \@@_format_if_digit:N #1 { TF }
+ {
+ \if_int_compare:w 9 < 1 #1 \exp_stop_f:
+ \prg_return_true: \else: \prg_return_false: \fi:
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]
+% {\@@_format_put:nw, \@@_format_put:ow, \@@_format_put:fw}
+% Put |#1| after an \cs{s_stop} delimiter.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_put:nw #1 #2 \s_stop { #2 \s_stop #1 }
+\cs_generate_variant:Nn \@@_format_put:nw { o , f }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, TF]{\@@_format_if_in:nN}
+% \begin{macro}[EXP]{\@@_format_if_in_aux:NN}
+% A copy of \cs{@@_if_contains_char:nNTF} to avoid relying on
+% this weird internal string function.
+% \begin{macrocode}
+\prg_new_conditional:Npnn \@@_format_if_in:nN #1#2 { TF }
+ {
+ \@@_format_if_in_aux:NN #2 #1
+ { #2 \prg_return_false: \exp_after:wN \prg_break: \else: }
+ \prg_break_point:
+ }
+\cs_new:Npn \@@_format_if_in_aux:NN #1#2
+ {
+ \if_charcode:w #1 #2
+ \prg_return_true:
+ \exp_after:wN \prg_break:
+ \fi:
+ \@@_format_if_in_aux:NN #1
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Parsing a format specification}
+%
+% \begin{macro}[EXP]{\@@_format_parse:n}
+% \begin{macro}[EXP]
+% {
+% \@@_format_parse_auxi:NN,
+% \@@_format_parse_auxii:nN,
+% \@@_format_parse_auxiii:nN,
+% \@@_format_parse_auxiv:nwN,
+% \@@_format_parse_auxv:nN,
+% \@@_format_parse_auxvi:nwN,
+% \@@_format_parse_auxvii:nN,
+% \@@_format_parse_end:nwn,
+% }
+% The goal is to parse
+% \begin{equation*}
+% \meta{format specification} = [[\meta{fill}]\meta{alignment}]
+% [\meta{sign}] [\meta{width}] [.\meta{precision}] [\meta{style}]
+% \end{equation*}
+% \begin{macrocode}
+\cs_new:Npn \@@_format_parse:n #1
+ {
+ \exp_last_unbraced:Nf \@@_format_parse_auxi:NN
+ { \__kernel_str_to_other:n {#1} } \s_stop \s_stop {#1}
+ }
+\cs_new:Npx \@@_format_parse_auxi:NN #1#2
+ {
+ \exp_not:N \@@_format_if_in:nNTF { < > = ^ } #2
+ { \exp_not:N \@@_format_parse_auxiii:nN { #1 #2 } }
+ {
+ \exp_not:N \@@_format_parse_auxii:nN
+ { \c_catcode_other_space_tl } #1 #2
+ }
+ }
+\cs_new:Npn \@@_format_parse_auxii:nN #1#2
+ {
+ \@@_format_if_in:nNTF { < > = ^ } #2
+ { \@@_format_parse_auxiii:nN { #1 #2 } }
+ { \@@_format_parse_auxiii:nN { #1 ? } #2 }
+ }
+\cs_new:Npx \@@_format_parse_auxiii:nN #1#2
+ {
+ \exp_not:N \@@_format_if_in:nNTF
+ { + - \c_catcode_other_space_tl }
+ #2
+ { \exp_not:N \@@_format_parse_auxiv:nwN { #1 #2 } ; }
+ { \exp_not:N \@@_format_parse_auxiv:nwN { #1 ? } ; #2 }
+ }
+\cs_new:Npn \@@_format_parse_auxiv:nwN #1#2; #3
+ {
+ \@@_format_if_digit:NTF #3
+ { \@@_format_parse_auxiv:nwN {#1} #2 #3 ; }
+ { \@@_format_parse_auxv:nN { #1 {#2} } #3 }
+ }
+\cs_new:Npn \@@_format_parse_auxv:nN #1#2
+ {
+ \token_if_eq_charcode:NNTF . #2
+ { \@@_format_parse_auxvi:nwN {#1} 0 ; }
+ { \@@_format_parse_auxvii:nN { #1 { } } #2 }
+ }
+\cs_new:Npn \@@_format_parse_auxvi:nwN #1#2; #3
+ {
+ \@@_format_if_digit:NTF #3
+ { \@@_format_parse_auxvi:nwN {#1} #2 #3 ; }
+ { \@@_format_parse_auxvii:nN { #1 {#2} } #3 }
+ }
+\cs_new:Npn \@@_format_parse_auxvii:nN #1#2
+ {
+ \token_if_eq_meaning:NNTF \s_stop #2
