pgf 2.0, third try

git-svn-id: svn://tug.org/texlive/trunk@6747 c570f23f-e606-0410-a88d-b1316a301751

8 files changed, 4956 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
new file mode 100644
index 00000000000..c901c3972f1
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
@@ -0,0 +1,10 @@
+% Copyright 2007 by Till Tantau
+%
+% 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.
+
+\input pgfmathcalc.code.tex
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathbase.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathbase.code.tex
new file mode 100644
index 00000000000..cd34d3a8db0
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathbase.code.tex
@@ -0,0 +1,262 @@
+% 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 provides basic macros for converting between bases.
+%
+% Version 1.414213 29/9/2007
+
+% \pgfmathbasetodec
+%
+% Convert a representation of an integer from 
+% the spcified base to base 10.
+%
+% #1 - a macro to store the result.
+% #2 - the representation of a number (i.e. not a register)
+% #3 - the current base.
+%
+% e.g.
+%
+% \pgfmathbasetodec\mynumber{10111}{2}
+%
+% \mynumber <- 23
+%
+\def\pgfmathbasetodec#1#2#3{%
+	\pgfmath@checknumber{#2}%
+	\pgfmath@checkbase{#3}%
+	\def\pgfmath@base{#3}%
+	\def\pgfmath@macro{#1}%
+	\c@pgfmath@counta1\relax%
+	\def\pgfmath@reversed{}%
+	\expandafter\pgfmathbasetodec@#2\pgfmathbasetodec}
+	
+\def\pgfmathbasetodec@#1{%
+	\ifx\pgfmathbasetodec#1%
+		\c@pgfmath@countb0%
+		\divide\c@pgfmath@counta by\pgfmath@base\relax%
+		\expandafter\pgfmathbasetodec@@%
+	\else%
+		\edef\pgfmath@reversed{\pgfmath@reversed#1}%
+		\expandafter\multiply\expandafter\c@pgfmath@counta\pgfmath@base\relax%
+		\expandafter\pgfmathbasetodec@%
+	\fi}
+
+\def\pgfmathbasetodec@@{\expandafter\pgfmathbasetodec@@@\pgfmath@reversed\pgfmathbasetodec}
+	
+\def\pgfmathbasetodec@@@#1{%
+	\ifx\pgfmathbasetodec#1\relax%
+		\expandafter\edef\pgfmath@macro{\the\c@pgfmath@countb}%
+		\let\pgfmath@next\pgfmathbasetodec@@@@%
+	\else%
+		\chardef\pgfmath@charnum`#1\relax%
+		\c@pgfmath@countc\pgfmath@charnum%
+		\ifnum\c@pgfmath@countc>96\relax%
+			\advance\c@pgfmath@countc-87\relax%
+		\else
+			\ifnum\c@pgfmath@countc>64\relax%
+				\advance\c@pgfmath@countc-55\relax%
+			\else
+				\advance\c@pgfmath@countc-48\relax%
+		\fi\fi%
+		\ifnum\c@pgfmath@countc<\pgfmath@base\relax%
+			\multiply\c@pgfmath@countc\c@pgfmath@counta\relax%
+			\advance\c@pgfmath@countb\c@pgfmath@countc%
+			\divide\c@pgfmath@counta by\pgfmath@base\relax%
+			\let\pgfmath@next\pgfmathbasetodec@@@%
+		\else
+			\pgfmath@error{Digit `#1' invalid for base \pgfmath@base}%
+			\let\pgfmath@next\relax%
+		\fi%	
+	\fi%
+	\pgfmath@next}
+\def\pgfmathbasetodec@@@@{%
+	\expandafter\pgfmath@ensurenumberlength\expandafter{\pgfmath@macro}%
+}
+
+% \pgfmathdectobase
+%
+% Convert a representation of an integer from 
+% base 10 to the spcified base. Letters for bases
+% greater than 10 are in lowercase.
+%
+% #1 - a macro to store the result.
+% #2 - a number in base 10 (in a macro, not a register)
+% #3 - the required base.
+%
+% e.g.
