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% Copyright 2019 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%
}