+ { \@@_format_parse_end:nwn { #1 ? } #2 }
+ { \@@_format_parse_end:nwn { #1 #2 } }
+ }
+\cs_new:Npn \@@_format_parse_end:nwn #1 #2 \s_stop \s_stop #3
+ {
+ \tl_if_empty:nF {#2}
+ { \__kernel_msg_expandable_error:nnn { str } { invalid-format } {#3} }
+ #1
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Alignment}
+%
+% The $4$ functions in this section receive an \meta{body}, a
+% \meta{sign}, a \meta{width} and a \meta{fill} character (exactly one
+% character). For non-numeric types, the \meta{sign} is empty and the
+% \meta{body} is the (other) string we want to format. For numeric
+% types, we wish to format \meta{sign} \meta{body} (both are other
+% strings). The alignment types |<|, |>| and |^| keep \meta{sign} and
+% \meta{body} together. The |=| alignment type, however, inserts the
+% padding between the \meta{sign} and the \meta{body}, hence the need to
+% keep those separate.
+%
+% \begin{macro}[EXP]{\@@_format_align_<:nnnN}
+% \begin{quote}
+% \cs{@@_format_align_<:nnnN} \Arg{body} \Arg{sign} \Arg{width}
+% \meta{fill}
+% \end{quote}
+% Aligning \enquote{\meta{sign} \meta{body}} to the left
+% entails appending |#4| the correct number of times. Then convert
+% the result to a string.
+% \begin{macrocode}
+\cs_new:cpn { @@_format_align_<:nnnN } #1#2#3#4
+ {
+ \use:nf { #2 #1 }
+ {
+ \prg_replicate:nn
+ { \int_max:nn { #3 - \@@_count:n { #2 #1 } } { 0 } }
+ {#4}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_align_>:nnnN}
+% \begin{quote}
+% \cs{@@_format_align_>:nnnN} \Arg{body} \Arg{sign} \Arg{width}
+% \meta{fill}
+% \end{quote}
+% Aligning an \enquote{\meta{sign} \meta{body}} to the right
+% entails prepending |#4| the correct number of times. Then convert
+% the result to a string.
+% \begin{macrocode}
+\cs_new:cpn { @@_format_align_>:nnnN } #1#2#3#4
+ {
+ \prg_replicate:nn
+ { \int_max:nn { #3 - \@@_count:n { #2 #1 } } { 0 } }
+ {#4}
+ #2 #1
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begingroup\catcode`\^=12
+% \begin{macro}[EXP]{\@@_format_align_^:nnnN}
+% \begin{quote}
+% \cs{@@_format_align_^:nnnN} \Arg{body} \Arg{sign} \Arg{width}
+% \meta{fill}
+% \end{quote}
+% Centering \enquote{\meta{sign} \meta{body}} entails
+% prepending and appending |#4| the correct number of times. If the
+% number of |#4| to be added is odd, we add one more after than
+% before.
+% \begin{macrocode}
+\cs_new:cpn { @@_format_align_^:nnnN } #1#2#3#4
+ {
+ \use:fnf
+ {
+ \prg_replicate:nn
+ {
+ \int_max:nn { 0 }
+ { #3 - \@@_count:n { #2 #1 } - 1 }
+ / 2
+ }
+ {#4}
+ }
+ { #2 #1 }
+ {
+ \prg_replicate:nn
+ {
+ \int_max:nn { 0 }
+ { #3 - \@@_count:n { #2 #1 } }
+ / 2
+ }
+ {#4}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+% \endgroup
+%
+% \begin{macro}[EXP]{\@@_format_align_=:nnnN}
+% \begin{quote}
+% \cs{@@_format_align_=:nnnN} \Arg{body} \Arg{sign} \Arg{width}
+% \meta{fill}
+% \end{quote}
+% The special numeric alignment |=| means that we insert the
+% appropriate number of copies of |#4| between the \meta{sign} and the
+% \meta{body}. Then convert the result to a string.
