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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
-
-% This file defines the mathematical functions and operators.
-%
-% Adding/redefining extra operators/functions:
-%
-% Each operator/function XXX has two forms:
-%
-%
-% \pgfmathXXX#1... a public version which evaluates any
-% arguments passed to it and passes the
-% results on to...
-%
-% \pgfmathXXX@#1... a non-public version which performs
-% required calculation on arguments which
-% must have already been evaluated (i.e.
-% *without* dimensions).
-%
-% If a function XXX is to be included in the parser, it is
-% recommended, for consistency, that where possible, the
-% pgfmathparser file should define the macro \pgfmath@parseXXX.
-% The parser should (ideally) then call \pgfmathXXX@.
-%
-% It is also recommened that all calculations (where necessary)
-% take place within a TeX group. \pgfmath@returnone#1 makes and
-% expanded version of #1 global and stores this in \pgfmathresult
-% after the group is ended.
-%
-
-\input pgfmathtrig.code.tex% Load the trig. stuff.
-\input pgfmathrnd.code.tex% Load the random stuff.
-
-
-% \pgfmathadd
-%
-% Add #1 and #2.
-%
-\def\pgfmathadd#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathadd@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathadd@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \advance\pgfmath@x by\pgfmath@y%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathsubtract
-%
-% Subtract #2 from #1.
-%
-\def\pgfmathsubtract#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathsubtract@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathsubtract@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \advance\pgfmath@x-\pgfmath@y%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathmultiply
-%
-% Multiply #1 by #2.
-%
-\def\pgfmathmultiply#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathmultiply@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathmultiply@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \pgfmath@x\pgfmath@tonumber{\pgfmath@y}\pgfmath@x%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathdivide
-%
-% Divide #1 by #2.
-%
-\def\pgfmathdivide#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathdivide@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathdivide@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \def\pgfmath@sign{}%
- \ifdim\pgfmath@y=0pt\relax%
- \pgfmath@error{You've asked me to divide `#1' by `#2', %
- but I cannot divide any number by `#2'}%
- \fi%
- \afterassignment\pgfmath@xa%
- \expandafter\c@pgfmath@counta\the\pgfmath@y\relax%
- %
- % If y is an integer, use TeX arithmatic.
- %
- \ifdim\pgfmath@xa=0pt\relax%
- \divide\pgfmath@x\c@pgfmath@counta\relax%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
- \let\pgfmath@next\pgfmathdivide@@@%
- \else%
- %
- % Simple long division.
- %
- \ifdim\pgfmath@x<0pt\relax%
- \def\pgfmath@sign{-}%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \ifdim\pgfmath@y<0pt\relax%
- \edef\pgfmath@sign{\pgfmath@sign-}%
- \pgfmath@y-\pgfmath@y%
- \fi%
- \pgfmath@ya\pgfmath@y%
- \c@pgfmath@counta0\relax%
- \ifdim\pgfmath@x>\pgfmath@ya%
- \ifdim\pgfmath@ya<1638.4pt\relax%
- \pgfmathmultiply@dimenbyten\pgfmath@ya%
- \ifdim\pgfmath@ya>\pgfmath@x%
- \pgfmathdivide@dimenbyten\pgfmath@ya%
- \c@pgfmath@counta0\relax%
- \else%
- \ifdim\pgfmath@ya<1638.4pt\relax%
- \pgfmathmultiply@dimenbyten\pgfmath@ya%
- \ifdim\pgfmath@ya>\pgfmath@x%
- \pgfmathdivide@dimenbyten\pgfmath@ya%
- \c@pgfmath@counta1\relax%
- \else%
- \ifdim\pgfmath@ya<1638.4pt\relax%
- \pgfmathmultiply@dimenbyten\pgfmath@ya%
- \ifdim\pgfmath@ya>\pgfmath@x%
- \pgfmathdivide@dimenbyten\pgfmath@ya%
- \c@pgfmath@counta2\relax%
- \else%
- \ifdim\pgfmath@ya<1638.4pt\relax%
- \pgfmathmultiply@dimenbyten\pgfmath@ya%
- \ifdim\pgfmath@ya>\pgfmath@x%
- \pgfmathdivide@dimenbyten\pgfmath@ya%
- \c@pgfmath@counta3\relax%
- \else%
- \pgfmath@error{The result of `#1/#2' is too big for me}{}%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- %
- % If y < 1pt use reciprocal operation.