+%
+% \pgfmathdectobase\mynumber{127}{16}
+%
+% \mynumber <- 7f
+%
+\def\pgfmathdectobase#1#2#3{%
+	\pgfmath@checknumber{#2}%
+	\pgfmath@checkbase{#3}%
+	\c@pgfmath@counta#2\relax%
+	\def#1{}%
+	\pgfmathloop
+		\ifnum\c@pgfmath@counta>0\relax%
+			\c@pgfmath@countb\c@pgfmath@counta%
+			\divide\c@pgfmath@countb#3\relax%
+			\multiply\c@pgfmath@countb-#3\relax%
+			\advance\c@pgfmath@countb\c@pgfmath@counta%
+			\edef#1{\csname pgfmath@lowercase digit@\the\c@pgfmath@countb\endcsname#1}%
+			\divide\c@pgfmath@counta#3\relax%
+	\repeatpgfmathloop%
+	\pgfmath@ensurenumberlength{#1}}
+
+% \pgfmathdectoBase
+%
+% Convert a representation of an integer from 
+% base 10 to the spcified base. Letters for bases
+% greater than 10 are in uppercase.
+%
+% #1 - a macro to store the result.
+% #2 - a number in base 10 (in a macro, not a register)
+% #3 - the required base.
+%
+% e.g.
+%
+% \pgfmathdectoBase\mynumber{127}{16}
+%
+% \mynumber <- 7F
+%	
+\def\pgfmathdectoBase#1#2#3{%
+	\pgfmath@checkbase{#3}%
+	\pgfmath@checknumber{#2}%
+	\c@pgfmath@counta#2\relax%
+	\def#1{}%
+	\pgfmathloop
+		\ifnum\c@pgfmath@counta>0\relax%
+			\c@pgfmath@countb\c@pgfmath@counta%
+			\divide\c@pgfmath@countb#3\relax%
+			\multiply\c@pgfmath@countb-#3\relax%
+			\advance\c@pgfmath@countb\c@pgfmath@counta%
+			\edef#1{\csname pgfmath@uppercase digit@\the\c@pgfmath@countb\endcsname#1}%
+			\divide\c@pgfmath@counta#3\relax%
+	\repeatpgfmathloop%
+	\pgfmath@ensurenumberlength{#1}}
+
+\def\pgfmath@createdigits{%
+	\def\pgfmath@digitstyle{lowercase digit}%
+	\c@pgfmath@counta0\relax%
+	\pgfmath@createdigits@0123456789abcdefghijklmnopqrstuvwxyz\pgfmath@createdigits%
+	\def\pgfmath@digitstyle{uppercase digit}%
+	\c@pgfmath@counta0\relax%
+	\pgfmath@createdigits@0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\pgfmath@createdigits}
+
+\def\pgfmath@createdigits@#1{%
+	\ifx\pgfmath@createdigits#1\relax%
+	\else%
+		\expandafter\pgfmath@def\expandafter{\pgfmath@digitstyle}{\the\c@pgfmath@counta}{#1}%
+		\advance\c@pgfmath@counta1\relax%
+		\expandafter\pgfmath@createdigits@%
+	\fi}
+\pgfmath@createdigits
+
+% \pgfmathbasetobase
+%
+% Convert a representation of an integer from 
+% between the specified bases. Letters for target
+% bases greater than 10 are in lppercase.
+%
+% #1 - a macro to store the result.
+% #2 - a number (in a macro, not a register)
+% #3 - the source base.
+% #4 - the target base.
+%
+% e.g.
+%
+% \pgfmathbasetobase\mynumber{4321}{5}{9}
+%
+% \mynumber <- 721
+%	
+\def\pgfmathbasetobase#1#2#3#4{%
+	\pgfmathbasetodec{\pgfmath@temp}{#2}{#3}%
+	\pgfmathdectobase{#1}{\pgfmath@temp}{#4}
+}
+
+% \pgfmathbasetobase
+%
+% Convert a representation of an integer from 
+% between the specified bases. Letters for target
+% bases greater than 10 are in uppercase.
+%
+% #1 - a macro to store the result.
+% #2 - a number (in a macro, not a register)
+% #3 - the source base.
+% #4 - the target base.
+%
+% e.g.