+% \begin{macrocode}
+\cs_new:cpn { @@_format_align_=:nnnN } #1#2#3#4
+ {
+ \use:nf {#2}
+ {
+ \prg_replicate:nn
+ { \int_max:nn { #3 - \@@_count:n { #2 #1 } } { 0 } }
+ {#4}
+ }
+ #1
+ }
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Formatting token lists}
+%
+% \begin{macro}[EXP]{\tl_format:Nn, \tl_format:cn, \tl_format:nn}
+% Call \cs{@@_format_tl:NNNnnNn} to read the parsed \meta{format
+% specification}. Then convert the result to a string.
+% \begin{macrocode}
+\cs_new:Npn \tl_format:Nn { \exp_args:No \tl_format:nn }
+\cs_generate_variant:Nn \tl_format:Nn { c }
+\cs_new:Npn \tl_format:nn #1#2
+ {
+ \tl_to_str:f
+ {
+ \exp_last_unbraced:Nf \@@_format_tl:NNNnnNn
+ { \@@_format_parse:n {#2} }
+ {#1}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_tl:NNNnnNn}
+% \begin{quote}
+% \cs{@@_format_tl:NNNnnNn} \meta{fill} \meta{alignment} \meta{sign}
+% \Arg{width} \Arg{precision} \meta{style} \Arg{token list}
+% \end{quote}
+% First check that the \meta{alignment} is not |=|, and set the
+% default alignment |?| to |<|. Place the modified information after
+% a trailing \cs{s_stop} for later retrieval. Then check that there
+% was no \meta{sign}. The width will be useful later, store it after
+% \cs{s_stop}. Afterwards, store the precision, and the function
+% \cs{@@_range:nnn} that will be used to extract the first
+% |#5| characters of the string.
+% There is a need to use the internal function, as otherwise
+% leading spaces would get stripped by |f|-expansion. Finally, check
+% that the \meta{style} is |?| or |s|.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_tl:NNNnnNn #1#2#3#4#5#6
+ {
+ \token_if_eq_charcode:NNTF #2 =
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-align-format } {#2} {tl}
+ \@@_format_put:nw { #1 < }
+ }
+ {
+ \token_if_eq_charcode:NNTF #2 ?
+ { \@@_format_put:nw { #1 < } }
+ { \@@_format_put:nw { #1 #2 } }
+ }
+ \token_if_eq_charcode:NNF #3 ?
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-sign-format } {#3} {tl}
+ }
+ \@@_format_put:nw { {#4} }
+ \tl_if_empty:nTF {#5}
+ { \@@_format_put:nw { \@@_range:nnn { {1} {-1} } } }
+ { \@@_format_put:nw { \@@_range:nnn { {1} {#5} } } }
+ \token_if_eq_charcode:NNF #6 s
+ {
+ \token_if_eq_charcode:NNF #6 ?
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-style-format } {#6} {tl}
+ }
+ }
+ \@@_format_tl_s:NNnnNNn
+ \s_stop
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_tl_s:NNnnNNn}
+% \begin{quote}
+% \cs{@@_format_tl_s:NNnnNNn} \cs{s_stop} \meta{function}
+% \Arg{arguments} \Arg{width} \meta{fill} \meta{alignment}
+% \Arg{token list}
+% \end{quote}
+% The \meta{function} and \meta{arguments} are built in such a way
+% that |f|-expanding \meta{function} \Arg{other string}
+% \meta{arguments} yields the piece of the \meta{other string} that we
+% want to output. The \meta{other string} is built from the
+% \meta{token list} by |f|-expanding \cs{__kernel_str_to_other:n}.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_tl_s:NNnnNNn #1#2#3#4#5#6#7
+ {
+ \exp_args:Nc \exp_args:Nf
+ { @@_format_align_#6:nnnN }
+ { \exp_args:Nf #2 { \__kernel_str_to_other:n {#7} } #3 }
+ { }
+ {#4} #5
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Formatting sequences}
+%
+% \begin{macro}[EXP]{\seq_format:Nn, \seq_format:cn}
+% Each item is formatted as a token list according to the
+% specification. First parse the format and expand the sequence, then
+% loop through the items. Eventually, convert to a string.