- %
- \ifdim\pgfmath@y<1pt\relax%
- \ifdim\pgfmath@y<.00007pt\relax%
- \pgfmath@error{The result of `#1/#2' is too big for me}{}%
- \fi%
- \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}%
- \pgfmath@x\pgfmathresult\pgfmath@x%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
- \let\pgfmath@next\pgfmathdivide@@@%
- \else%
- \pgfmath@y\pgfmath@ya%
- \def\pgfmathresult{}%
- \let\pgfmath@next\pgfmathdivide@@%
- \fi%
- \fi%
- \pgfmath@next%
-}
-
-\def\pgfmathdivide@dimenbyten#1{%
- \edef\pgfmath@temp{\pgfmath@tonumber{#1}}%
- \expandafter\pgfmathdivide@@dimenbyten\pgfmath@temp\@@#1\@@}
-\def\pgfmathdivide@@dimenbyten#1.#2\@@#3\@@{%
- \pgfmath@tempcnta#1\relax%
- \divide\pgfmath@tempcnta10\relax%
- \pgfmath@tempcntb\pgfmath@tempcnta%
- \multiply\pgfmath@tempcnta-10\relax%
- \advance\pgfmath@tempcnta#1\relax%
- #3\the\pgfmath@tempcntb.\the\pgfmath@tempcnta#2pt\relax%
-}
-
-\def\pgfmathmultiply@dimenbyten#1{%
- \edef\pgfmath@temp{\pgfmath@tonumber{#1}}%
- \expandafter\pgfmathmultiply@@dimenbyten\pgfmath@temp\@@#1\@@}
-\def\pgfmathmultiply@@dimenbyten#1.#2#3\@@#4\@@{#4#1#2.#3pt\relax}
-
-\def\pgfmathdivide@@{%
- \ifdim\pgfmath@x>\pgfmath@y%
- \pgfmath@yb6.0\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 6*y
- \advance\pgfmath@yb-\pgfmath@y%
- \advance\pgfmath@yb-\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 4*y
- \advance\pgfmath@yb-\pgfmath@y%
- \advance\pgfmath@yb-\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 2*y
- \advance\pgfmath@yb-\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 1*y
- \c@pgfmath@countb0\relax%
- \else%
- \c@pgfmath@countb1\relax%
- \fi%
- \else%
- \advance\pgfmath@yb\pgfmath@y% 3*y
- \ifdim\pgfmath@yb>\pgfmath@x%
- \c@pgfmath@countb2\relax%
- \else%
- \c@pgfmath@countb3\relax%
- \fi%
- \fi%
- \else%
- \advance\pgfmath@yb\pgfmath@y% 5*y
- \ifdim\pgfmath@yb>\pgfmath@x%
- \c@pgfmath@countb4\relax%
- \else%
- \c@pgfmath@countb5\relax%
- \fi%
- \fi%
- \else%
- \advance\pgfmath@yb\pgfmath@y%
- \advance\pgfmath@yb\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 8*y
- \advance\pgfmath@yb-\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 7*y
- \c@pgfmath@countb6\relax%
- \else%
- \c@pgfmath@countb7\relax%
- \fi%
- \else%
- \advance\pgfmath@yb\pgfmath@y%
- \ifdim\pgfmath@yb>\pgfmath@x% 9*y
- \c@pgfmath@countb8\relax%
- \else%
- \c@pgfmath@countb9\relax%
- \fi%
- \fi%
- \fi%
- \else%
- \c@pgfmath@countb=0\relax%
- \fi%
- \ifnum\c@pgfmath@countb=0\relax%
- \edef\pgfmathresult{\pgfmathresult0}%
- \else%
- \pgfmath@yb\c@pgfmath@countb\pgfmath@y%
- \advance\pgfmath@x-\pgfmath@yb%
- \edef\pgfmathresult{\pgfmathresult\the\c@pgfmath@countb}%
- \fi%
- \pgfmathdivide@dimenbyten\pgfmath@y%
- \ifnum\c@pgfmath@counta=0\relax%
- \edef\pgfmathresult{\pgfmathresult.}%
- \fi%
- \advance\c@pgfmath@counta-1\relax%
- \ifdim\pgfmath@y=0pt\relax%
- \let\pgfmath@next\pgfmathdivide@@@%
- \else%
- \let\pgfmath@next\pgfmathdivide@@%
- \fi%
- \pgfmath@next%
-}
-
-\def\pgfmathdivide@@@{%
- \pgfmath@x\pgfmath@sign\pgfmathresult pt\relax%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-
-% \pgfmathgreaterthan
-%
-% 1.0 if #1 > #2. Otherwise 0.0
-%
-\def\pgfmathgreaterthan#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathgreaterthan@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathgreaterthan@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \advance\pgfmath@x-\pgfmath@y%
- \ifdim\pgfmath@x>0pt\relax%
- \pgfmath@x1pt\relax%
- \else%
- \pgfmath@x0pt\relax%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathlessthan
-%
-% 1.0 if #1< #2. Otherwise 0.0
-%
-\def\pgfmathlessthan#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathlessthan@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathlessthan@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \advance\pgfmath@x-\pgfmath@y\relax%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x1pt\relax%
- \else%
- \pgfmath@x0pt\relax%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathequalto
-%
-% 1.0 if #1 = #2. Otherwise 0.0
-%
-\def\pgfmathequalto#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathequalto@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathequalto@#1#2{%
- \begingroup%
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \advance\pgfmath@x-\pgfmath@y%
- \ifdim\pgfmath@x=0pt\relax%
- \pgfmath@x1pt\relax%
- \else%
- \pgfmath@x0pt\relax%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathreciprocal
-%
-% 1 / #1
-%
-\def\pgfmathreciprocal#1{%
- \pgfmathparse{#1}%
- \pgfmathreciprocal@{\pgfmathresult}}
-\def\pgfmathreciprocal@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \ifdim\pgfmath@x=0pt\relax%
- \pgfmath@error{You asked me to calculate `1/#1', but I cannot divide any number by zero}{}%
- \fi%
- \edef\pgfmath@reciprocaltemp{\pgfmath@tonumber{\pgfmath@x}}%
- \expandafter\pgfmathreciprocal@@\pgfmath@reciprocaltemp0000000\pgfmath@}
-\def\pgfmathreciprocal@@#1.#2#3#4#5#6#7\pgfmath@{%
- \c@pgfmath@counta#2#3#4#5#6\relax%
- % If the number is an integer, use TeX arithmatic.
