diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx | 84 |
1 files changed, 42 insertions, 42 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx index 32b3340cabe..f5ffadf5220 100644 --- a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx +++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx @@ -1,13 +1,13 @@ % \iffalse meta-comment % -%% File: l3fp-trig.dtx Copyright (C) 2011-2014,2016,2017 The LaTeX3 Project +%% File: l3fp-trig.dtx Copyright (C) 2011-2017 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 +% 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. @@ -21,7 +21,7 @@ % for those people who are interested. % %<*driver> -\documentclass[full]{l3doc} +\documentclass[full,kernel]{l3doc} \begin{document} \DocInput{\jobname.dtx} \end{document} @@ -38,7 +38,7 @@ % {latex-team@latex-project.org}^^A % }^^A % } -% \date{Released 2017/11/14} +% \date{Released 2017/12/05} % % \maketitle % @@ -58,7 +58,7 @@ %<@@=fp> % \end{macrocode} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % { % \@@_parse_word_acos:N , % \@@_parse_word_acosd:N , @@ -105,7 +105,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % { % \@@_parse_word_acot:N , \@@_parse_word_acotd:N, % \@@_parse_word_atan:N , \@@_parse_word_atand:N, @@ -149,7 +149,7 @@ % % \subsubsection{Filtering special cases} % -% \begin{macro}[int, EXP]{\@@_sin_o:w} +% \begin{macro}[EXP]{\@@_sin_o:w} % This function, and its analogs for \texttt{cos}, \texttt{csc}, % \texttt{sec}, \texttt{tan}, and \texttt{cot} instead of % \texttt{sin}, are followed either by \cs{use_i:nn} and a float in @@ -182,7 +182,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_cos_o:w} +% \begin{macro}[EXP]{\@@_cos_o:w} % The cosine of $\pm 0$ is $1$. The cosine of $\pm\infty$ raises an % invalid operation exception. The cosine of \nan{} is itself. % Otherwise, the \texttt{trig} function reduces the argument to at @@ -209,7 +209,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_csc_o:w} +% \begin{macro}[EXP]{\@@_csc_o:w} % The cosecant of $\pm 0$ is $\pm \infty$ with the same sign, with a % division by zero exception (see \cs{@@_cot_zero_o:Nfw} defined % below), which requires the function name. The cosecant of @@ -239,7 +239,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_sec_o:w} +% \begin{macro}[EXP]{\@@_sec_o:w} % The secant of $\pm 0$ is $1$. The secant of $\pm \infty$ raises an % invalid operation exception. The secant of \nan{} is itself. % Otherwise, the \texttt{trig} function reduces the argument and turns @@ -265,7 +265,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_tan_o:w} +% \begin{macro}[EXP]{\@@_tan_o:w} % The tangent of $\pm 0$ or \nan{} is the same floating point number. % The tangent of $\pm\infty$ raises an invalid operation exception. % Once more, the \texttt{trig} function does the argument reduction @@ -292,8 +292,8 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_cot_o:w} -% \begin{macro}[aux, EXP]{\@@_cot_zero_o:Nfw} +% \begin{macro}[EXP]{\@@_cot_o:w} +% \begin{macro}[EXP]{\@@_cot_zero_o:Nfw} % The cotangent of $\pm 0$ is $\pm \infty$ with the same sign, with a % division by zero exception (see \cs{@@_cot_zero_o:Nfw}. The % cotangent of $\pm\infty$ raises an invalid operation exception. The @@ -333,7 +333,7 @@ % % \subsubsection{Distinguishing small and large arguments} % -% \begin{macro}[aux, EXP]{\@@_trig:NNNNNwn} +% \begin{macro}[EXP]{\@@_trig:NNNNNwn} % The first argument is \cs{use_i:nn} if the operand is in radians and % \cs{use_ii:nn} if it is in degrees. Arguments |#2| to~|#5| control % what trigonometric function we compute, and |#6| to~|#8| are pieces @@ -377,7 +377,7 @@ % % \subsubsection{Small arguments} % -% \begin{macro}[aux, EXP]{\@@_trig_small:ww} +% \begin{macro}[EXP]{\@@_trig_small:ww} % This receives a small extended-precision number in radians and % converts it to a fixed point number. Some trailing digits may be % lost in the conversion, so we keep the original floating point @@ -391,7 +391,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_trigd_small:ww} +% \begin{macro}[EXP]{\@@_trigd_small:ww} % Convert the extended-precision number to radians, then call % \cs{@@_trig_small:ww} to massage it in the form appropriate for the % \texttt{_series} auxiliary. @@ -407,7 +407,7 @@ % % \subsubsection{Argument reduction in degrees} % -% \begin{macro}[aux, rEXP] +% \begin{macro}[rEXP] % { % \@@_trigd_large:ww, \@@_trigd_large_auxi:nnnnwNNNN, % \@@_trigd_large_auxii:wNw, \@@_trigd_large_auxiii:www @@ -513,7 +513,7 @@ % $0.6\cdot\text{ulp}$ in all cases. % % ^^A todo: if the exponent range is reduced, store 1/2pi as a simple tl -% \begin{variable}[aux, EXP]{\@@_trig_inverse_two_pi:} +% \begin{variable}[EXP]{\@@_trig_inverse_two_pi:} % This macro expands to |,,!| or~|,!| followed by $10112$~decimals of % $10^{-16}/(2\pi)$. The number of decimals we really need is the % maximum exponent plus the number of digits we later need,~$52$, @@ -688,7 +688,7 @@ % \end{macrocode} % \end{variable} % -% \begin{macro}[aux, rEXP] +% \begin{macro}[rEXP] % { % \@@_trig_large:ww, % \@@_trig_large_auxi:wwwwww, @@ -733,7 +733,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, rEXP] +% \begin{macro}[rEXP] % { % \@@_trig_large_auxv:www, % \@@_trig_large_auxvi:wnnnnnnnn, @@ -780,12 +780,12 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, rEXP] +% \begin{macro}[rEXP] % { % \@@_trig_large_auxvii:w, % \@@_trig_large_auxviii:w, % } -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % { % \@@_trig_large_auxix:Nw, % \@@_trig_large_auxx:wNNNNN, @@ -853,7 +853,7 @@ % % \subsubsection{Computing the power series} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % {\@@_sin_series_o:NNwwww, \@@_sin_series_aux_o:NNnwww} % Here we receive a conversion function \cs{@@_ep_to_float_o:wwN} or % \cs{@@_ep_inv_to_float_o:wwN}, a \meta{sign} ($0$ or~$2$), a @@ -941,7 +941,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % {\@@_tan_series_o:NNwwww, \@@_tan_series_aux_o:Nnwww} % Contrarily to \cs{@@_sin_series_o:NNwwww} which received a % conversion auxiliary as~|#1|, here, |#1| is $0$ for tangent @@ -1087,8 +1087,8 @@ % % \subsubsection{Arctangent and arccotangent} % -% \begin{macro}[int, EXP]{\@@_atan_o:Nw, \@@_acot_o:Nw} -% \begin{macro}[aux, EXP]{\@@_atan_dispatch_o:NNnNw} +% \begin{macro}[EXP]{\@@_atan_o:Nw, \@@_acot_o:Nw} +% \begin{macro}[EXP]{\@@_atan_dispatch_o:NNnNw} % The parsing step manipulates \texttt{atan} and \texttt{acot} like % \texttt{min} and \texttt{max}, reading in an array of operands, but % also leaves \cs{use_i:nn} or \cs{use_ii:nn} depending on whether the @@ -1126,7 +1126,7 @@ % \end{macro} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_atanii_o:Nww, \@@_acotii_o:Nww} +% \begin{macro}[EXP]{\@@_atanii_o:Nww, \@@_acotii_o:Nww} % If either operand is \texttt{nan}, we return it. If both are % normal, we call \cs{@@_atan_normal_o:NNnwNnw}. If both are zero or % both infinity, we call \cs{@@_atan_inf_o:NNNw} with argument~$2$, @@ -1163,7 +1163,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_atan_inf_o:NNNw} +% \begin{macro}[EXP]{\@@_atan_inf_o:NNNw} % This auxiliary is called whenever one number is $\pm 0$ or % $\pm\infty$ (and neither is \nan{}). Then the result only depends % on the signs, and its value is a multiple of $\pi/4$. We use the @@ -1189,7 +1189,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_atan_normal_o:NNnwNnw} +% \begin{macro}[EXP]{\@@_atan_normal_o:NNnwNnw} % Here we simply reorder the floating point data into a pair of signed % extended-precision numbers, that is, a sign, an exponent ending with % a comma, and a six-block mantissa ending with a semi-colon. This @@ -1207,7 +1207,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_atan_test_o:NwwNwwN} +% \begin{macro}[EXP]{\@@_atan_test_o:NwwNwwN} % This receives: the sign~|#1| of~$y$, its exponent~|#2|, its $24$ % digits~|#3| in groups of~$4$, and similarly for~$x$. We prepare to % call \cs{@@_atan_combine_o:NwwwwwN} which expects the sign~|#1|, the @@ -1241,8 +1241,8 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, rEXP]{\@@_atan_div:wnwwnw, \@@_atan_near:wwwn} -% \begin{macro}[aux, EXP]{\@@_atan_near_aux:wwn} +% \begin{macro}[rEXP]{\@@_atan_div:wnwwnw, \@@_atan_near:wwwn} +% \begin{macro}[EXP]{\@@_atan_near_aux:wwn} % This receives two positive numbers $a$ and~$b$ (equal to $\lvert % x\rvert$ and~$\lvert y\rvert$ in some order), each as an exponent % and $6$~blocks of $4$~digits, such that $0<a<b$. If $0.41421b<a$, @@ -1284,7 +1284,7 @@ % \end{macro} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_atan_auxi:ww, \@@_atan_auxii:w} +% \begin{macro}[EXP]{\@@_atan_auxi:ww, \@@_atan_auxii:w} % Convert~$z$ from a representation as an exponent and a fixed point % number in $[0.01,1)$ to a fixed point number only, then set up the % call to \cs{@@_atan_Taylor_loop:www}, followed by the fixed point @@ -1304,7 +1304,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % {\@@_atan_Taylor_loop:www, \@@_atan_Taylor_break:w} % We compute the series of $(\operatorname{atan} z)/z$. A typical intermediate % stage has $|#1|=2k-1$, $|#2| = @@ -1335,7 +1335,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP] +% \begin{macro}[EXP] % {\@@_atan_combine_o:NwwwwwN, \@@_atan_combine_aux:ww} % This receives a \meta{sign}, an \meta{octant}, a fixed point value % of $(\operatorname{atan} z)/z$, a fixed point number~$z$, and another @@ -1399,7 +1399,7 @@ % % \subsubsection{Arcsine and arccosine} % -% \begin{macro}[int, EXP]{\@@_asin_o:w} +% \begin{macro}[EXP]{\@@_asin_o:w} % Again, the first argument provided by \pkg{l3fp-parse} is % \cs{use_i:nn} if we are to work in radians and \cs{use_ii:nn} for % degrees. Then comes a floating point number. The arcsine of $\pm @@ -1427,7 +1427,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_acos_o:w} +% \begin{macro}[EXP]{\@@_acos_o:w} % The arccosine of $\pm 0$ is $\pi / 2$ (in degrees,~$90$). The % arccosine of $\pm\infty$ raises an invalid operation exception. The % arccosine of \nan{} is itself. Otherwise, call an auxiliary common @@ -1456,7 +1456,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_asin_normal_o:NfwNnnnnw} +% \begin{macro}[EXP]{\@@_asin_normal_o:NfwNnnnnw} % If the exponent~|#5| is at most $0$, the operand lies % within $(-1,1)$ and the operation is permitted: call % \cs{@@_asin_auxi_o:NnNww} with the appropriate arguments. If the @@ -1485,7 +1485,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_asin_auxi_o:NnNww, \@@_asin_isqrt:wn} +% \begin{macro}[EXP]{\@@_asin_auxi_o:NnNww, \@@_asin_isqrt:wn} % We compute $x/\sqrt{1-x^2}$. This function is used by \texttt{asin} % and \texttt{acos}, but also by \texttt{acsc} and \texttt{asec} after % inverting the operand, thus it must manipulate extended-precision @@ -1527,7 +1527,7 @@ % % \subsubsection{Arccosecant and arcsecant} % -% \begin{macro}[int, EXP]{\@@_acsc_o:w} +% \begin{macro}[EXP]{\@@_acsc_o:w} % Cases are mostly labelled by~|#2|, except when |#2| is~$2$: then we % use |#3#2|, which is $02=2$ when the number is $+\infty$ and % $22$~when the number is $-\infty$. The arccosecant of $\pm 0$ @@ -1553,7 +1553,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[int, EXP]{\@@_asec_o:w} +% \begin{macro}[EXP]{\@@_asec_o:w} % The arcsecant of $\pm 0$ raises an invalid operation exception. The % arcsecant of $\pm\infty$ is $\pi / 2$ (in degrees,~$90$). The % arcosecant of \nan{} is itself. Otherwise, do some more tests, @@ -1581,7 +1581,7 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}[aux, EXP]{\@@_acsc_normal_o:NfwNnw} +% \begin{macro}[EXP]{\@@_acsc_normal_o:NfwNnw} % If the exponent is non-positive, the operand is less than~$1$ in % absolute value, which is always an invalid operation: complain. % Otherwise, compute the inverse of the operand, and feed it to |