+% \begin{macrocode}
+\cs_new:Npn \seq_format:Nn #1#2
+ {
+ \tl_to_str:f
+ {
+ \@@_format_seq:ff
+ { \exp_after:wN \use_i:nn \exp_after:wN \exp_stop_f: #1 }
+ { \@@_format_parse:n {#2} }
+ }
+ }
+\cs_generate_variant:Nn \seq_format:Nn { c }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_seq:nn, \@@_format_seq:ff}
+% The first argument is the contents of a \texttt{seq} variable. The
+% second is a parsed \meta{format specification}. Set up the loop.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_seq:nn #1#2
+ {
+ \@@_format_seq_loop:nnNn { } {#2}
+ #1
+ { ? \@@_format_seq_end:w } { }
+ }
+\cs_generate_variant:Nn \@@_format_seq:nn { ff }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_seq_loop:nnNn}
+% \begin{quote}
+% \cs{@@_format_seq_loop:nnNn} \Arg{done} \Arg{parsed format}
+% \cs{__seq_item:n} \Arg{item}
+% \end{quote}
+% The first argument is the result of formatting the items read so
+% far. The third argument is a single token (\cs{__seq_item:n}),
+% until we reach the end of the sequence, where |\use_none:n #3| ends
+% the loop.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_seq_loop:nnNn #1#2#3#4
+ {
+ \use_none:n #3
+ \exp_args:Nf \@@_format_seq_loop:nnNn
+ { \use:nf {#1} { \@@_format_tl:NNNnnNn #2 {#4} } }
+ {#2}
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_seq_end:w}
+% Pick the right piece in the loop above.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_seq_end:w #1#2#3#4 { \use_ii:nnn #3 }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Formatting integers}
+%
+% \begin{macro}[EXP]{\int_format:nn}
+% Evaluate the first argument and feed it to \cs{@@_format_int:nn}.
+% \begin{macrocode}
+\cs_new:Npn \int_format:nn #1
+ { \exp_args:Nf \@@_format_int:nn { \int_eval:n {#1} } }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_int:nn}
+% Parse the \meta{format specification} and feed it to
+% \cs{@@_format_int:NNNnnNn}. Then convert the result to a string
+% \begin{macrocode}
+\cs_new:Npn \@@_format_int:nn #1#2
+ {
+ \tl_to_str:f
+ {
+ \exp_last_unbraced:Nf \@@_format_int:NNNnnNn
+ { \@@_format_parse:n {#2} }
+ {#1}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_int:NNNnnNn}
+% \begin{quote}
+% \cs{@@_format_int:NNNnnNn} \meta{fill} \meta{alignment}
+% \meta{sign} \Arg{width} \Arg{precision} \meta{style} \Arg{integer}
+% \end{quote}
+% First set the
+% default alignment |?| to |>|. Place the modified information after
+% a trailing \cs{s_stop} for later retrieval. Then check the
+% \meta{sign}: if the integer is negative, always put~|-|. Otherwise,
+% if the format's \meta{sign} is |~|, put a space (with category
+% \enquote{other}); if it is~|+| put |+|; if it is |-| (default), put
+% nothing, represented as a brace group. The width |#4| will be
+% useful later, store it after \cs{s_stop}. Afterwards, check that
+% the \meta{precision} was absent. Finally, dispatch depending on the
+% \meta{style}.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_int:NNNnnNn #1#2#3#4#5#6#7
+ {
+ \token_if_eq_charcode:NNTF #2 ?