- \ifnum\c@pgfmath@counta=0\relax%
- \pgfmath@x1pt\relax%
- \divide\pgfmath@x#1\relax%
- \else%
- \ifnum#1>100\relax%
- \c@pgfmath@counta#1#2#3#4\relax%
- \c@pgfmath@countb1000000000\relax%
- \divide\c@pgfmath@countb\c@pgfmath@counta%
- \c@pgfmath@counta\c@pgfmath@countb%
- \divide\c@pgfmath@counta10000\relax%
- \pgfmath@x\c@pgfmath@counta pt\relax%
- \multiply\c@pgfmath@counta-10000\relax%
- \advance\c@pgfmath@countb\c@pgfmath@counta%
- \pgfmath@y\c@pgfmath@countb pt\relax%
- \divide\pgfmath@y1000000\relax%
- \advance\pgfmath@x\pgfmath@y%
- \else%
- \c@pgfmath@counta#1#2#3#4#5#6\relax%
- \c@pgfmath@countb1000000000\relax%
- \divide\c@pgfmath@countb\c@pgfmath@counta%
- \c@pgfmath@counta\c@pgfmath@countb%
- \divide\c@pgfmath@counta10000\relax%
- \pgfmath@x\c@pgfmath@counta pt\relax%
- \multiply\c@pgfmath@counta-10000\relax%
- \advance\c@pgfmath@countb\c@pgfmath@counta%
- \pgfmath@y\c@pgfmath@countb pt\relax%
- \pgfmath@y.1\pgfmath@y% Yes! This way is more accurate. Go figure...
- \pgfmath@y.1\pgfmath@y%
- \pgfmath@y.1\pgfmath@y%
- \pgfmath@y.1\pgfmath@y%
- \advance\pgfmath@x\pgfmath@y%
- \fi%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathln
-%
-% Calculate ln(#1}
-%
-% This is based on an algorithm due to Rouben Rostamian and
-% uses coefficients contributed by Alain Matthes.
-%
-\def\pgfmathln#1{\pgfmathparse{#1}\pgfmathln@{\pgfmathresult}}
-\def\pgfmathln@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \ifdim\pgfmath@x>0pt\else%
- \pgfmath@error{I cannot calculate the logarithm of `#1'}{}%
- \fi%
- \c@pgfmath@counta0\relax%
- \ifdim\pgfmath@x>2pt\relax%
- \ifdim\pgfmath@x<128pt\relax%
- \ifdim\pgfmath@x<8pt\relax%
- \ifdim\pgfmath@x<4pt\relax%
- \divide\pgfmath@x2\relax%
- \c@pgfmath@counta1\relax%
- \else%
- \divide\pgfmath@x4\relax%
- \c@pgfmath@counta2\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x<32pt\relax%
- \ifdim\pgfmath@x<16pt\relax%
- \divide\pgfmath@x8\relax%
- \c@pgfmath@counta3\relax%
- \else%
- \divide\pgfmath@x16\relax%
- \c@pgfmath@counta4\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x<64pt\relax%
- \divide\pgfmath@x32\relax%
- \c@pgfmath@counta5\relax%
- \else%
- \divide\pgfmath@x64\relax%
- \c@pgfmath@counta6\relax%
- \fi%
- \fi%
- \fi%
- \else%
- \ifdim\pgfmath@x<2048pt\relax%
- \ifdim\pgfmath@x<512pt\relax%
- \ifdim\pgfmath@x<256pt\relax%
- \divide\pgfmath@x128\relax%
- \c@pgfmath@counta7\relax%
- \else%
- \divide\pgfmath@x256\relax%
- \c@pgfmath@counta8\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x<1024pt\relax%
- \divide\pgfmath@x512\relax%
- \c@pgfmath@counta9\relax%
- \else%
- \divide\pgfmath@x1024\relax%
- \c@pgfmath@counta10\relax%
- \fi%
- \fi%
- \else%
- \ifdim\pgfmath@x<8192pt\relax%
- \ifdim\pgfmath@x<4096pt\relax%
- \divide\pgfmath@x2048\relax%
- \c@pgfmath@counta11\relax%
- \else%
- \divide\pgfmath@x4096\relax%
- \c@pgfmath@counta12\relax%
- \fi%
- \else%
- \divide\pgfmath@x8192\relax%
- \c@pgfmath@counta13\relax%
- \fi%
- \fi%
- \fi%
- \else%
- \ifdim\pgfmath@x<1pt\relax%
- \ifdim\pgfmath@x>0.0078125pt\relax% 2^-7
- \ifdim\pgfmath@x>0.125pt\relax% 2^-3
- \ifdim\pgfmath@x>0.5pt\relax% 2^-1
- \multiply\pgfmath@x2\relax%
- \c@pgfmath@counta-1\relax%
- \else%
- \multiply\pgfmath@x4\relax%
- \c@pgfmath@counta-2\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x>0.03125pt\relax% 2^-5
- \ifdim\pgfmath@x>0.0625pt\relax%
- \multiply\pgfmath@x8\relax%
- \c@pgfmath@counta-3\relax%
- \else%
- \multiply\pgfmath@x16\relax%
- \c@pgfmath@counta-4\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x>0.015625pt\relax% 2^-6
- \multiply\pgfmath@x32\relax%
- \c@pgfmath@counta-5\relax%
- \else%
- \multiply\pgfmath@x64\relax%
- \c@pgfmath@counta-6\relax%
- \fi%
- \fi%
- \fi%
- \else%
- \ifdim\pgfmath@x>0.000244140625pt\relax% 2^-11
- \ifdim\pgfmath@x>0.001953125pt\relax% 2^-9
- \ifdim\pgfmath@x>0.00390625pt\relax% 2^-8
- \multiply\pgfmath@x128\relax%
- \c@pgfmath@counta-7\relax%
- \else%
- \multiply\pgfmath@x256\relax%
- \c@pgfmath@counta-8\relax%
- \fi%
- \else%
- \ifdim\pgfmath@x>0.0009765625pt\relax% 2^-10
- \multiply\pgfmath@x512\relax%