+%
+% \pgfmathbasetobase\mynumber{1234}{5}{12}
+%
+% \mynumber <- 142
+%	
+\def\pgfmathbasetoBase#1#2#3#4{%
+	\pgfmathbasetodec{\pgfmath@temp}{#2}{#3}%
+	\pgfmathdectoBase{#1}{\pgfmath@temp}{#4}
+}
+
+\def\pgfmath@checkbase#1{%
+	\ifnum#1<2\relax%
+		\pgfmath@error{Cannot process numbers in base `#1'.}%
+	\else%
+		\ifnum#1>36\relax%
+			\pgfmath@error{Cannot process numbers in base `#1'.}%
+	\fi\fi}
+	
+\def\pgfmath@checknumber#1{%
+	\expandafter\pgfmath@checknumber@#1\pgfmath@}
+\def\pgfmath@checknumber@#1#2\pgfmath@{%
+	\ifx#1-%
+		\pgfmath@error{Cannot process negative numbers.}%
+	\fi}
+
+% \pgfmath@ensurenumberlength
+%
+% Internal macro for making a representation of a number have
+% a specific length, byt prefixing zeros to the number.
+%
+% #1 - a macro contatining a representation of an integer.
+% #2 - the number of digits to ensure.
+%
+% e.g.
+%
+% \foo <- 7FF
+%
+% \pgfmathsetnumberlength{8}%
+% \pgfmath@ensurenumberlength\foo
+%
+% \foo <- 000007FF
+%
+\def\pgfmath@ensurenumberlength#1{%
+	\def\pgfmath@tempa{#1}%
+	\expandafter\c@pgfmath@counta\pgfmath@basenumberlength\relax%
+	\expandafter\pgfmath@ensurenumberlength@#1\pgfmath@ensurenumberlength}
+\def\pgfmath@ensurenumberlength@#1{%
+	\ifx\pgfmath@ensurenumberlength#1\relax%
+		\expandafter\pgfmath@ensurenumberlength@@%
+	\else%
+		\advance\c@pgfmath@counta-1\relax%
+		\expandafter\pgfmath@ensurenumberlength@
+	\fi}
+
+\def\pgfmath@ensurenumberlength@@{%
+	\edef\pgfmath@tempb{\pgfmath@tempa}%
+	\pgfmath@ensurenumberlength@@@}
+\def\pgfmath@ensurenumberlength@@@{%
+	\ifnum\c@pgfmath@counta>0\relax%
+		\advance\c@pgfmath@counta-1\relax%
+		\edef\pgfmath@tempb{0\pgfmath@tempb}%
+		\expandafter\pgfmath@ensurenumberlength@@@%
+	\fi%
+	\expandafter\edef\pgfmath@tempa{\pgfmath@tempb}}
+	
+\def\pgfmathsetbasenumberlength#1{\def\pgfmath@basenumberlength{#1}}
+\pgfmathsetbasenumberlength{1}%
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
new file mode 100644
index 00000000000..29a2be58693
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
@@ -0,0 +1,253 @@
+% 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 loads all the parsing, functions and operator stuff
+%
+% Version 1.414213 29/9/2007
+
+\input pgfmathutil.code.tex
+\input pgfmathparser.code.tex
+\input pgfmathoperations.code.tex
+\input pgfmathbase.code.tex
+
+% \pgfmathsetlength, \pgfmathaddtolength
+%
+% #1 = dimension register
+% #2 = expression
+%
+% Description:
+%
+% These functions work similar to \setlength and \addtolength. Only,
+% they allow #2 to contain an expression, which is evaluated before
+% assignment. Furthermore, the font is setup before the assignment is
+% done, so that dimensions like 1em are evaluated correctly.
+%
+% If #2 starts with "+", then a simple assignment is done (but the
+% font is still setup). This is orders of magnitude faster than a
+% parsed assignment.