+ { \@@_format_put:nw { #1 > } }
+ { \@@_format_put:nw { #1 #2 } }
+ \int_compare:nNnTF {#7} < 0
+ { \@@_format_put:nw { - } }
+ {
+ \str_case:nnF {#3}
+ {
+ { ~ } { \@@_format_put:ow { \c_catcode_other_space_tl } }
+ { + } { \@@_format_put:nw { + } }
+ }
+ { \@@_format_put:nw { { } } }
+ }
+ \@@_format_put:nw { {#4} }
+ \tl_if_empty:nF {#5}
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-precision-format } {#5} {int}
+ }
+ \str_case:nnF {#6}
+ {
+ { ? } { \@@_format_int:NwnnNNn \use:n }
+ { d } { \@@_format_int:NwnnNNn \use:n }
+ { b } { \@@_format_int:NwnnNNn \int_to_bin:n }
+ { o } { \@@_format_int:NwnnNNn \int_to_oct:n }
+ { X } { \@@_format_int:NwnnNNn \int_to_Hex:n }
+ }
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-style-format } {#6} { int }
+ \@@_format_int:NwnnNNn \use:n
+ }
+ \s_stop {#7}
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_int:NwnnNNn}
+% \begin{quote}
+% \cs{@@_format_int:NwnnNNn} \meta{function} \cs{s_stop}
+% \Arg{width} \Arg{sign} \meta{fill} \meta{alignment} \Arg{integer}
+% \end{quote}
+% Use the |format_align| function corresponding to the
+% \meta{alignment}, with the following arguments:
+% \begin{itemize}
+% \item the string formed by combining the sign |#4| with the result
+% of converting the absolute value of the \meta{integer} |#7|
+% according to the conversion function |#1|;
+% \item the \meta{width};
+% \item the \meta{fill} character.
+% \end{itemize}
+% \begin{macrocode}
+\cs_new:Npn \@@_format_int:NwnnNNn #1#2 \s_stop #3#4#5#6#7
+ {
+ \exp_args:Nc \exp_args:Nf
+ { @@_format_align_#6:nnnN }
+ { #1 { \int_abs:n {#7} } }
+ {#4}
+ {#3} #5
+ }
+% \end{macrocode}
+% ^^A todo: note similarity with \@@_format_tl_s:NNnnNNn
+% \end{macro}
+%
+% \subsection{Formatting floating points}
+%
+% \begin{macro}[EXP]{\fp_format:nn}
+% Evaluate the first argument to a floating point number, and feed it
+% to \cs{@@_format_fp:nn}. It would be more efficient to use internal
+% floating point numbers but efficiency is not essential and the code
+% is cleaner this way.
+% \begin{macrocode}
+\cs_new:Npn \fp_format:nn #1
+ { \exp_args:Nf \@@_format_fp:nn { \fp_to_tl:n {#1} } }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp:nn}
+% Parse the \meta{format specification} and feed it to
+% \cs{@@_format_fp:NNNnnNn}. Then convert the result to a string
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp:nn #1#2
+ {
+ \tl_to_str:f
+ {
+ \exp_last_unbraced:Nf \@@_format_fp:NNNnnNn
+ { \@@_format_parse:n {#2} }
+ {#1}
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp:NNNnnNn}
+% \begin{quote}
+% \cs{@@_format_fp:NNNnnNn} \meta{fill} \meta{alignment}
+% \meta{format sign} \Arg{width} \Arg{precision} \meta{style}
+% \Arg{floating point}
+% \end{quote}
+% First set the default alignment |?| to |>|. Place the modified
+% information after a trailing \cs{s_stop} for later retrieval. Then
+% check the \meta{format sign} and the \meta{fp sign}: if the floating
+% point is negative, always put~|-|. Otherwise (including
+% \texttt{nan}), if the format's \meta{sign} is |~|, put a space (with
+% category \enquote{other}); if it is~|+| put |+|; if it is |-|
+% (default), put nothing, represented as a brace group. The width
+% |#4| will be useful later, store it after \cs{s_stop}. Afterwards,
+% check the \meta{precision}: if it was not given, replace it by $6$
+% (default precision) unless no \meta{style} was given: in that case
+% we want to use whatever precision is needed to fully describe the
+% number. Finally, dispatch depending on the \meta{style}.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp:NNNnnNn
+ #1#2#3#4#5#6#7
+ {
+ \token_if_eq_charcode:NNTF #2 ?
+ { \@@_format_put:nw { #1 > } }
+ { \@@_format_put:nw { #1 #2 } }
+ \tl_if_head_eq_charcode:nNTF {#7} -
+ { \@@_format_put:nw { - } }
+ {
+ \str_case:nnF {#3}
+ {
+ { ~ } { \@@_format_put:ow { \c_catcode_other_space_tl } }
+ { + } { \@@_format_put:nw { + } }
+ }
+ { \@@_format_put:nw { { } } }
+ }
+ \@@_format_put:nw { {#4} }
+ \tl_if_empty:nTF {#5}
+ {
+ \token_if_eq_meaning:NNTF #6 ?
