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diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex new file mode 100644 index 00000000000..65460e4b3cc --- /dev/null +++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex @@ -0,0 +1,320 @@ +% Copyright 2007 by Mark Wibrow +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% See the file doc/generic/pgf/licenses/LICENSE for more details. + +% This file defines the mathematical functions and operators. +% +% Version 1.414213 29/9/2007 + +% veclen function adpated from ideas due to Rouben Rostamian. +% +% Calcluate the Eulidean length of a 2D vector. +% +% +\pgfmathdeclarefunction{veclen}{2}{% + \begingroup% + \pgfmath@x#1pt\relax% + \pgfmath@y#2pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \ifdim\pgfmath@y<0pt\relax% + \pgfmath@y-\pgfmath@y% + \fi% + \ifdim\pgfmath@x=0pt\relax% + \pgfmath@x\pgfmath@y% + \else% + \ifdim\pgfmath@y=0pt\relax% + \else% + \ifdim\pgfmath@x>\pgfmath@y% + \pgfmath@xa\pgfmath@x% + \pgfmath@x\pgfmath@y% + \pgfmath@y\pgfmath@xa% + \fi% + % We use a scaling factor to reduce errors. + \ifdim\pgfmath@y>10000pt\relax% + \c@pgfmath@counta1500\relax% + \else% + \ifdim\pgfmath@y>1000pt\relax% + \c@pgfmath@counta150\relax% + \else% + \ifdim\pgfmath@y>100pt\relax% + \c@pgfmath@counta50\relax% + \else% + \c@pgfmath@counta1\relax% + \fi% + \fi% + \fi% + \divide\pgfmath@x\c@pgfmath@counta\relax% + \divide\pgfmath@y\c@pgfmath@counta\relax% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}% + \pgfmath@x\pgfmathresult\pgfmath@x% + \pgfmath@xa\pgfmath@tonumber{\pgfmath@x}\pgfmath@x% + \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@xa}}% + % + % Use A+x^2*(B+x^2*(C+x^2*(D+E*x^2))) + % where + % A = +1.000012594 + % B = +0.4993615349 + % C = -0.1195159052 + % D = +0.04453994279 + % E = -0.01019210944 + % + \pgfmath@x-0.01019210944\pgfmath@xa% + \advance\pgfmath@x0.04453994279pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x-0.1195159052pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x0.4993615349pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x1.000012594pt\relax% + \ifdim\pgfmath@y<0pt\relax% + \pgfmath@y-\pgfmath@y% + \fi% + \pgfmath@x\pgfmath@tonumber{\pgfmath@y}\pgfmath@x% + % Invert the scaling factor. + \multiply\pgfmath@x\c@pgfmath@counta\relax% + \fi% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +% Hyperbolic functions contributed by Martin Heller. +% +\pgfmathdeclarefunction{cosh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathexp@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathexp@{-\pgfmath@arg}% + \advance\pgfmath@x by\pgfmathresult pt\relax% + \divide\pgfmath@x by2\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup} + +\pgfmathdeclarefunction{sinh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathexp@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathexp@{-\pgfmath@arg}% + \advance\pgfmath@x by-\pgfmathresult pt\relax% + \divide\pgfmath@x by2\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup +}% + +\pgfmathdeclarefunction{tanh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathsinh@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathcosh@{\pgfmath@arg}% + \pgfmath@y=\pgfmathresult pt\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgfmath@x}}{\pgfmath@tonumber{\pgfmath@y}}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup +}% + +% \pgfmathscientific +% +% Return the value of #1e#2 +% +% e.g. \pgfmathscientific{1.23456789123}{4} +% +% defines \pgfmathresult as 12345.67891 +% +% NB These arguments *are not parsed*, as the long mantissa would be lost. +% +\def\pgfmathscientific#1#2{% + \begingroup% + \edef\pgfmath@sci@exponent{#2}% + \pgfmath@x#1pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \edef\pgfmath@sci@sign{-}% + \expandafter\edef\expandafter\pgfmath@temp\expandafter{\expandafter\pgfmath@gobbleone#1}% + \else% + \edef\pgfmath@sci@sign{+}% + \edef\pgfmath@temp{#1}% + \fi% + \expandafter\pgfmath@in@\expandafter.\expandafter{#1}% + \ifpgfmath@in@% + \else% + \edef\pgfmath@temp{\pgfmath@temp.0}% + \fi% + \expandafter\pgfmath@scientific@@\pgfmath@temp00000000000\pgfmath@} + +\def\pgfmath@scientific@@#1.