+
+\def\pgfmathsetlength#1#2{%
+	\expandafter\pgfmath@onquick#2\pgfmath@%
+	{%
+		% Ok, quick version:
+		\begingroup%
+			\pgfmath@selectfont%
+			\pgfmath@x#2\unskip%
+			\pgfmath@returnone\pgfmath@x%
+		\endgroup%
+		#1\pgfmathresult pt\relax%
+	}%
+	{%
+		\pgfmathparse{#2}%
+		#1\pgfmathresult pt\relax%
+	}%
+	\ignorespaces%
+}
+
+% \pgfmathaddtolength
+%
+% Add to #1 the result of evaluating #2.
+%
+% #1 - a dimension register
+% #2 - an expression
+%
+\def\pgfmathaddtolength#1#2{%
+	\expandafter\pgfmath@onquick#2\pgfmath@%
+  {%
+  	\begingroup%
+  		\pgfmath@selectfont%
+  		\pgfmath@x#1\relax%
+  		\advance\pgfmath@x#2\unskip%
+  		\pgfmath@returnone\pgfmath@x%
+    \endgroup%
+    #1\pgfmathresult pt\relax%
+  }%
+  {%
+  	\pgfmathparse{#2}%
+  	\advance#1\pgfmathresult pt\relax%
+  }%
+  \ignorespaces%
+}
+
+% \pgfmathsetcount
+%
+% Assign #1 the truncated evaluation of #2.
+%
+% #1 - a count register
+% #2 - an expression
+%
+\def\pgfmathsetcount#1#2{%
+  \expandafter\pgfmath@onquick#2\pgfmath@%
+  {%
+    #1#2\relax%
+  }%
+  {%
+    \pgfmathparse{#2}%
+    \afterassignment\pgfmath@gobbletilpgfmath@%
+    #1\pgfmathresult\relax\pgfmath@%
+  }%
+  \ignorespaces%
+}
+
+% \pgfmathaddtocount
+%
+% Add to #1 the truncated evaluation of #2.
+%
+% #1 - a count register
+% #2 - an expression
+%
+\def\pgfmathaddtocount#1#2{%
+  \expandafter\pgfmath@onquick#2\pgfmath@%
+  {%
+    \advance#1#2\relax%
+  }%
+  {%
+    \edef\pgfmath@addtocounttemp{\the#1}%
+    \pgfmathparse{#2}%
+    \afterassignment\pgfmath@gobbletilpgfmath@%
+    #1\pgfmathresult\relax\pgfmath@%
+    \advance#1\pgfmath@addtocounttemp\relax%
+  }%
+  \ignorespaces%
+}
+
+% \pgfmathnewcounter
+%
+% LaTeX style counter which also works in plain TeX. Defines
+% \c@<name> as a count register and also defines \the<name>.
+%
+% #1 the name of the counter.
+%
+% Example:
+%
+% \pgfmathnewcounter{counter}
+% \pgfmathsetcounter{counter}{12}
+% \thecounter  (same as \the\c@counter)
+%
+\def\pgfmathnewcounter#1{%
+	\expandafter\ifx\csname c@#1\endcsname\relax%
+		\def\pgfmath@marshal{\csname newcount\endcsname}% Ha! Who cares about \outer?
+		\expandafter\pgfmath@marshal\csname c@#1\endcsname%
+		\expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}%
+	\fi%
+}
+
+% \pgfmathsetcounter
+%
+% Set the counter #1 to the evaluation of #2.
+%
+% #1 - a counter name
+% #2 - an expression
+%
+\def\pgfmathsetcounter#1#2{%
+ 	\expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}%
+}
+
+% \pgfmathaddtocounter
+%
+% Add the counter #1 to the evaluation of #2.
+%
+% #1 - a counter name
+% #2 - an expression
+%
+\def\pgfmathaddtocounter#1#2{%
+  \expandafter\pgfmathaddtocount\csname c@#1\endcsname{#2}%
+}
+
+% \pgfmathmakecounterglobal
+%
+% Make the current value of a counter globally defined.
+%
+% #1 - a (valid) counter name.
+%
+\def\pgfmath@pgftext{pgf}
+\def\pgfmath@tikztext{tikz}
+\def\pgfmathmakecounterglobal#1{%
+	\pgfmath@ifundefined{c@#1}{}{%
+		\expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}%
+		\ifpgfmath@in@%
+		\else%
+			\expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}%
+			\ifpgfmath@in@%
+			\else%
+				\expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax%
+			\fi%
+		\fi%
+	}%
+}
+
+% \pgfmathsetmacro
+%
+% \edef#1 as the result of evaluating #2.
+%
+% #1 - a macro
+% #2 - an expression
+%
+\def\pgfmathsetmacro#1#2{%
+	\begingroup%
+		\pgfmathsetlength\pgfmath@x{#2}%
+		\edef#1{\pgfmath@tonumber{\pgfmath@x}}%
+		\pgfmath@smuggleone{#1}%
+	\endgroup%
+}
+
+% \pgfmathsetlengthmacro
+%
+% \edef#1 as the result of evaluating #2 with pt.
+%
+% #1 - a macro
+% #2 - an expression
+%
+\def\pgfmathsetlengthmacro#1#2{%
+	\begingroup%
+		\pgfmathsetlength\pgfmath@x{#2}%
+		\edef#1{\the\pgfmath@x}%
+		\pgfmath@smuggleone{#1}%
+	\endgroup%
+}
+
+% \pgfmathtruncatemacro
+%
+% \edef#1 as the truncated result of evaluating #2.
+%
+% #1 - a macro
+% #2 - an expression
+%
+\def\pgfmathtruncatemacro#1#2{%
+	\begingroup%
+		\pgfmathsetcount\c@pgfmath@counta{#2}%
+		\edef#1{\the\c@pgfmath@counta}%
+		\pgfmath@smuggleone{#1}%
+	\endgroup%
+}
+
+% Check whether a given parameter starts with quick.
+%
+% The command should be followed by nonempty text, ending with
+% \pgfmath@ as a stop-token. Then should follow
+%
+% #1 - code to execute if text starts with +
+% #2 - code to execute if text does not
+%
+% Example:
+%
+% \pgfmath@onquick+0pt\pgfmath@{is quick}{is slow}
+
+\def\pgfmath@onquick{%
+  \afterassignment\pgfmath@afterquick%
+  \let\pgfmath@next=%
+}
+
+\def\pgfmath@afterquick#1\pgfmath@{%
+  \ifx\pgfmath@next+%
+    \expandafter\pgfmath@firstoftwo%
+  \else%
+    \expandafter\pgfmath@secondoftwo%
+  \fi%
+}
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex
new file mode 100644
index 00000000000..452b9fa0b2c
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex
@@ -0,0 +1,1488 @@
+% 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
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
new file mode 100644
index 00000000000..3d69d34b73c
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
@@ -0,0 +1,970 @@
+% Copyright 2007 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 parses/evaluates a decimal expression.
+%
+% Version 1.414213 29/9/2007
+
+% \pgfmathparse, \pgfmathqparse
+%
+% Evaluates a decimal expression.
+%
+% #1 - the expression.
+%
+% returns
+%
+% x = the result as a dimension.
+%
+% E.g.
+% \pgfmathparse{3pt*2cm+1.5}
+% \pgfmathqparse{3pt*2cm+1.5pt}
+%
+% Every number in \pgfmathqparse *must*
+% specify a unit.
+%
+\newif\ifpgfmath@quickparse
+
+\def\pgfmathparse{%
+	\pgfmath@quickparsefalse%
+	\pgfmathparse@}
+
+\def\pgfmathqparse{%
+	\pgfmath@quickparsetrue%
+	\pgfmathparse@}
+		
+\def\pgfmath@calcreal#1{#1}%
+\def\pgfmath@calcminof#1#2{min(#1,#2)}%
+\def\pgfmath@calcmaxof#1#2{max(#1,#2)}%
+\def\pgfmath@calcratio#1#2{#1/#2}%
+
+\def\pgfmathparse@#1{%
+  \begingroup%    
+    % Reinstall correct font, so that dimensions like 1em are correct
+    \pgfmath@selectfont%
+    \let\real\pgfmath@calcreal%
+    \let\minof\pgfmath@calcminof%
+    \let\maxof\pgfmath@calcmaxof%
+    \let\ratio\pgfmath@calcratio%
+    \edef\pgfmath@temp{#1}%
+    \pgfmath@resetparsingparameters%
+    \global\pgfmathunitsdeclaredfalse%
+    \ifpgfmath@quickparse%
+      \let\pgfmath@parseoperand\pgfmath@quickparseoperand%
+    \else%
+      \let\pgfmath@parseoperand\pgfmath@parseoperand%
+    \fi%
+    \let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+    \expandafter\pgfmath@parse@\pgfmath@temp @@@@@@@@@@@\pgfmath@empty}
+
+
+% \pgfmath@resetparsingparameters
+%
+% Reset the stack at the begining of the parse/group.
