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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/pgf/base/tex/pgfmathfunctions.misc.code.tex
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+% 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 adapted from ideas due to Rouben Rostamian.
+%
+% Calculate the Euclidean 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%
+ \ifnum\c@pgfmath@counta<-4\relax%
+ \pgfmath@x0pt\relax%
+ \else%
+ \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\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%
+}
+
+% dim function: return dimension of an array
+% dim({1,2,3}) return 3
+% dim({{1,2,3},{4,5,6}}) return 2
+\pgfmathdeclarefunction{dim}{1}{%
+ \begingroup
+ \pgfmath@count=0\relax
+ \expandafter\pgfmath@dim@i\pgfutil@firstofone#1\pgfmath@token@stop
+ \edef\pgfmathresult{\the\pgfmath@count}%
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup}
+
+\def\pgfmath@dim@i#1{%
+ \ifx\pgfmath@token@stop#1%
+ \else
+ \advance\pgfmath@count by 1\relax
+ \expandafter\pgfmath@dim@i
+ \fi}
+
+
+% 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 computability with old code.
+\def\pgfmathmax#1#2{%
+ \pgfmathparse{#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 computability with old code.
+\def\pgfmathmin#1#2{%
+ \pgfmathparse{#1,#2}%
+ \expandafter\pgfmathmin@\expandafter{\pgfmathresult}%
+}
+
+
+
+% scalar function.
+%
+\pgfmathdeclarefunction{scalar}{1}{%
+ \def\pgfmathresult{#1}%
+ \global\pgfmathunitsdeclaredfalse%
+}