+ { \@@_format_put:nw { { } } }
+ { \@@_format_put:nw { { 6} } }
+ }
+ { \@@_format_put:nw { {#5} } }
+ \str_case:nnF {#6}
+ {
+ { e } { \@@_format_fp:wnnnNNn \@@_format_fp_e:nn }
+ { f } { \@@_format_fp:wnnnNNn \@@_format_fp_f:nn }
+ { g } { \@@_format_fp:wnnnNNn \@@_format_fp_g:nn }
+ { ? } { \@@_format_fp:wnnnNNn \@@_format_fp_g:nn }
+ }
+ {
+ \__kernel_msg_expandable_error:nnnn
+ { str } { invalid-style-format } {#6} { fp }
+ \@@_format_fp:wnnnNNn \@@_format_fp_g:nn
+ }
+ \s_stop {#7}
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp:wnnnNNn}
+% \begin{quote}
+% \cs{@@_format_fp:wnnnNNn} \meta{formatting function} \cs{s_stop}
+% \Arg{precision} \Arg{width} \Arg{sign} \meta{fill}
+% \meta{alignment} \Arg{floating point}
+% \end{quote}
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp:wnnnNNn
+ #1 \s_stop #2 #3 #4 #5#6 #7
+ {
+ \exp_args:Nc \exp_args:Nf
+ { @@_format_align_#6:nnnN }
+ { #1 {#7} {#2} }
+ {#4}
+ {#3} #5
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp_round:nn}
+% Round the given floating point and take the absolute value (in this
+% order, to play nicely with unusual rounding modes if we ever
+% implement these).
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp_round:nn #1 #2
+ { \fp_to_tl:n { abs ( round ( #1 , #2 - logb(#1) - 1 ) ) } }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp_e:nn}
+% \begin{macro}[EXP]{\@@_format_fp_e_aux:nn, \@@_format_fp_e_aux:wwn}
+% With the |e| type, first round to |#4+1| significant figures (one
+% before the decimal separator, |#4| after), then filter out special
+% cases, then convert to scientific notations. This order is
+% important because rounding can produce infinities or zeros and
+% because \cs{fp_to_scientific:n} does not accept |nan| nor |inf|.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp_e:nn #1#2
+ {
+ \exp_args:Nf \@@_format_fp_e_aux:nn
+ { \@@_format_fp_round:nn {#1} { #2 + 1 } }
+ {#2}
+ }
+\cs_new:Npn \@@_format_fp_e_aux:nn #1#2
+ {
+ \str_case:nnF {#1}
+ {
+ { inf } { inf }
+ { nan } { nan }
+ }
+ {
+ \exp_last_unbraced:Nf \@@_format_fp_e_aux:wwn
+ { \fp_to_scientific:n {#1} } ;
+ {#2}
+ }
+ }
+\cs_new:Npn \@@_format_fp_e_aux:wwn #1 . #2 e #3 ; #4
+ {
+ \@@_format_put:nw { e #3 }
+ \int_compare:nNnTF {#4} < \c__fp_prec_int
+ {
+ \@@_format_put:fw { \str_range:nnn { #2 } { 1 } { #4 } }
+ \@@_format_put:nw { #1 . }
+ }
+ {
+ \@@_format_put:fw
+ { \prg_replicate:nn { #4 - \c__fp_prec_int + 1 } { 0 } }
+ \@@_format_put:nw { #1 . #2 }
+ }
+ \use_none:n \s_stop
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp_f:nn}
+% \begin{macro}[EXP]{\@@_format_fp_f_aux:wwwn}
+% With the |f| type, first round to |#4| (absolute) decimal places
+% then filter out special cases, then in normal cases pad with zeros.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp_f:nn #1#2
+ {
+ \exp_args:Nf \@@_format_fp_f_aux:nn
+ { \fp_to_tl:n { abs ( round ( #1 , #2 ) ) } }
+ {#2}
+ }
+\cs_new:Npn \@@_format_fp_f_aux:nn #1#2
+ {
+ \str_case:nnF {#1}
+ {
+ { inf } { inf }
+ { nan } { nan }
+ }
+ {
+ \exp_last_unbraced:Nf \@@_format_fp_f_aux:wwwn
+ { \fp_to_decimal:n {#1} } . . ; {#2}
+ }
+ }
+\cs_new:Npn \@@_format_fp_f_aux:wwwn #1 . #2 . #3 ; #4
+ {
+ \use:nf { #1 . #2 }
+ { \prg_replicate:nn { #4 - \@@_count:n {#2} } {0} }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp_g:nn}
+% \begin{macro}[EXP]{\@@_format_fp_g_aux:wn}
+% \begin{macro}[EXP]{\@@_format_fp_to_scientific:n, \@@_format_fp_trim:w}
+% With the |g| type, a special case is when |#2| is empty (no style
+% nor precision in the original specification): then we output the
+% number without rounding (and without its sign). Otherwise round to
+% |#2| significant figures before filtering out special cases. (A
+% \meta{precision} of $0$ is treated like a precision of $1$.)
