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|
% \iffalse meta-comment
%
%% File: l3fp-convert.dtx Copyright(C) 2011-2018 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 "l3kernel bundle" (The Work in LPPL)
% and all files in that bundle must be distributed together.
%
% -----------------------------------------------------------------------
%
% The development version of the bundle can be found at
%
% https://github.com/latex3/latex3
%
% for those people who are interested.
%
%<*driver>
\documentclass[full,kernel]{l3doc}
\begin{document}
\DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
% \title{^^A
% The \textsf{l3fp-convert} package\\ Floating point conversion^^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 2018-12-06}
%
% \maketitle
%
% \begin{documentation}
%
% \end{documentation}
%
% \begin{implementation}
%
% \section{\texttt{l3fp-convert} implementation}
%
% \begin{macrocode}
%<*initex|package>
% \end{macrocode}
%
% \begin{macrocode}
%<@@=fp>
% \end{macrocode}
%
% \subsection{Dealing with tuples}
%
% \begin{macro}[EXP]
% {\@@_tuple_convert:Nw, \@@_tuple_convert_loop:nNw, \@@_tuple_convert_end:w}
% The first argument is for instance \cs{@@_to_tl_dispatch:w}, which
% converts any floating point object to the appropriate
% representation. We loop through all items, putting |,~| between all
% of them and making sure to remove the leading |,~|.
% \begin{macrocode}
\cs_new:Npn \@@_tuple_convert:Nw #1 \s_@@_tuple \@@_tuple_chk:w #2 ;
{
\int_case:nnF { \@@_array_count:n {#2} }
{
{ 0 } { ( ) }
{ 1 } { \@@_tuple_convert_end:w @ { #1 #2 , } }
}
{
\@@_tuple_convert_loop:nNw { } #1
#2 { ? \@@_tuple_convert_end:w } ;
@ { \use_none:nn }
}
}
\cs_new:Npn \@@_tuple_convert_loop:nNw #1#2#3#4; #5 @ #6
{
\use_none:n #3
\exp_args:Nf \@@_tuple_convert_loop:nNw { #2 #3#4 ; } #2 #5
@ { #6 , ~ #1 }
}
\cs_new:Npn \@@_tuple_convert_end:w #1 @ #2
{ \exp_after:wN ( \exp:w \exp_end_continue_f:w #2 ) }
% \end{macrocode}
% \end{macro}
%
% \subsection{Trimming trailing zeros}
%
% \begin{macro}[EXP]{\@@_trim_zeros:w}
% \begin{macro}[EXP]
% {\@@_trim_zeros_loop:w, \@@_trim_zeros_dot:w, \@@_trim_zeros_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 \@@_trim_zeros:w #1 ;
{
\@@_trim_zeros_loop:w #1
; \@@_trim_zeros_loop:w 0; \@@_trim_zeros_dot:w .; \s_stop
}
\cs_new:Npn \@@_trim_zeros_loop:w #1 0; #2 { #2 #1 ; #2 }
\cs_new:Npn \@@_trim_zeros_dot:w #1 .; { \@@_trim_zeros_end:w #1 ; }
\cs_new:Npn \@@_trim_zeros_end:w #1 ; #2 \s_stop { #1 }
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Scientific notation}
%
% \begin{macro}[EXP]
% {\fp_to_scientific:N, \fp_to_scientific:c, \fp_to_scientific:n}
% The three public functions evaluate their argument, then pass it to
% \cs{@@_to_scientific_dispatch:w}.
% \begin{macrocode}
\cs_new:Npn \fp_to_scientific:N #1
{ \exp_after:wN \@@_to_scientific_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_scientific:N { c }
\cs_new:Npn \fp_to_scientific:n
{
\exp_after:wN \@@_to_scientific_dispatch:w
\exp:w \exp_end_continue_f:w \@@_parse:n
}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]
% {\@@_to_scientific_dispatch:w, \@@_to_scientific_recover:w, \@@_tuple_to_scientific:w}
% We allow tuples.
% \begin{macrocode}
\cs_new:Npn \@@_to_scientific_dispatch:w #1
{
\@@_change_func_type:NNN
#1 \@@_to_scientific:w \@@_to_scientific_recover:w
#1
}
\cs_new:Npn \@@_to_scientific_recover:w #1 #2 ;
{
\@@_error:nffn { fp-unknown-type } { \tl_to_str:n { #2 ; } } { } { }
nan
}
\cs_new:Npn \@@_tuple_to_scientific:w
{ \@@_tuple_convert:Nw \@@_to_scientific_dispatch:w }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]
% {
% \@@_to_scientific:w,
% \@@_to_scientific_normal:wnnnnn,
% \@@_to_scientific_normal:wNw
% }
% Expressing an internal floating point number in scientific notation
% is quite easy: no rounding, and the format is very well defined.
% First cater for the sign: negative numbers ($|#2|=2$) start
% with~|-|; we then only need to care about positive numbers and
% \texttt{nan}. Then filter the special cases: $\pm0$~are represented
% as~|0|; infinities are converted to a number slightly larger than
% the largest after an \enquote{invalid_operation} exception;
% \texttt{nan} is represented as~|0| after an
% \enquote{invalid_operation} exception. In the normal case,
% decrement the exponent and unbrace the $4$ brace groups, then in a
% second step grab the first digit (previously hidden in braces) to
% order the various parts correctly.
% \begin{macrocode}
\cs_new:Npn \@@_to_scientific:w \s_@@ \@@_chk:w #1#2
{
\if_meaning:w 2 #2 \exp_after:wN - \exp:w \exp_end_continue_f:w \fi:
\if_case:w #1 \exp_stop_f:
\@@_case_return:nw { 0.000000000000000e0 }
\or: \exp_after:wN \@@_to_scientific_normal:wnnnnn
\or:
\@@_case_use:nw
{
\@@_invalid_operation:nnw
{ \fp_to_scientific:N \c_@@_overflowing_fp }
{ fp_to_scientific }
}
\or:
\@@_case_use:nw
{
\@@_invalid_operation:nnw
{ \fp_to_scientific:N \c_zero_fp }
{ fp_to_scientific }
}
\fi:
\s_@@ \@@_chk:w #1 #2
}
\cs_new:Npn \@@_to_scientific_normal:wnnnnn
\s_@@ \@@_chk:w 1 #1 #2 #3#4#5#6 ;
{
\exp_after:wN \@@_to_scientific_normal:wNw
\exp_after:wN e
\int_value:w \@@_int_eval:w #2 - 1
; #3 #4 #5 #6 ;
}
\cs_new:Npn \@@_to_scientific_normal:wNw #1 ; #2#3;
{ #2.#3 #1 }
% \end{macrocode}
% \end{macro}
%
% \subsection{Decimal representation}
%
% \begin{macro}[EXP]
% {\fp_to_decimal:N, \fp_to_decimal:c, \fp_to_decimal:n}
% All three public variants are based on the same
% \cs{@@_to_decimal_dispatch:w}
% after evaluating their argument to an internal floating point.
% \begin{macrocode}
\cs_new:Npn \fp_to_decimal:N #1
{ \exp_after:wN \@@_to_decimal_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_decimal:N { c }
\cs_new:Npn \fp_to_decimal:n
{
\exp_after:wN \@@_to_decimal_dispatch:w
\exp:w \exp_end_continue_f:w \@@_parse:n
}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]
% {\@@_to_decimal_dispatch:w, \@@_to_decimal_recover:w, \@@_tuple_to_decimal:w}
% We allow tuples.
% \begin{macrocode}
\cs_new:Npn \@@_to_decimal_dispatch:w #1
{
\@@_change_func_type:NNN
#1 \@@_to_decimal:w \@@_to_decimal_recover:w
#1
}
\cs_new:Npn \@@_to_decimal_recover:w #1 #2 ;
{
\@@_error:nffn { fp-unknown-type } { \tl_to_str:n { #2 ; } } { } { }
nan
}
\cs_new:Npn \@@_tuple_to_decimal:w
{ \@@_tuple_convert:Nw \@@_to_decimal_dispatch:w }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]
% {
% \@@_to_decimal:w,
% \@@_to_decimal_normal:wnnnnn,
% \@@_to_decimal_large:Nnnw,
% \@@_to_decimal_huge:wnnnn,
% }
% The structure is similar to \cs{@@_to_scientific:w}.
% Insert |-| for
% negative numbers. Zero gives $0$, $\pm\infty$ and \nan{} yield an
% \enquote{invalid operation} exception; note that $\pm\infty$
% produces a very large output, which we don't expand now since it
% most likely won't be needed. Normal numbers with an exponent in the
% range $[1,15]$ have that number of digits before the decimal
% separator: \enquote{decimate} them, and remove leading zeros with
% \cs{int_value:w}, then trim trailing zeros and dot. Normal
% numbers with an exponent $16$ or larger have no decimal separator,
% we only need to add trailing zeros. When the exponent is
% non-positive, the result should be $0.\meta{zeros}\meta{digits}$,
% trimmed.
% \begin{macrocode}
\cs_new:Npn \@@_to_decimal:w \s_@@ \@@_chk:w #1#2
{
\if_meaning:w 2 #2 \exp_after:wN - \exp:w \exp_end_continue_f:w \fi:
\if_case:w #1 \exp_stop_f:
\@@_case_return:nw { 0 }
\or: \exp_after:wN \@@_to_decimal_normal:wnnnnn
\or:
\@@_case_use:nw
{
\@@_invalid_operation:nnw
{ \fp_to_decimal:N \c_@@_overflowing_fp }
{ fp_to_decimal }
}
\or:
\@@_case_use:nw
{
\@@_invalid_operation:nnw
{ 0 }
{ fp_to_decimal }
}
\fi:
\s_@@ \@@_chk:w #1 #2
}
\cs_new:Npn \@@_to_decimal_normal:wnnnnn
\s_@@ \@@_chk:w 1 #1 #2 #3#4#5#6 ;
{
\int_compare:nNnTF {#2} > 0
{
\int_compare:nNnTF {#2} < \c_@@_prec_int
{
\@@_decimate:nNnnnn { \c_@@_prec_int - #2 }
\@@_to_decimal_large:Nnnw
}
{
\exp_after:wN \exp_after:wN
\exp_after:wN \@@_to_decimal_huge:wnnnn
\prg_replicate:nn { #2 - \c_@@_prec_int } { 0 } ;
}
{#3} {#4} {#5} {#6}
}
{
\exp_after:wN \@@_trim_zeros:w
\exp_after:wN 0
\exp_after:wN .
\exp:w \exp_end_continue_f:w \prg_replicate:nn { - #2 } { 0 }
#3#4#5#6 ;
}
}
\cs_new:Npn \@@_to_decimal_large:Nnnw #1#2#3#4;
{
\exp_after:wN \@@_trim_zeros:w \int_value:w
\if_int_compare:w #2 > 0 \exp_stop_f:
#2
\fi:
\exp_stop_f:
#3.#4 ;
}
\cs_new:Npn \@@_to_decimal_huge:wnnnn #1; #2#3#4#5 { #2#3#4#5 #1 }
% \end{macrocode}
% \end{macro}
%
% \subsection{Token list representation}
%
% \begin{macro}[EXP]{\fp_to_tl:N, \fp_to_tl:c, \fp_to_tl:n}
% These three public functions evaluate their argument, then pass it
% to \cs{@@_to_tl_dispatch:w}.
% \begin{macrocode}
\cs_new:Npn \fp_to_tl:N #1 { \exp_after:wN \@@_to_tl_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_tl:N { c }
\cs_new:Npn \fp_to_tl:n
{
\exp_after:wN \@@_to_tl_dispatch:w
\exp:w \exp_end_continue_f:w \@@_parse:n
}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\@@_to_tl_dispatch:w, \@@_to_tl_recover:w, \@@_tuple_to_tl:w}
% We allow tuples.
% \begin{macrocode}
\cs_new:Npn \@@_to_tl_dispatch:w #1
{ \@@_change_func_type:NNN #1 \@@_to_tl:w \@@_to_tl_recover:w #1 }
\cs_new:Npn \@@_to_tl_recover:w #1 #2 ;
{
\@@_error:nffn { fp-unknown-type } { \tl_to_str:n { #2 ; } } { } { }
nan
}
\cs_new:Npn \@@_tuple_to_tl:w
{ \@@_tuple_convert:Nw \@@_to_tl_dispatch:w }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]
% {
% \@@_to_tl:w, \@@_to_tl_normal:nnnnn,
% \@@_to_tl_scientific:wnnnnn, \@@_to_tl_scientific:wNw
% }
% A structure similar to \cs{@@_to_scientific_dispatch:w} and
% \cs{@@_to_decimal_dispatch:w}, but without the \enquote{invalid operation}
% exception. First filter special cases. We express normal numbers
% in decimal notation if the exponent is in the range $[-2,16]$, and
% otherwise use scientific notation.
% \begin{macrocode}
\cs_new:Npn \@@_to_tl:w \s_@@ \@@_chk:w #1#2
{
\if_meaning:w 2 #2 \exp_after:wN - \exp:w \exp_end_continue_f:w \fi:
\if_case:w #1 \exp_stop_f:
\@@_case_return:nw { 0 }
\or: \exp_after:wN \@@_to_tl_normal:nnnnn
\or: \@@_case_return:nw { inf }
\else: \@@_case_return:nw { nan }
\fi:
}
\cs_new:Npn \@@_to_tl_normal:nnnnn #1
{
\int_compare:nTF
{ -2 <= #1 <= \c_@@_prec_int }
{ \@@_to_decimal_normal:wnnnnn }
{ \@@_to_tl_scientific:wnnnnn }
\s_@@ \@@_chk:w 1 0 {#1}
}
\cs_new:Npn \@@_to_tl_scientific:wnnnnn
\s_@@ \@@_chk:w 1 #1 #2 #3#4#5#6 ;
{
\exp_after:wN \@@_to_tl_scientific:wNw
\exp_after:wN e
\int_value:w \@@_int_eval:w #2 - 1
; #3 #4 #5 #6 ;
}
\cs_new:Npn \@@_to_tl_scientific:wNw #1 ; #2#3;
{ \@@_trim_zeros:w #2.#3 ; #1 }
% \end{macrocode}
% \end{macro}
%
% \subsection{Formatting}
%
% This is not implemented yet, as it is not yet clear what a correct
% interface would be, for this kind of structured conversion from a
% floating point (or other types of variables) to a string. Ideas
% welcome.
%
% \subsection{Convert to dimension or integer}
%
% \begin{macro}[EXP]{\fp_to_dim:N, \fp_to_dim:c, \fp_to_dim:n}
% \begin{macro}[EXP]{\@@_to_dim_dispatch:w, \@@_to_dim_recover:w, \@@_to_dim:w}
% All three public variants are based on the same
% \cs{@@_to_dim_dispatch:w} after evaluating their argument to an
% internal floating point.
% We only allow floating point numbers, not tuples.
% \begin{macrocode}
\cs_new:Npn \fp_to_dim:N #1
{ \exp_after:wN \@@_to_dim_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_dim:N { c }
\cs_new:Npn \fp_to_dim:n
{
\exp_after:wN \@@_to_dim_dispatch:w
\exp:w \exp_end_continue_f:w \@@_parse:n
}
\cs_new:Npn \@@_to_dim_dispatch:w #1#2 ;
{
\@@_change_func_type:NNN #1 \@@_to_dim:w \@@_to_dim_recover:w
#1 #2 ;
}
\cs_new:Npn \@@_to_dim_recover:w #1
{ \@@_invalid_operation:nnw { 0pt } { fp_to_dim } }
\cs_new:Npn \@@_to_dim:w #1 ; { \@@_to_decimal:w #1 ; pt }
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[EXP]{\fp_to_int:N, \fp_to_int:c, \fp_to_int:n}
% \begin{macro}[EXP]{\@@_to_int_dispatch:w, \@@_to_int_recover:w}
% For the most part identical to \cs{fp_to_dim:N} but without |pt|,
% and where \cs{@@_to_int:w} does more work.
% To convert to an integer, first round to $0$ places (to the nearest
% integer), then express the result as a decimal number: the
% definition of \cs{@@_to_decimal_dispatch:w} is such that there are no
% trailing dot nor zero.
% \begin{macrocode}
\cs_new:Npn \fp_to_int:N #1 { \exp_after:wN \@@_to_int_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_int:N { c }
\cs_new:Npn \fp_to_int:n
{
\exp_after:wN \@@_to_int_dispatch:w
\exp:w \exp_end_continue_f:w \@@_parse:n
}
\cs_new:Npn \@@_to_int_dispatch:w #1#2 ;
{
\@@_change_func_type:NNN #1 \@@_to_int:w \@@_to_int_recover:w
#1 #2 ;
}
\cs_new:Npn \@@_to_int_recover:w #1
{ \@@_invalid_operation:nnw { 0 } { fp_to_int } }
\cs_new:Npn \@@_to_int:w #1;
{
\exp_after:wN \@@_to_decimal:w \exp:w \exp_end_continue_f:w
\@@_round:Nwn \@@_round_to_nearest:NNN #1; { 0 }
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Convert from a dimension}
%
% \begin{macro}[EXP]{\dim_to_fp:n}
% \begin{macro}[EXP]
% {
% \@@_from_dim_test:ww,
% \@@_from_dim:wNw,
% \@@_from_dim:wNNnnnnnn,
% \@@_from_dim:wnnnnwNw,
% }
% The dimension expression (which can in fact be a glue expression) is
% evaluated, converted to a number (\emph{i.e.}, expressed in scaled
% points), then multiplied by $2^{-16} = 0.0000152587890625$ to give a
% value expressed in points. The auxiliary \cs{@@_mul_npos_o:Nww}
% expects the desired \meta{final sign} and two floating point
% operands (of the form \cs{s_@@} \ldots{} |;|) as arguments.
% This set of functions is also used to convert dimension registers to
% floating points while parsing expressions: in this context there is
% an additional exponent, which is the first argument of
% \cs{@@_from_dim_test:ww}, and is combined with the exponent $-4$
% of $2^{-16}$. There is also a need to expand afterwards: this is
% performed by \cs{@@_mul_npos_o:Nww}, and cancelled by
% \cs{prg_do_nothing:} here.
% \begin{macrocode}
\__kernel_patch_args:nNNpn { { (#1) } }
\cs_new:Npn \dim_to_fp:n #1
{
\exp_after:wN \@@_from_dim_test:ww
\exp_after:wN 0
\exp_after:wN ,
\int_value:w \tex_glueexpr:D #1 ;
}
\cs_new:Npn \@@_from_dim_test:ww #1, #2
{
\if_meaning:w 0 #2
\@@_case_return:nw { \exp_after:wN \c_zero_fp }
\else:
\exp_after:wN \@@_from_dim:wNw
\int_value:w \@@_int_eval:w #1 - 4
\if_meaning:w - #2
\exp_after:wN , \exp_after:wN 2 \int_value:w
\else:
\exp_after:wN , \exp_after:wN 0 \int_value:w #2
\fi:
\fi:
}
\cs_new:Npn \@@_from_dim:wNw #1,#2#3;
{
\@@_pack_twice_four:wNNNNNNNN \@@_from_dim:wNNnnnnnn ;
#3 000 0000 00 {10}987654321; #2 {#1}
}
\cs_new:Npn \@@_from_dim:wNNnnnnnn #1; #2#3#4#5#6#7#8#9
{ \@@_from_dim:wnnnnwNn #1 {#2#300} {0000} ; }
\cs_new:Npn \@@_from_dim:wnnnnwNn #1; #2#3#4#5#6; #7#8
{
\@@_mul_npos_o:Nww #7
\s_@@ \@@_chk:w 1 #7 {#5} #1 ;
\s_@@ \@@_chk:w 1 0 {#8} {1525} {8789} {0625} {0000} ;
\prg_do_nothing:
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Use and eval}
%
% \begin{macro}[EXP]{\fp_use:N, \fp_use:c, \fp_eval:n}
% Those public functions are simple copies of the decimal conversions.
% \begin{macrocode}
\cs_new_eq:NN \fp_use:N \fp_to_decimal:N
\cs_generate_variant:Nn \fp_use:N { c }
\cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\fp_abs:n}
% Trivial but useful. See the implementation of \cs{fp_add:Nn} for an
% explanation of why to use \cs{@@_parse:n}, namely, for better error
% reporting.
% \begin{macrocode}
\cs_new:Npn \fp_abs:n #1
{ \fp_to_decimal:n { abs \@@_parse:n {#1} } }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\fp_max:nn, \fp_min:nn}
% Similar to \cs{fp_abs:n}, for consistency with \cs{int_max:nn}, \emph{etc.}
% \begin{macrocode}
\cs_new:Npn \fp_max:nn #1#2
{ \fp_to_decimal:n { max ( \@@_parse:n {#1} , \@@_parse:n {#2} ) } }
\cs_new:Npn \fp_min:nn #1#2
{ \fp_to_decimal:n { min ( \@@_parse:n {#1} , \@@_parse:n {#2} ) } }
% \end{macrocode}
% \end{macro}
%
% \subsection{Convert an array of floating points to a comma list}
%
% \begin{macro}[EXP]{\@@_array_to_clist:n}
% \begin{macro}[EXP]{\@@_array_to_clist_loop:Nw}
% Converts an array of floating point numbers to a comma-list. If
% speed here ends up irrelevant, we can simplify the code for the
% auxiliary to become
% \begin{verbatim}
% \cs_new:Npn \__fp_array_to_clist_loop:Nw #1#2;
% {
% \use_none:n #1
% { , ~ } \fp_to_tl:n { #1 #2 ; }
% \__fp_array_to_clist_loop:Nw
% }
% \end{verbatim}
% The \cs{use_ii:nn} function is expanded after \cs{@@_expand:n} is
% done, and it removes |,~| from the start of the representation.
% \begin{macrocode}
\cs_new:Npn \@@_array_to_clist:n #1
{
\tl_if_empty:nF {#1}
{
\@@_expand:n
{
{ \use_ii:nn }
\@@_array_to_clist_loop:Nw #1 { ? \prg_break: } ;
\prg_break_point:
}
}
}
\cs_new:Npx \@@_array_to_clist_loop:Nw #1#2;
{
\exp_not:N \use_none:n #1
\exp_not:N \exp_after:wN
{
\exp_not:N \exp_after:wN ,
\exp_not:N \exp_after:wN \c_space_tl
\exp_not:N \exp:w
\exp_not:N \exp_end_continue_f:w
\exp_not:N \@@_to_tl_dispatch:w #1 #2 ;
}
\exp_not:N \@@_array_to_clist_loop:Nw
}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macrocode}
%</initex|package>
% \end{macrocode}
%
% \end{implementation}
%
% \PrintChanges
%
% \PrintIndex
|