- \c@pgfmath@counta-9\relax%
- \else%
- \multiply\pgfmath@x1024\relax%
- \c@pgfmath@counta-10\relax%
- \fi%
- \fi%
- \else%
- \ifdim\pgfmath@x>0.0001220703125pt\relax% 2^13
- \ifdim\pgfmath@x>0.0002441406256pt\relax% 2^12
- \multiply\pgfmath@x2048\relax%
- \c@pgfmath@counta-11\relax%
- \else%
- \multiply\pgfmath@x4096\relax%
- \c@pgfmath@counta-12\relax%
- \fi%
- \else%
- \multiply\pgfmath@x8192\relax%
- \c@pgfmath@counta-13\relax%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- %
- % Use A+(B+(C+(D+(E+F*x)*x)*x)*x)*x
- %
- % where:
- % A = -2.787927935
- % B = 5.047861502
- % C = -3.489886985
- % D = 1.589480044
- % E = -.4025153233
- % F = 0.04300521312
- %
- \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
- \pgfmath@x0.04300521312\pgfmath@x%
- \advance\pgfmath@x-.4025153233pt\relax%
- \pgfmath@x\pgfmath@temp\pgfmath@x%
- \advance\pgfmath@x1.589480044pt\relax%
- \pgfmath@x\pgfmath@temp\pgfmath@x%
- \advance\pgfmath@x-3.489886985pt\relax%
- \pgfmath@x\pgfmath@temp\pgfmath@x%
- \advance\pgfmath@x5.047861502pt\relax%
- \pgfmath@x\pgfmath@temp\pgfmath@x%
- \advance\pgfmath@x-2.787927935pt\relax%
- \advance\pgfmath@x\c@pgfmath@counta pt\relax%
- \pgfmath@x0.6931471806\pgfmath@x%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathabs
-%
-% Calculate |#1|
-%
-\def\pgfmathabs#1{%
- \pgfmathparse{#1}%
- \pgfmathabsolute@{\pgfmathresult}}
-\def\pgfmathabs@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathmod
-%
-% Calculate #1 mod #2.
-%
-\def\pgfmathmod#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathmod@{\pgfmathresult}{\pgfmath@arg}%
-}
-\def\pgfmathmod@#1#2{%
- \begingroup%
- \pgfmath@xa#1pt%
- \pgfmath@xb#2pt%
- \pgfmath@x\pgfmath@xa%
- \c@pgfmath@counta\pgfmath@xa%
- \c@pgfmath@countb\pgfmath@xb%
- \divide\c@pgfmath@counta\c@pgfmath@countb%
- \multiply\pgfmath@xb\c@pgfmath@counta%
- \advance\pgfmath@x-\pgfmath@xb%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathsqrt
-%
-% Square-root of #1.
-%
-%
-\def\pgfmathsqrt#1{\pgfmathparse{#1}\pgfmathsqrt@{\pgfmathresult}}
-\def\pgfmathsqrt@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@error{I cannot calculate the square-root of the negative number `#1'}{}%
- \else%
- \ifdim\pgfmath@x<10pt\relax%
- \def\pgfmath@zeros{0}%
- \def\pgfmath@targetiterations{1}%
- \else%
- \ifdim\pgfmath@x<100pt\relax%
- \def\pgfmath@zeros{}%
- \def\pgfmath@targetiterations{1}%
- \else%
- \ifdim\pgfmath@x<1000pt\relax%
- \def\pgfmath@zeros{0}%
- \def\pgfmath@targetiterations{2}%
- \else%
- \ifdim\pgfmath@x<10000pt\relax%
- \def\pgfmath@zeros{}%
- \def\pgfmath@targetiterations{2}%
- \else%
- \def\pgfmath@zeros{0}%
- \def\pgfmath@targetiterations{3}%
- \fi\fi\fi\fi\fi%
- \edef\pgfmath@temp{\pgfmath@zeros\pgfmath@tonumber{\pgfmath@x}}%
- \expandafter\pgfmath@sqrt@\pgfmath@temp\pgfmath@%
-}
-\def\pgfmath@sqrt@#1.#2\pgfmath@{\pgfmath@@sqrt@#1#2\pgfmath@empty\pgfmath@empty\pgfmath@}
-
-\def\pgfmath@@sqrt@#1#2{%
- \c@pgfmath@countb#1#2\relax%
- \ifnum\c@pgfmath@countb>35\relax%
- \ifnum\c@pgfmath@countb>63\relax%
- \ifnum\c@pgfmath@countb>80\relax%
- \c@pgfmath@counta9\relax%
- \else%
- \c@pgfmath@counta8\relax%
- \fi%
- \else%
- \ifnum\c@pgfmath@countb>48\relax%
- \c@pgfmath@counta7\relax%
- \else%
- \c@pgfmath@counta6\relax%
- \fi%
- \fi%
- \else%
- \ifnum\c@pgfmath@countb>15\relax%
- \ifnum\c@pgfmath@countb>24\relax%
- \c@pgfmath@counta5\relax%
- \else%
- \c@pgfmath@counta4\relax%
- \fi%
- \else%
- \ifnum\c@pgfmath@countb>3\relax%
- \ifnum\c@pgfmath@countb>8\relax%
- \c@pgfmath@counta3\relax%
- \else%
- \c@pgfmath@counta2\relax%
- \fi%
- \else%
- \ifnum\c@pgfmath@countb>0\relax%
- \c@pgfmath@counta1\relax%
- \else%
- \c@pgfmath@counta0\relax%
- \fi%
- \fi%
- \fi%
- \fi%
- \edef\pgfmath@root{\the\c@pgfmath@counta}%
- \edef\pgfmath@rootspecial{\the\c@pgfmath@counta}%
- \multiply\c@pgfmath@counta-\c@pgfmath@counta\relax%
- \advance\c@pgfmath@counta#1#2\relax%
- \edef\pgfmath@remainder{\the\c@pgfmath@counta}%
- \pgfmath@@@sqrt@%
-}
-
-\def\pgfmath@@@sqrt@#1#2{%
- \ifx\pgfmath@empty#1%
- \edef\pgfmath@remainder{\pgfmath@remainder00}%