+% Distinguish exponents $-4\leq \meta{exponent} < \meta{precision}$
+% from others and use essentially the |f| or |e| presentations in
+% these two cases, but trimming trailing zeros. Because we don't need
+% to keep a fixed number of digits after the decimal point we can
+% simply use \cs{fp_to_decimal:n} and \cs{fp_to_scientific:n}, and in
+% the second case post-process the result by trimming zeros and a
+% period.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp_g:nn #1#2
+ {
+ \tl_if_empty:nTF {#2} { \fp_to_tl:n { abs(#1) } }
+ {
+ \exp_args:Nf \@@_format_fp_g_aux:nn
+ { \@@_format_fp_round:nn {#1} { \int_max:nn {1} {#2} } }
+ { \int_max:nn {1} {#2} }
+ }
+ }
+\cs_new:Npn \@@_format_fp_g_aux:nn #1#2
+ {
+ \str_case:nnF {#1}
+ {
+ { 0 } { 0 }
+ { inf } { inf }
+ { nan } { nan }
+ }
+ {
+ \fp_compare:nTF { 1e-4 <= #1 < 1e#2 }
+ { \fp_to_decimal:n {#1} }
+ {
+ \exp_last_unbraced:Nf \@@_format_fp_trim:w
+ { \fp_to_scientific:n {#1} }
+ }
+ }
+ }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_format_fp_trim:w}
+% \begin{macro}[EXP]
+% {\@@_format_fp_trim_loop:w, \@@_format_fp_trim_dot:w, \@@_format_fp_trim_end:w}
+% If |#1| ends with a $0$, the \texttt{loop} auxiliary takes that zero
+% as an end-delimiter for its first argument, and the second argument
+% is the same \texttt{loop} auxiliary. Once the last trailing zero is
+% reached, the second argument is the \texttt{dot} auxiliary,
+% which removes a trailing dot if any. We then clean-up with the
+% \texttt{end} auxiliary, keeping only the number.
+% \begin{macrocode}
+\cs_new:Npn \@@_format_fp_trim:w #1 e
+ {
+ \@@_format_fp_trim_loop:w #1
+ ; \@@_format_fp_trim_loop:w 0; \@@_format_fp_trim_dot:w .; \s_stop e
+ }
+\cs_new:Npn \@@_format_fp_trim_loop:w #1 0; #2 { #2 #1 ; #2 }
+\cs_new:Npn \@@_format_fp_trim_dot:w #1 .; { \@@_format_fp_trim_end:w #1 ; }
+\cs_new:Npn \@@_format_fp_trim_end:w #1 ; #2 \s_stop { #1 }
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Messages}
+%
+% All of the messages are produced expandably, so there is no need for
+% an extra-text.
+% \begin{macrocode}
+\__kernel_msg_new:nnn { str } { invalid-format }
+ { Invalid~format~'#1'. }
+\__kernel_msg_new:nnn { str } { invalid-align-format }
+ { Invalid~alignment~'#1'~for~type~'#2'. }
+\__kernel_msg_new:nnn { str } { invalid-sign-format }
+ { Invalid~sign~'#1'~for~type~'#2'. }
+\__kernel_msg_new:nnn { str } { invalid-precision-format }
+ { Invalid~precision~'#1'~for~type~'#2'. }
+\__kernel_msg_new:nnn { str } { invalid-style-format }
+ { Invalid~style~'#1'~for~type~'#2'. }
+% \end{macrocode}
+%
+% \begin{macrocode}
+%</initex|package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex