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% \iffalse meta-comment
%%
%% File: l3fp-assign.dtx Copyright (C) 2011-2012 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
%%
%% http://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 released version of this bundle is available from CTAN.
%%
%% -----------------------------------------------------------------------
%%
%% The development version of the bundle can be found at
%%
%% http://www.latex-project.org/svnroot/experimental/trunk/
%%
%% for those people who are interested.
%%
%%%%%%%%%%%
%% NOTE: %%
%%%%%%%%%%%
%%
%% Snapshots taken from the repository represent work in progress and may
%% not work or may contain conflicting material! We therefore ask
%% people _not_ to put them into distributions, archives, etc. without
%% prior consultation with the LaTeX Project Team.
%%
%% -----------------------------------------------------------------------
%%
%
%<*driver>
\RequirePackage{l3bootstrap}
\GetIdInfo$Id: l3fp-assign.dtx 4082 2012-08-12 12:14:17Z bruno $
{L3 Floating-point assignments}
\documentclass[full]{l3doc}
\begin{document}
\DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
% \title{The \textsf{l3fp-assign} package\thanks{This file
% has version number \ExplFileVersion, last
% revised \ExplFileDate.}\\
% Floating point expressions}
% \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 \ExplFileDate}
% \maketitle
%
% \begin{documentation}
%
% \end{documentation}
%
% \begin{implementation}
%
% \section{\pkg{l3fp-assign} implementation}
%
% \begin{macrocode}
%<*initex|package>
% \end{macrocode}
%
% \begin{macrocode}
%<@@=fp>
% \end{macrocode}
%
% \subsection{Assigning values}
%
% \begin{macro}{\fp_new:N}
% Floating point variables are initialized to be $+0$.
% \begin{macrocode}
\cs_new_protected:Npn \fp_new:N #1
{ \cs_new_eq:NN #1 \c_zero_fp }
\cs_generate_variant:Nn \fp_new:N {c}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}
% {
% \fp_set:Nn, \fp_set:cn,
% \fp_gset:Nn, \fp_gset:cn,
% \fp_const:Nn, \fp_const:cn
% }
% Simply use \cs{@@_parse:n} within various \texttt{x}-expanding
% assignments.
% \begin{macrocode}
\cs_new_protected:Npn \fp_set:Nn #1#2
{ \tl_set:Nx #1 { \@@_parse:n {#2} } }
\cs_new_protected:Npn \fp_gset:Nn #1#2
{ \tl_gset:Nx #1 { \@@_parse:n {#2} } }
\cs_new_protected:Npn \fp_const:Nn #1#2
{ \tl_const:Nx #1 { \@@_parse:n {#2} } }
\cs_generate_variant:Nn \fp_set:Nn {c}
\cs_generate_variant:Nn \fp_gset:Nn {c}
\cs_generate_variant:Nn \fp_const:Nn {c}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}
% {
% \fp_set_eq:NN , \fp_set_eq:cN , \fp_set_eq:Nc , \fp_set_eq:cc,
% \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc
% }
% Copying a floating point is the same as copying the underlying token
% list.
% \begin{macrocode}
\cs_new_eq:NN \fp_set_eq:NN \tl_set_eq:NN
\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
\cs_generate_variant:Nn \fp_set_eq:NN { c , Nc , cc }
\cs_generate_variant:Nn \fp_gset_eq:NN { c , Nc , cc }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fp_zero:N, \fp_zero:c, \fp_gzero:N, \fp_gzero:c}
% Setting a floating point to zero: copy \cs{c_zero_fp}.
% \begin{macrocode}
\cs_new_protected:Npn \fp_zero:N #1 { \fp_set_eq:NN #1 \c_zero_fp }
\cs_new_protected:Npn \fp_gzero:N #1 { \fp_gset_eq:NN #1 \c_zero_fp }
\cs_generate_variant:Nn \fp_zero:N { c }
\cs_generate_variant:Nn \fp_gzero:N { c }
% \end{macrocode}
% \end{macro}
%
% \begin{macro}
% {\fp_zero_new:N, \fp_zero_new:c, \fp_gzero_new:N, \fp_gzero_new:c}
% Set the floating point to zero, or define it if needed.
% \begin{macrocode}
\cs_new_protected:Npn \fp_zero_new:N #1
{ \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
\cs_new_protected:Npn \fp_gzero_new:N #1
{ \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
\cs_generate_variant:Nn \fp_zero_new:N { c }
\cs_generate_variant:Nn \fp_gzero_new:N { c }
% \end{macrocode}
% \end{macro}
%
% \subsection{Updating values}
%
% These match the equivalent functions in \pkg{l3int} and \pkg{l3skip}.
%
% \begin{macro}
% {
% \fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn,
% \fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn,
% }
% \begin{macro}[aux]{\@@_add:NNNn}
% For the sake of error recovery we should not simply set |#1| to
% $|#1| \pm (|#2|)$: for instance, if |#2| is % ^^A(
% |0)+2|, the parsing error would be raised at the last closing
% parenthesis rather than at the closing parenthesis in the user
% argument. Thus we evaluate |#2| instead of just putting
% parentheses. As an optimization we use \cs{@@_parse:n} rather than
% \cs{fp_eval:n}, which would convert the result away from the
% internal representation and back.
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_add:Nn { \@@_add:NNNn \fp_set:Nn + }
\cs_new_protected_nopar:Npn \fp_gadd:Nn { \@@_add:NNNn \fp_gset:Nn + }
\cs_new_protected_nopar:Npn \fp_sub:Nn { \@@_add:NNNn \fp_set:Nn - }
\cs_new_protected_nopar:Npn \fp_gsub:Nn { \@@_add:NNNn \fp_gset:Nn - }
\cs_new_protected:Npn \@@_add:NNNn #1#2#3#4
{ #1 #3 { #3 #2 \@@_parse:n {#4} } }
\cs_generate_variant:Nn \fp_add:Nn { c }
\cs_generate_variant:Nn \fp_gadd:Nn { c }
\cs_generate_variant:Nn \fp_sub:Nn { c }
\cs_generate_variant:Nn \fp_gsub:Nn { c }
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Showing values}
%
% \begin{macro}{\fp_show:N, \fp_show:c, \fp_show:n}
% This shows the result of computing its argument. The
% \cs{__msg_show_variable:x} auxiliary expects its input in a slightly odd
% form, starting with |>|, and displays the rest.
% \begin{macrocode}
\cs_new_protected:Npn \fp_show:N #1
{ \__msg_show_variable:x { > \fp_to_tl:N #1 } }
\cs_new_protected:Npn \fp_show:n #1
{ \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
\cs_generate_variant:Nn \fp_show:N { c }
% \end{macrocode}
% \end{macro}
%
% \subsection{Some useful constants and scratch variables}
%
% \begin{variable}{\c_one_fp, \c_e_fp}
% Some constants.
% \begin{macrocode}
\fp_const:Nn \c_e_fp { 2.718 2818 2845 9045 }
\fp_const:Nn \c_one_fp { 1 }
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\c_pi_fp, \c_one_degree_fp}
% We do not round $\pi$ to the closest multiple of $10^{-15}$, which
% would underestimate it by roughly $2.4\cdot 10^{-16}$, but instead
% round it up to the next nearest multiple, which is an overestimate
% by roughly $7.7\cdot 10^{-16}$. This particular choice of rounding
% has very nice properties: it is exactly divisible by $4$ and by
% $180$ as a $16$-digit precision floating point number, hence
% ensuring that $\sin(180\mathrm{deg}) = \sin(\pi) = 0$ exactly, with
% no rounding artifact.
% \begin{macrocode}
\fp_const:Nn \c_pi_fp { 3.141 5926 5358 9794 }
\fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 }
% \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_tmpa_fp, \l_tmpb_fp, \g_tmpa_fp, \g_tmpb_fp}
% Scratch variables are simply initialized there.
% \begin{macrocode}
\fp_new:N \l_tmpa_fp
\fp_new:N \l_tmpb_fp
\fp_new:N \g_tmpa_fp
\fp_new:N \g_tmpb_fp
% \end{macrocode}
% \end{variable}
%
% \begin{macrocode}
%</initex|package>
% \end{macrocode}
%
% \end{implementation}
%
% \PrintChanges
%
% \PrintIndex
|