- \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
- \else%
- \ifx\pgfmath@empty#2%
- \edef\pgfmath@remainder{\pgfmath@remainder#10}%
- \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
- \else%
- \edef\pgfmath@remainder{\pgfmath@remainder#1#2}%
- \def\pgfmath@tokens{}%
- \fi\fi%
- \c@pgfmath@counta\pgfmath@rootspecial\relax%
- \multiply\c@pgfmath@counta20\relax%
- \c@pgfmath@countb\c@pgfmath@counta%
- \multiply\c@pgfmath@countb6\relax%
- \advance\c@pgfmath@countb36\relax%
- \c@pgfmath@countc\c@pgfmath@counta\relax%
- \multiply\c@pgfmath@countc2\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \advance\c@pgfmath@countb-\c@pgfmath@countc%
- \advance\c@pgfmath@countb-20\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \advance\c@pgfmath@countb-\c@pgfmath@countc%
- \advance\c@pgfmath@countb-12\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \advance\c@pgfmath@countb-\c@pgfmath@counta%
- \advance\c@pgfmath@countb-3\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \def\pgfmath@digit{0}%
- \else%
- \def\pgfmath@digit{1}%
- \fi%
- \else%
- \advance\c@pgfmath@countb\c@pgfmath@counta%
- \advance\c@pgfmath@countb5\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \def\pgfmath@digit{2}%
- \else%
- \def\pgfmath@digit{3}%
- \fi%
- \fi%
- \else%
- \advance\c@pgfmath@countb\c@pgfmath@counta%
- \advance\c@pgfmath@countb9\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \def\pgfmath@digit{4}%
- \else%
- \def\pgfmath@digit{5}%
- \fi%
- \fi%
- \else%
- \advance\c@pgfmath@countb\c@pgfmath@countc%
- \advance\c@pgfmath@countb28\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \advance\c@pgfmath@countb-\c@pgfmath@counta%
- \advance\c@pgfmath@countb-15\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \def\pgfmath@digit{6}%
- \else%
- \def\pgfmath@digit{7}%
- \fi%
- \else%
- \advance\c@pgfmath@countb\c@pgfmath@counta%
- \advance\c@pgfmath@countb17\relax%
- \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
- \def\pgfmath@digit{8}%
- \else%
- \def\pgfmath@digit{9}%
- \fi%
- \fi%
- \fi%
- \edef\pgfmath@rootspecial{\pgfmath@rootspecial\pgfmath@digit}%
- \advance\c@pgfmath@counta\pgfmath@digit\relax%
- \multiply\c@pgfmath@counta-\pgfmath@digit\relax%
- \advance\c@pgfmath@counta\pgfmath@remainder\relax%
- \edef\pgfmath@remainder{\the\c@pgfmath@counta}%
- \c@pgfmath@counta\pgfmath@targetiterations\relax%
- \advance\c@pgfmath@counta-1\relax%
- \edef\pgfmath@targetiterations{\the\c@pgfmath@counta}%
- \ifnum\c@pgfmath@counta=0\relax%
- \edef\pgfmath@root{\pgfmath@root.\pgfmath@digit}%
- \else%
- \edef\pgfmath@root{\pgfmath@root\pgfmath@digit}%
- \fi%
- \ifnum\c@pgfmath@counta=-4\relax% -n+1 digits of precision.
- \let\pgfmath@next\pgfmath@sqrt@end%
- \else%
- \let\pgfmath@next\pgfmath@@@sqrt@%
- \fi%
- \expandafter\pgfmath@next\pgfmath@tokens%
-}
-
-\def\pgfmath@sqrt@end#1\pgfmath@{%
- \edef\pgfmathresult{\pgfmath@root}%
- \pgfmath@smuggleone\pgfmathresult%
- \endgroup}
-
-% \pgfmathpow
-%
-% Calculates #1 ^ #2
-%
-\def\pgfmathpow#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathpow@{\pgfmathresult}{\pgfmath@arg}}
-\def\pgfmathpow@#1#2{%
- \begingroup%
- \pgfmath@xa#1pt%
- \pgfmath@xb#2pt%
- \afterassignment\pgfmath@x%
- \expandafter\c@pgfmath@counta\the\pgfmath@xb\relax%
- \ifnum\c@pgfmath@counta<0\relax%
- \c@pgfmath@counta-\c@pgfmath@counta%
- \pgfmathreciprocal@{#1}%
- \pgfmath@xa\pgfmathresult pt\relax%
- \fi
- \ifdim\pgfmath@x=0pt\relax%
- \pgfmath@x1pt\relax%
- \pgfmathloop%
- \ifnum\c@pgfmath@counta>0\relax%
- \ifodd\c@pgfmath@counta%
- \pgfmath@x\pgfmath@tonumber{\pgfmath@x}\pgfmath@xa%
- \fi
- \ifnum\c@pgfmath@counta>1\relax%
- \pgfmath@xa\pgfmath@tonumber{\pgfmath@xa}\pgfmath@xa%
- \fi%
- \divide\c@pgfmath@counta2\relax%
- \repeatpgfmathloop%
- \else%
- \pgfmathln@{#1}%
- \pgfmath@x\pgfmathresult pt\relax%
- \pgfmath@x\pgfmath@tonumber{\pgfmath@xb}\pgfmath@x%
- \pgfmathexp@{\pgfmath@tonumber{\pgfmath@x}}%
- \pgfmath@x\pgfmathresult pt\relax%
- \fi%
- \pgfmath@returnone\pgf@x%
- \endgroup%
-}
-
-% \pgfmathround
-%
-% Asymmetric Half-up rounding.
-%
-\def\pgfmathround#1{\pgfmathparse{#1}\pgfmathround@{\pgfmathresult}}
-\def\pgfmathround@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \afterassignment\pgfmath@xa%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
- \pgfmath@xb\pgfmath@x%
- \ifdim\pgfmath@xb<0pt\relax%
- \ifdim\pgfmath@xa<0.5pt\relax%
- \else%
- \advance\c@pgfmath@counta-1\relax%
- \fi%
- \else%
- \ifdim\pgfmath@xa<0.5pt\relax%
- \else%
- \advance\c@pgfmath@counta1\relax%
- \fi%
- \fi%
- \pgfmath@returnone\the\c@pgfmath@counta pt%
- \endgroup%
-}%
-
-% \pgfmathfloor
-%
-% Floor function.
-%
-\def\pgfmathfloor#1{\pgfmathparse{#1}\pgfmathfloor@{\pgfmathresult}}
-\def\pgfmathfloor@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \pgfmath@x\c@pgfmath@counta pt\relax%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}%
-
-% \pgfmathceil
-%
-% Ceiling function.
-%
-\def\pgfmathceil#1{\pgfmathparse{#1}\pgfmathceil@{\pgfmathresult}}
-\def\pgfmathceil@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \pgfmath@y\pgfmath@x%
- \advance\pgfmath@y-\c@pgfmath@counta pt\relax%
- \pgfmath@x\c@pgfmath@counta pt\relax%
- \ifdim\pgfmath@y>0pt\relax%
- \advance\pgfmath@x1pt\relax%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}%
-
-% \pgfmathexp
-%
-% A Maclaurens expansion for e^#1.
-% 0 <= #1 < ln(16384).
-%
-\def\pgfmathexp#1{\pgfmathparse{#1}\pgfmathexp@{\pgfmathresult}}
-\def\pgfmathexp@#1{%
- \begingroup%
- \edef\pgfmath@arg{#1}%
- \pgfmath@x1pt\relax%
- \pgfmath@xa1pt\relax%
- \pgfmath@xb\pgfmath@x%
- \pgfmathloop%
- \pgfmath@xc\pgfmathcounter pt\relax%
- \c@pgfmath@counta\pgfmath@xc%
- \divide\c@pgfmath@counta65536\relax%
- \pgfmath@xc1pt\relax%
- \divide\pgfmath@xc\c@pgfmath@counta%
- \pgfmath@xa\pgfmath@tonumber{\pgfmath@xc}\pgfmath@xa%
- \expandafter\pgfmath@xa\pgfmath@arg\pgfmath@xa%
- \advance\pgfmath@x\pgfmath@xa%
- \ifdim\pgfmath@x=\pgfmath@xb%
- \else%
- \pgfmath@xb\pgfmath@x%
- \repeatpgfmathloop%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-
-
-% \pgfmathvectorlength
-%
-% Calcluate the Eulidean length of a 2D vector.
-%
-% This based on polynomial approximation co-efficents
-% contributed by Rouben Rostamian.
-%
-% #1 - the x component of the vector.
-% #2 - the y component of the vector.
-%
-\def\pgfmathveclen#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathveclen@{\pgfmathresult}{\pgfmath@arg}%
-}
-\def\pgfmathveclen@#1#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%
-}
-
-% \pgfmathmax
-%
-% Return the maximum of #1 or #2
-%
-\def\pgfmathmax#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathmax@{\pgfmathresult}{\pgfmath@arg}}%
-\def\pgfmathmax@#1#2{%
- \begingroup
- \pgfmath@x#1pt%
- \pgfmath@y#2pt\relax%
- \ifdim\pgfmath@x>\pgfmath@y%
- \pgfmath@returnone\pgfmath@x%
- \else%
- \pgfmath@returnone\pgfmath@y%
- \fi%
- \endgroup
-}
-
-% \pgfmathmax
-%
-% Return the minimim of #1 or #2
-%
-\def\pgfmathmin#1#2{%
- \edef\pgfmath@marshal{%
- \noexpand\pgfmathparse{#2}
- \noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
- \noexpand\pgfmathparse{#1}%
- }%
- \pgfmath@marshal%
- \pgfmathmin@{\pgfmathresult}{\pgfmath@arg}}%
-\def\pgfmathmin@#1#2{%
- \begingroup
- \pgfmath@x#1pt%
- \pgfmath@y#2pt%
- \relax%
- \ifdim\pgfmath@x<\pgfmath@y%
- \pgfmath@returnone\pgfmath@x%
- \else%
- \pgfmath@returnone\pgfmath@y%
- \fi%
- \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{-}%
- \edef\pgfmath@temp{\pgfmath@gobbleone#1}%
- \else%
- \edef\pgfmath@sci@sign{+}%
- \edef\pgfmath@temp{#1}%
- \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}
-
-
-
-
-
-% *** The following commands DO NOT WORK without the rest of PGF ***
-%
-% (a dumping ground for stuff that doesn't really belong anywhere else)
-
-% \pgfmathanglebetweenpoints
-%
-% Define \pgfmathresult as the angle between points #1 and #2
-% Should get the quadrants right as well.