+%
+\def\pgfmath@resetparsingparameters{%
+	\pgfmath@stack{\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+	\def\pgfmath@stacknextoperator{\pgfmath@empty}% Will not work with \let
+}
+% \pgfmath@parse@
+%
+% Start parsing. Expect one of
+% 1) the end of the parse
+% 2) the start of a group
+% 3) a (possible) operand.
+%
+\def\pgfmath@parse@#1{%
+	\def\pgfmath@token{}%
+	\ifx#1@%
+		\let\pgfmath@parsenext\pgfmath@endparse%
+	\else%
+		\ifx#1(%
+			\let\pgfmath@parsenext\pgfmath@startparsegroup%
+		\else%
+			\edef\pgfmath@token{#1}%
+			\let\pgfmath@parsenext\pgfmath@parseoperand%
+	\fi\fi%
+	\pgfmath@parsenext%
+}
+
+% If no TeX units are declared *at any point* in the parse
+% the result is scaled by \pgfmathresultunitscale.
+\newif\ifpgfmathunitsdeclared
+\def\pgfmathsetresultunitscale#1{\def\pgfmathresultunitscale{#1}}
+\def\pgfmathresultunitscale{1}
+
+% \pgfmath@endparse
+%
+% Everything stops here.
+%
+\def\pgfmath@endparse#1\pgfmath@empty{%
+    \pgfmath@processalloperations%
+    \pgfmath@stackpop{\pgfmathresult}%
+    \begingroup%
+      \ifpgfmathunitsdeclared%
+        \pgfmath@x1pt\relax%
+      \else%
+        \afterassignment\pgfmath@gobbletilpgfmath@%
+        \pgfmath@x\pgfmathresultunitscale pt\relax\pgfmath@%
+      \fi%
+      \expandafter\pgfmath@x\pgfmathresult\pgfmath@x%
+      \pgfmath@returnone\pgfmath@x%
+    \endgroup%
+    \pgfmath@smuggleone{\pgfmathresult}%
+  \endgroup%
+  \ignorespaces%
+}
+
+% \pgfmath@startparsegroup
+%
+% When opening ( is scanned start a new group.
+%
+\def\pgfmath@startparsegroup{%
+	\begingroup%
+		\let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+		\pgfmath@resetparsingparameters%
+		\pgfmath@parse@}
+
+% \pgfmath@endparsegroup
+%
+% When closing ) is scanned, processes all waiting
+% operations (within the group) and close the group.
+%
+\def\pgfmath@endparsegroup{%
+		\pgfmath@processalloperations%
+		\pgfmath@stackpop{\pgfmathresult}%
+		\expandafter\pgfmath@x\pgfmathresult pt\relax%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+	\pgfmath@parsepostgroup%
+}
+
+% \pgfmath@parseoperator
+%
+% An operator is expected here. 
+% Or the end of the parse or parse group.
+% 
+\def\pgfmath@parseoperator#1{%
+	\def\pgfmath@token{}%
+	% Push the operand in \pgfmathresult on to the stack. 
