% \iffalse meta-comment % %% File: l3fp-logic.dtx Copyright (C) 2011-2014 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> \documentclass[full]{l3doc} \GetIdInfo$Id: l3fp-logic.dtx 5354 2014-08-23 01:35:39Z bruno $ {L3 Floating-point conditionals} \begin{document} \DocInput{\jobname.dtx} \end{document} % % \fi % % \title{The \textsf{l3fp-logic} package\thanks{This file % has version number \ExplFileVersion, last % revised \ExplFileDate.}\\ % Floating point conditionals} % \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-logic} Implementation} % % \begin{macrocode} %<*initex|package> % \end{macrocode} % % \begin{macrocode} %<@@=fp> % \end{macrocode} % % \subsection{Syntax of internal functions} % % \begin{itemize} % \item \cs{@@_compare_npos:nwnw} \Arg{expo_1} \meta{body_1} |;| % \Arg{expo_2} \meta{body_2} |;| % \item \cs{@@_minmax_o:Nw} \meta{sign} \meta{floating point array} % \item \cs{@@_not_o:w} |?| \meta{floating point array} (with one floating point number only) % \item \cs{@@_\string&_o:ww} \meta{floating point} \meta{floating point} % \item \cs{@@_\string|_o:ww} \meta{floating point} \meta{floating point} % \item \cs{@@_ternary:NwwN}, \cs{@@_ternary_auxi:NwwN}, % \cs{@@_ternary_auxii:NwwN} have to be understood. % \end{itemize} % % \subsection{Existence test} % % \begin{macro}[pTF]{\fp_if_exist:N, \fp_if_exist:c} % Copies of the \texttt{cs} functions defined in \pkg{l3basics}. % \begin{macrocode} \prg_new_eq_conditional:NNn \fp_if_exist:N \cs_if_exist:N { TF , T , F , p } \prg_new_eq_conditional:NNn \fp_if_exist:c \cs_if_exist:c { TF , T , F , p } % \end{macrocode} % \end{macro} % % \subsection{Comparison} % % \begin{macro}[pTF, EXP]{\fp_compare:n} % \begin{macro}[aux, EXP]{\@@_compare_return:w} % Within floating point expressions, comparison operators are treated % as operations, so we evaluate |#1|, then compare with $0$. % \begin{macrocode} \prg_new_conditional:Npnn \fp_compare:n #1 { p , T , F , TF } { \exp_after:wN \@@_compare_return:w \tex_romannumeral:D -`0 \@@_parse:n {#1} } \cs_new:Npn \@@_compare_return:w \s_@@ \@@_chk:w #1#2; { \if_meaning:w 0 #1 \prg_return_false: \else: \prg_return_true: \fi: } % \end{macrocode} % \end{macro} % \end{macro} % % \begin{macro}[pTF, EXP]{\fp_compare:nNn} % \begin{macro}[aux, EXP]{\@@_compare_aux:wn} % Evaluate |#1| and |#3|, using an auxiliary to expand both, and feed % the two floating point numbers swapped to \cs{@@_compare_back:ww}, % defined below. Compare the result with |`#2-`=|, which is $-1$ for % |<|, $0$ for |=|, $1$ for |>| and $2$ for |?|. % \begin{macrocode} \prg_new_conditional:Npnn \fp_compare:nNn #1#2#3 { p , T , F , TF } { \if_int_compare:w \exp_after:wN \@@_compare_aux:wn \tex_romannumeral:D -`0 \@@_parse:n {#1} {#3} = \__int_eval:w `#2 - `= \__int_eval_end: \prg_return_true: \else: \prg_return_false: \fi: } \cs_new:Npn \@@_compare_aux:wn #1; #2 { \exp_after:wN \@@_compare_back:ww \tex_romannumeral:D -`0 \@@_parse:n {#2} #1; } % \end{macrocode} % \end{macro} % \end{macro} % % \begin{macro}[aux, EXP]{\@@_compare_back:ww, \@@_compare_nan:w} % \begin{quote} % \cs{@@_compare_back:ww} \meta{y} |;| \meta{x} |;| % \end{quote} % Expands (in the same way as \cs{int_eval:n}) to $-1$ if $xy$, and $2$ otherwise (denoted as $x?y$). If % either operand is \texttt{nan}, stop the comparison with % \cs{@@_compare_nan:w} returning $2$. If $x$ is negative, swap the % outputs $1$ and $-1$ (\emph{i.e.}, $>$ and $<$); we can henceforth % assume that $x\geq 0$. If $y\geq 0$, and they have the same type, % either they are normal and we compare them with % \cs{@@_compare_npos:nwnw}, or they are equal. If $y\geq 0$, but of % a different type, the highest type is a larger number. Finally, if % $y\leq 0$, then $x>y$, unless both are zero. % \begin{macrocode} \cs_new:Npn \@@_compare_back:ww \s_@@ \@@_chk:w #1 #2 #3; \s_@@ \@@_chk:w #4 #5 #6; { \__int_value:w \if_meaning:w 3 #1 \exp_after:wN \@@_compare_nan:w \fi: \if_meaning:w 3 #4 \exp_after:wN \@@_compare_nan:w \fi: \if_meaning:w 2 #5 - \fi: \if_meaning:w #2 #5 \if_meaning:w #1 #4 \if_meaning:w 1 #1 \@@_compare_npos:nwnw #6; #3; \else: 0 \fi: \else: \if_int_compare:w #4 < #1 - \fi: 1 \fi: \else: \if_int_compare:w #1#4 = \c_zero 0 \else: 1 \fi: \fi: \exp_stop_f: } \cs_new:Npn \@@_compare_nan:w #1 \exp_stop_f: { \c_two } % \end{macrocode} % \end{macro} % % \begin{macro}[int, EXP]{\@@_compare_npos:nwnw} % \begin{macro}[aux, EXP]{\@@_compare_significand:nnnnnnnn} % \begin{quote} % \cs{@@_compare_npos:nwnw} % \Arg{expo_1} \meta{body_1} |;| % \Arg{expo_2} \meta{body_2} |;| % \end{quote} % Within an \cs{__int_value:w} \ldots{} \cs{exp_stop_f:} construction, % this expands to $0$ if the two numbers are equal, $-1$ if the first % is smaller, and $1$ if the first is bigger. First compare the % exponents: the larger one denotes the larger number. If they are % equal, we must compare significands. If both the first $8$ digits and % the next $8$ digits coincide, the numbers are equal. If only the % first $8$ digits coincide, the next $8$ decide. Otherwise, the % first $8$ digits are compared. % \begin{macrocode} \cs_new:Npn \@@_compare_npos:nwnw #1#2; #3#4; { \if_int_compare:w #1 = #3 \exp_stop_f: \@@_compare_significand:nnnnnnnn #2 #4 \else: \if_int_compare:w #1 < #3 - \fi: 1 \fi: } \cs_new:Npn \@@_compare_significand:nnnnnnnn #1#2#3#4#5#6#7#8 { \if_int_compare:w #1#2 = #5#6 \exp_stop_f: \if_int_compare:w #3#4 = #7#8 \exp_stop_f: 0 \else: \if_int_compare:w #3#4 < #7#8 - \fi: 1 \fi: \else: \if_int_compare:w #1#2 < #5#6 - \fi: 1 \fi: } % \end{macrocode} % \end{macro} % \end{macro} % % \subsection{Floating point expression loops} % % \begin{macro}[rEXP] % { % \fp_do_until:nn, \fp_do_while:nn, % \fp_until_do:nn, \fp_while_do:nn % } % These are quite easy given the above functions. The |do_until| and % |do_while| versions execute the body, then test. The |until_do| and % |while_do| do it the other way round. % \begin{macrocode} \cs_new:Npn \fp_do_until:nn #1#2 { #2 \fp_compare:nF {#1} { \fp_do_until:nn {#1} {#2} } } \cs_new:Npn \fp_do_while:nn #1#2 { #2 \fp_compare:nT {#1} { \fp_do_while:nn {#1} {#2} } } \cs_new:Npn \fp_until_do:nn #1#2 { \fp_compare:nF {#1} { #2 \fp_until_do:nn {#1} {#2} } } \cs_new:Npn \fp_while_do:nn #1#2 { \fp_compare:nT {#1} { #2 \fp_while_do:nn {#1} {#2} } } % \end{macrocode} % \end{macro} % % \begin{macro}[rEXP] % { % \fp_do_until:nNnn, \fp_do_while:nNnn, % \fp_until_do:nNnn, \fp_while_do:nNnn % } % As above but not using the |nNn| syntax. % \begin{macrocode} \cs_new:Npn \fp_do_until:nNnn #1#2#3#4 { #4 \fp_compare:nNnF {#1} #2 {#3} { \fp_do_until:nNnn {#1} #2 {#3} {#4} } } \cs_new:Npn \fp_do_while:nNnn #1#2#3#4 { #4 \fp_compare:nNnT {#1} #2 {#3} { \fp_do_while:nNnn {#1} #2 {#3} {#4} } } \cs_new:Npn \fp_until_do:nNnn #1#2#3#4 { \fp_compare:nNnF {#1} #2 {#3} { #4 \fp_until_do:nNnn {#1} #2 {#3} {#4} } } \cs_new:Npn \fp_while_do:nNnn #1#2#3#4 { \fp_compare:nNnT {#1} #2 {#3} { #4 \fp_while_do:nNnn {#1} #2 {#3} {#4} } } % \end{macrocode} % \end{macro} % % \subsection{Extrema} % % \begin{macro}[int, EXP]{\@@_minmax_o:Nw} % The argument~|#1| is $2$~to find the maximum of an array~|#2| of % floating point numbers, and $0$~to find the minimum. We read % numbers sequentially, keeping track of the largest (smallest) number % found so far. If numbers are equal (for instance~$\pm0$), the first % is kept. We append $-\infty$ ($\infty$), for the case of an empty % array, currently impossible. Since no number is smaller (larger) % than that, it will never alter the maximum (minimum). The weird % fp-like trailing marker breaks the loop correctly: see the precise % definition of \cs{@@_minmax_loop:Nww}. % \begin{macrocode} \cs_new:Npn \@@_minmax_o:Nw #1#2 @ { \if_meaning:w 0 #1 \exp_after:wN \@@_minmax_loop:Nww \exp_after:wN \c_one \else: \exp_after:wN \@@_minmax_loop:Nww \exp_after:wN \c_minus_one \fi: #2 \s_@@ \@@_chk:w 2 #1 \s_@@_exact ; \s_@@ \@@_chk:w { 3 \@@_minmax_break_o:w } ; } % \end{macrocode} % \end{macro} % % \begin{macro}[aux, EXP]{\@@_minmax_loop:Nww} % The first argument is $-1$ or $1$ to denote the case where the % currently largest (smallest) number found (first floating point % argument) should be replaced by the new number (second floating % point argument). If the new number is \texttt{nan}, keep that as % the extremum, unless that extremum is already a \texttt{nan}. % Otherwise, compare the two numbers. If the new number is larger (in % the case of |max|) or smaller (in the case of |min|), the test % yields \texttt{true}, and we keep the second number as a new % maximum; otherwise we keep the first number. Then loop. % \begin{macrocode} \cs_new:Npn \@@_minmax_loop:Nww #1 \s_@@ \@@_chk:w #2#3; \s_@@ \@@_chk:w #4#5; { \if_meaning:w 3 #4 \if_meaning:w 3 #2 \@@_minmax_auxi:ww \else: \@@_minmax_auxii:ww \fi: \else: \if_int_compare:w \@@_compare_back:ww \s_@@ \@@_chk:w #4#5; \s_@@ \@@_chk:w #2#3; = #1 \@@_minmax_auxii:ww \else: \@@_minmax_auxi:ww \fi: \fi: \@@_minmax_loop:Nww #1 \s_@@ \@@_chk:w #2#3; \s_@@ \@@_chk:w #4#5; } % \end{macrocode} % \end{macro} % % \begin{macro}[aux, EXP]{\@@_minmax_auxi:ww, \@@_minmax_auxii:ww} % Keep the first/second number, and remove the other. % \begin{macrocode} \cs_new:Npn \@@_minmax_auxi:ww #1 \fi: \fi: #2 \s_@@ #3 ; \s_@@ #4; { \fi: \fi: #2 \s_@@ #3 ; } \cs_new:Npn \@@_minmax_auxii:ww #1 \fi: \fi: #2 \s_@@ #3 ; { \fi: \fi: #2 } % \end{macrocode} % \end{macro} % % \begin{macro}[aux, EXP]{\@@_minmax_break_o:w} % This function is called from within an \cs{if_meaning:w} test. Skip % to the end of the tests, close the current test with \cs{fi:}, clean % up, and return the appropriate number with one post-expansion. % \begin{macrocode} \cs_new:Npn \@@_minmax_break_o:w #1 \fi: \fi: #2 \s_@@ #3; #4; { \fi: \@@_exp_after_o:w \s_@@ #3; } % \end{macrocode} % \end{macro} % % \subsection{Boolean operations} % % \begin{macro}[int, EXP]{\@@_not_o:w} % Return \texttt{true} or \texttt{false}, with two expansions, one to % exit the conditional, and one to please \pkg{l3fp-parse}. The first % argument is provided by \pkg{l3fp-parse} and is ignored. % \begin{macrocode} \cs_new:cpn { @@_not_o:w } #1 \s_@@ \@@_chk:w #2#3; @ { \if_meaning:w 0 #2 \exp_after:wN \exp_after:wN \exp_after:wN \c_one_fp \else: \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp \fi: } % \end{macrocode} % \end{macro} % % \begin{macro}[int, EXP]+\@@_&_o:ww+ % \begin{macro}[int, EXP]+\@@_|_o:ww+ % \begin{macro}[aux, EXP]{\@@_and_return:wNw} % For \texttt{and}, if the first number is zero, return it (with the % same sign). Otherwise, return the second one. For \texttt{or}, the % logic is reversed: if the first number is non-zero, return it, % otherwise return the second number: we achieve that by hi-jacking % \cs{@@_\&_o:ww}, inserting an extra argument, \cs{else:}, before % \cs{s_@@}. In all cases, expand after the floating point number. % \begin{macrocode} \group_begin: \char_set_catcode_letter:N & \char_set_catcode_letter:N | \cs_new:Npn \@@_&_o:ww #1 \s_@@ \@@_chk:w #2#3; { \if_meaning:w 0 #2 #1 \@@_and_return:wNw \s_@@ \@@_chk:w #2#3; \fi: \@@_exp_after_o:w } \cs_new_nopar:Npn \@@_|_o:ww { \@@_&_o:ww \else: } \group_end: \cs_new:Npn \@@_and_return:wNw #1; \fi: #2#3; { \fi: #2 #1; } % \end{macrocode} % \end{macro} % \end{macro} % \end{macro} % % \subsection{Ternary operator} % %^^A todo: understand and optimize. % \begin{macro}[int, EXP] % {\@@_ternary:NwwN, \@@_ternary_auxi:NwwN, \@@_ternary_auxii:NwwN} % \begin{macro}[aux, EXP] % { % \@@_ternary_loop_break:w, \@@_ternary_loop:Nw, % \@@_ternary_map_break:, \@@_ternary_break_point:n % } % The first function receives the test and the true branch of the |?:| % ternary operator. It returns the true branch, unless the test % branch is zero. In that case, the function returns a very specific % \texttt{nan}. The second function receives the output of the first % function, and the false branch. It returns the previous input, % unless that is the special \texttt{nan}, in which case we return the % false branch. % \begin{macrocode} \cs_new:Npn \@@_ternary:NwwN #1 #2@ #3@ #4 { \if_meaning:w \@@_parse_infix_::N #4 \@@_ternary_loop:Nw #2 \s_@@ \@@_chk:w { \@@_ternary_loop_break:w } ; \@@_ternary_break_point:n { \exp_after:wN \@@_ternary_auxi:NwwN } \exp_after:wN #1 \tex_romannumeral:D -`0 \@@_exp_after_array_f:w #3 \s_@@_stop \exp_after:wN @ \tex_romannumeral:D \@@_parse_operand:Nw \c_two \@@_parse_expand:w \else: \__msg_kernel_expandable_error:nnnn { kernel } { fp-missing } { : } { ~for~?: } \exp_after:wN \@@_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \@@_exp_after_array_f:w #3 \s_@@_stop \exp_after:wN #4 \exp_after:wN #1 \fi: } \cs_new:Npn \@@_ternary_loop_break:w #1 \fi: #2 \@@_ternary_break_point:n #3 { \c_zero = \c_zero \fi: \exp_after:wN \@@_ternary_auxii:NwwN } \cs_new:Npn \@@_ternary_loop:Nw \s_@@ \@@_chk:w #1#2; { \if_int_compare:w #1 > \c_zero \exp_after:wN \@@_ternary_map_break: \fi: \@@_ternary_loop:Nw } \cs_new:Npn \@@_ternary_map_break: #1 \@@_ternary_break_point:n #2 {#2} \cs_new:Npn \@@_ternary_auxi:NwwN #1#2@#3@#4 { \exp_after:wN \@@_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \@@_exp_after_array_f:w #2 \s_@@_stop #4 #1 } \cs_new:Npn \@@_ternary_auxii:NwwN #1#2@#3@#4 { \exp_after:wN \@@_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \@@_exp_after_array_f:w #3 \s_@@_stop #4 #1 } % \end{macrocode} % \end{macro} % \end{macro} % % \begin{macrocode} % % \end{macrocode} % % \end{implementation} % % \PrintChanges % % \PrintIndex