-%
-\def\pgfmathanglebetweenpoints#1#2{%
- \begingroup%
- \pgf@process{\pgfpointdiff{#1}{#2}}%
- %
- % First approximate the angle of the external point...
- %
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@xb\pgf@x%
- \pgf@yb\pgf@y%
- \ifdim\pgf@xa<0pt\relax%
- \pgf@xa-\pgf@xa%
- \fi%
- \ifdim\pgf@ya<0pt\relax%
- \pgf@ya-\pgf@ya%
- \fi%
- \ifdim\pgf@ya>\pgf@xa%
- \pgf@x\pgf@xa%
- \pgf@y\pgf@ya%
- \else%
- \pgf@x\pgf@ya%
- \pgf@y\pgf@xa%
- \fi%
- \ifdim\pgf@y=0pt\relax%
- \pgf@x0pt%
- \else%
- \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}%
- \pgf@x\pgfmathresult\pgf@x%
- \fi%
- \multiply\pgf@x1000\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgf@counta\the\pgf@x\relax\pgfmath@%
- \expandafter\pgf@x\csname pgfmath@atan@\the\c@pgf@counta\endcsname pt\relax%
- \ifdim\pgfmath@ya>\pgfmath@xa\relax%
- \pgf@x-\pgf@x%
- \advance\pgf@x90pt%
- \fi%
- \ifdim\pgf@xb<0pt%
- \ifdim\pgf@yb>0pt%
- \pgf@x-\pgf@x%
- \fi%
- \advance\pgf@x180pt\relax%
- \else%
- \ifdim\pgf@yb<0pt%
- \pgf@x-\pgf@x%
- \advance\pgf@x360pt\relax%
- \fi\fi%
- \pgfmath@returnone\pgf@x%
- \endgroup%
-}
-
-%
-% \pgfmathrotatepointaround
-%
-% Rotate point #1 about point #2 by #3 degrees.
-%
-\def\pgfmathrotatepointaround#1#2#3{%
- \pgf@process{%
- \pgf@process{#2}%
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@xb\pgf@x%
- \pgf@yb\pgf@y%
- \pgf@process{#1}%
- \advance\pgf@x-\pgf@xa%
- \advance\pgf@y-\pgf@ya%
- \pgfmathsetmacro\angle{#3}%
- \pgfmathsin@{\angle}%
- \let\sineangle\pgfmathresult%
- \pgfmathcos@{\angle}%
- \let\cosineangle\pgfmathresult%
- \pgf@xa\cosineangle\pgf@x%
- \advance\pgf@xa-\sineangle\pgf@y%
- \pgf@ya\sineangle\pgf@x%
- \advance\pgf@ya\cosineangle\pgf@y%
- \pgf@x\pgf@xb%
- \pgf@y\pgf@yb%
- \advance\pgf@x\pgf@xa%
- \advance\pgf@y\pgf@ya%
- }%
-}
-
-% \pgfmathanglebetweenlines
-%
-% Calculate the clockwise angle between a line from point #1
-% to point #2 and a line from #3 to point #4.
-%
-\def\pgfmathanglebetweenlines#1#2#3#4{%
- \begingroup%
- \pgfmathanglebetweenpoints{#1}{#2}%
- \let\firstangle\pgfmathresult%
- \pgfmathanglebetweenpoints{#3}{#4}%
- \let\secondangle\pgfmathresult%
- \ifdim\firstangle pt>\secondangle pt\relax%
- \pgfmathadd@{\secondangle}{360}%
- \let\secondangle\pgfmathresult%
- \fi%
- \pgfmathsubtract@{\secondangle}{\firstangle}%
- \pgfmath@smuggleone\pgfmathresult%
- \endgroup%
-}
-
-% \pgfmathpointreflectalongaxis
-%
-% Reflects point #2 around an axis centered on #2 at an angle #3.
-%
-\def\pgfmathreflectpointalongaxis#1#2#3{%
- \pgf@process{%
- \pgfmathanglebetweenpoints{#2}{#1}%
- \pgfmath@tempdima\pgfmathresult pt\relax%
- \pgfmathparse{#3}%
- \advance\pgfmath@tempdima-\pgfmathresult pt\relax%
- \pgfmath@tempdima-2.0\pgfmath@tempdima%
- \pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}%
- }%
-}
-
-
-% \pgfmathpointintersectionoflineandarc
-%
-% A bit experimental at the moment:
-%
-% Locates the point where a line crosses an eliptical arc. If the line
-% does not cross the arc, a meaningless point will result.
-%
-% #1 the point of the line on the "convex" side of the arc.
-% #2 the point of the line on the "concave" side of the arc.
-% #3 the center of the eliptical arc.
-% #4 start angle of the arc.
-% #5 end angle of the arc.
-% #6 radii of the arc.