#2#3#4#5#6{% + \edef\pgfmath@sci@int{#1}% + \edef\pgfmath@sci@mantissaA{#2#3#4#5#6}% + \pgfmath@scientific@@@} + +\def\pgfmath@scientific@@@#1#2#3#4#5#6\pgfmath@{% + \edef\pgfmath@sci@mantissaB{#1#2#3#4#5}% + \c@pgfmath@counta\pgfmath@sci@exponent\relax% + \c@pgfmath@countb\c@pgfmath@counta% + \ifnum\c@pgfmath@counta<0\relax% + \c@pgfmath@counta-\c@pgfmath@counta% + \fi% + \pgfmathpow@{10}{\the\c@pgfmath@counta}% + \afterassignment\pgfmath@gobbletilpgfmath@ + \c@pgfmath@countc\pgfmathresult\relax\pgfmath@ + \edef\pgfmath@sci@factor{\the\c@pgfmath@countc}% + \ifnum\c@pgfmath@countb<0\relax% + % xE-y: easy... + \pgfmath@x\pgfmath@sci@int.\pgfmath@sci@mantissaA pt\relax% + \divide\pgfmath@x\pgfmath@sci@factor\relax% + \else% + % xE+y: + % Must do this way so as not lose digits in a long mantissa. Sigh... + \c@pgfmath@counta\pgfmath@sci@int% + \c@pgfmath@countb\pgfmath@sci@mantissaA% + \multiply\c@pgfmath@counta\pgfmath@sci@factor\relax% + \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% + \c@pgfmath@countc\c@pgfmath@countb% + \divide\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@counta\c@pgfmath@countb% + \multiply\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@countc-\c@pgfmath@countb% + \c@pgfmath@countb\pgfmath@sci@mantissaB\relax% + \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% + \divide\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@countc\c@pgfmath@countb% + \advance\c@pgfmath@countc100000\relax% + \edef\pgfmath@sci@result{\pgfmath@sci@sign\the\c@pgfmath@counta.\expandafter\pgfmath@gobbleone\the\c@pgfmath@countc pt}% + \pgfmath@x\pgfmath@sci@result\relax% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup} + + + +% width function. +% +\pgfmathdeclarefunction{width}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\wd\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + +% height function. +% +\pgfmathdeclarefunction{height}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\ht\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +% depth function. +% +\pgfmathdeclarefunction{depth}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\dp\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + +% array function. +% +\pgfmathdeclarefunction{array}{2}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@\pgfmath@count=#2\relax\pgfmath@% + \expandafter\pgfmatharray@@#1\pgfmath@stop% +} + +\def\pgfmath@token@stop{\pgfmath@stop}% +\def\pgfmatharray@@#1{% + \def\pgfmath@temp{#1}% + \advance\pgfmath@count by-1\relax% + \ifx\pgfmath@temp\pgfmath@token@stop% + \pgfmath@error{Array index out of bounds.}{}% + \def\pgfmathresult{0}% + \pgfmath@smuggleone\pgfmathresult\endgroup% + \let\pgfmath@next=\relax% + \else% + \ifnum\pgfmath@count=-1\relax% + \def\pgfmathresult{#1}% + \let\pgfmath@next=\pgfmatharray@@@% + \else% + \let\pgfmath@next=\pgfmatharray@@% + \fi% + \fi% + \pgfmath@next} + +\def\pgfmatharray@@@#1\pgfmath@stop{% + \pgfmath@smuggleone\pgfmathresult\endgroup% +} + + +% max function. +% +\pgfmathdeclarefunction{max}{...}{% + \begingroup% + \pgfmath@x=-16383pt\relax% + \pgfmathmax@@#1{}} + +\def\pgfmathmax@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \let\pgfmath@next=\pgfmathmax@@@% + \else% + \ifdim#1pt>\pgfmath@x% + \pgfmath@x=#1pt\relax% + \fi% + \let\pgfmath@next=\pgfmathmax@@% + \fi% + \pgfmath@next} + +\def\pgfmathmax@@@{\pgfmath@returnone\pgfmath@x\endgroup}% + +% For compatability with old code. +\def\pgfmathmax#1#2{% + \pgfmathparse{getargs(#1,#2)}% + \expandafter\pgfmathmax@\expandafter{\pgfmathresult}% +} + +% min function. +% +\pgfmathdeclarefunction{min}{...}{% + \begingroup% + \pgfmath@x=16383pt\relax% + \pgfmathmin@@#1{}} + +\def\pgfmathmin@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \let\pgfmath@next=\pgfmathmin@@@% + \else% + \ifdim#1pt<\pgfmath@x% + \pgfmath@x=#1pt\relax% + \fi% + \let\pgfmath@next=\pgfmathmin@@% + \fi% + \pgfmath@next} + +\def\pgfmathmin@@@{\pgfmath@returnone\pgfmath@x\endgroup}% + +% For compatability with old code. +\def\pgfmathmin#1#2{% + \pgfmathparse{getargs(#1,#2)}% + \expandafter\pgfmathmin@\expandafter{\pgfmathresult}% +} + |