-%
-\def\pgfmathpointintersectionoflineandarc#1#2#3#4#5#6{%
- \pgf@process{%
- %
- % Get the required angle.
- %
- \pgfmathanglebetweenpoints{#2}{#1}%
- \let\x\pgfmathresult%
- %
- % Get the radii of the arc.
- %
- \pgfmath@in@{and }{#6}%
- \ifpgfmath@in@%
- \pgf@polar@#6\@@%
- \else%
- \pgf@polar@#6 and #6\@@%
- \fi%
- \edef\xarcradius{\the\pgf@x}%
- \edef\yarcradius{\the\pgf@y}%
- %
- % Get the start and end angles of the arc...
- %
- \pgfmathsetmacro\s{#4}%
- \pgfmathsetmacro\e{#5}%
- %
- % ...and also with rounding.
- %
- \pgfmathmod@{\s}{360}%
- \ifdim\pgfmathresult pt<0pt\relax%
- \pgfmathadd@{\pgfmathresult}{360}%
- \fi%
- \let\ss\pgfmathresult%
- \pgfmathmod@{\e}{360}%
- \ifdim\pgfmathresult pt<0pt\relax%
- \pgfmathadd@{\pgfmathresult}{360}%
- \fi%
- \let\ee\pgfmathresult%
- %
- % Hackery for when arc straddles zero.
- %
- \ifdim\ee pt<\ss pt\relax%
- \pgfmathadd@{\x}{180}%
- \pgfmathmod@{\pgfmathresult}{360}%
- \let\x\pgfmathresult%
- \fi%
- \def\m{360}% Measure of nearness.
- \pgfmathadd@{\s}{\e}%
- \pgfmathdivide@{\pgfmathresult}{2}%
- \let\n\pgfmathresult% The best estimate (default to middle of arc).
- \pgfmathloop%
- \pgfmathadd@{\s}{\e}%
- \pgfmathdivide@{\pgfmathresult}{2}%
- \let\p\pgfmathresult%
- \ifdim\p pt=\s pt\relax%
- \else%
- \pgfmathanglebetweenpoints{#2}{%
- \pgfpointadd{#3}{%
- \pgf@x\xarcradius\relax%
- \pgfmathcos@{\p}%
- \pgf@x\pgfmathresult\pgf@x%
- \pgf@y\yarcradius\relax%
- \pgfmathsin@{\p}%
- \pgf@y\pgfmathresult\pgf@y%
- }%
- }%
- %
- % Hackery for when arc straddles zero.
- %
- \ifdim\ee pt<\ss pt\relax%
- \pgfmathadd@{\pgfmathresult}{180}%
- \pgfmathmod@{\pgfmathresult}{360}%
- \fi%
- \let\q\pgfmathresult%
- %
- % More hackery...
- %
- \ifdim\x pt>335pt\relax%
- \ifdim\q pt<45pt\relax%
- \pgfmathadd@{\q}{360}%
- \let\q\pgfmathresult%
- \fi%
- \fi%
- \ifdim\x pt=\q pt% Found it!
- \pgfmathbreakloop% Breaks after current iteration is complete.
- \else
- \ifdim\x pt<\q pt\relax%
- \let\e\p%
- \else%
- \let\s\p%
- \fi%
- \fi%
- \pgfmathsubtract@{\x}{\q}%
- \pgfmathabs@{\pgfmathresult}%
- %
- % Save the estimate if it is better than any previous estimate.
- %
- \ifdim\pgfmathresult pt<\m pt\relax%
- \let\m\pgfmathresult%
- \let\n\p%
- \fi%
- \repeatpgfmathloop%
- \pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}%
- }%
-}
-
-% \pgfmathangleonellipse
-%
-% Find the angle corresponding to a point on the border of an ellispe.
-%
-% #1 - the point on the border.
-% #2 - the radii of the ellipse.
-%
-\def\pgfmathangleonellipse#1#2{%
- \begingroup%
- \pgfmath@in@{and }{#2}%
- \ifpgfmath@in@%
- \pgf@polar@#2\@@%
- \else%
- \pgf@polar@#2 and #2\@@%
- \fi%
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@process{#1}%
- \ifdim\pgf@x=0pt\relax%
- \pgfutil@tempdima1pt\relax%
- \else%
- \pgfutil@tempdima\pgf@x%
- \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}%
- \pgfutil@tempdima\pgfmathresult pt\relax%
- \fi%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima1pt\relax%
- \else%
- \pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}%
- \pgfutil@tempdima\pgfmathresult\pgfutil@tempdima%
- \pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}%
- \fi%
- %
- \pgfutil@tempdima\pgfmathresult pt\relax%
- \ifdim\pgfutil@tempdima<0pt\relax%
- \advance\pgfutil@tempdima360pt\relax%
- \fi%
- \ifdim\pgf@x<0pt\relax%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima180pt\relax%
- \else%
- \ifdim\pgf@y<0pt\relax%
- \advance\pgfutil@tempdima180pt\relax%
- \else%
- \advance\pgfutil@tempdima-180pt\relax%
- \fi%
- \fi%
- \else%
- \ifdim\pgf@x=0pt\relax%
- \ifdim\pgf@y<0pt\relax%
- \pgfutil@tempdima270pt\relax%
- \else%
- \pgfutil@tempdima90pt\relax%
- \fi%
- \else%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima0pt\relax%
- \fi%
- \fi%
- \fi%
- \pgfmath@returnone\pgfutil@tempdima%
- \endgroup%
-} \ No newline at end of file