+	\expandafter\pgfmath@stackpushoperand\expandafter{\pgfmathresult}%
+	\ifx#1@%
+		\let\pgfmath@parsenext\pgfmath@endparse%
+	\else%
+		\ifx#1+%
+			\let\pgfmath@parsenext\pgfmath@parseadd%
+		\else%
+			\ifx#1-%
+				\let\pgfmath@parsenext\pgfmath@parsesubtract%
+			\else%
+				\ifx#1*%
+					\let\pgfmath@parsenext\pgfmath@parsemultiply%
+				\else%
+					\ifx#1/%
+						\let\pgfmath@parsenext\pgfmath@parsedivide%
+					\else
+						\ifx#1)%
+							\let\pgfmath@parsenext\pgfmath@endparsegroup%
+						\else%
+							\ifx#1r%
+								\let\pgfmath@parsenext\pgfmath@parseradians%
+							\else%
+								\ifx#1>%
+									\let\pgfmath@parsenext\pgfmath@parsegreaterthan%
+								\else%
+									\ifx#1<%
+										\let\pgfmath@parsenext\pgfmath@parselessthan%
+									\else%
+										\if#1=%
+											\let\pgfmath@parsenext\pgfmath@parseequalto%
+										\else%
+											\if#1^%
+												\let\pgfmath@parsenext\pgfmath@parsepower%
+											\else%
+												\pgfmath@error{Unknown operator `#1'}%
+												\let\pgfmath@parsenext\relax%
+	\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi%
+	\pgfmath@parsenext%
+}
+
+% Use a \toks register as a stack.
+\newtoks\pgfmath@stack
+
+% \pgfmath@stackpushoperator
+% 
+% Push an operator (actually its macro e.g., \pgfmathadd@)
+% on to the stack. And keep track of it using the macro
+% \pgfmath@stacknextoperator.
+%
+\def\pgfmath@stackpushoperator#1{%
+	\edef\pgfmath@temp{\noexpand#1\the\pgfmath@stack}%
+	\expandafter\pgfmath@stack\expandafter{\pgfmath@temp}%
+	\def\pgfmath@stacknextoperator{#1}}% <- Must \def. Cannot \let.
+
+% \pgfmath@stackpushoperand
+%
+% Push an operand (i.e. a number) on the stack. It is
+% put within a TeX group to make popping a lot simpler.
+%
+\def\pgfmath@stackpushoperand#1{%
+	\edef\pgfmath@temp{{#1}\the\pgfmath@stack}%
+	\expandafter\pgfmath@stack\expandafter{\pgfmath@temp}%
+}
+
+% \pgfmath@stackpeek
+%
+% Peek (i.e. without removal) at the top of the stack.
+%
+\def\pgfmath@stackpeek{\expandafter\pgfmath@stackpeek@\the\pgfmath@stack\pgfmath@}
+\def\pgfmath@stackpeek@#1#2\pgfmath@{#1}%
+
+% \pgfmath@stackpop
+%
+% Pop (i.e. remove) the top of the stack into #1.
+%
+\def\pgfmath@stackpop#1{\expandafter\pgfmath@stackpop@\expandafter#1\the\pgfmath@stack\pgfmath@}
+\def\pgfmath@stackpop@#1#2#3\pgfmath@{\edef#1{#2}\pgfmath@stack{#3}}%
+
+% \pgfmath@stackpopoperation
+%
+% Remove and perform an operation from the stack.
+%
+\def\pgfmath@stackpopoperation{%
+	\expandafter\pgfmath@stackpopoperation@\the\pgfmath@stack\pgfmath@%
+}
+\def\pgfmath@stackpopoperation@#1#2#3#4#5\pgfmath@{%
+	\ifx\pgfmath@empty#1\relax%
+			\pgfmath@stack{\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+	\else%
+		\ifx\pgfmath@empty#2\relax%
+			\pgfmath@stack{{#1}\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+		\else%
+			#2{#3}{#1}%
+			\pgfmath@stack{#4#5}%
+			\expandafter\pgfmath@stackpushoperand\expandafter{\pgfmathresult}%
+	\fi\fi%
+	\def\pgfmath@stacknextoperator{#4}}
+
+% \pgfmath@processalloperations
+%
+% Process all operation in the stack. The 
+% overall result is at the top of the stack.
+%
+\def\pgfmath@processalloperations{%
+	\expandafter\pgfmath@in@\pgfmath@stacknextoperator{\pgfmath@empty}%
+	\ifpgfmath@in@%
+		\let\pgfmath@processnext\relax%		
+	\else%
+		\pgfmath@stackpopoperation%
+		\let\pgfmath@processnext\pgfmath@processalloperations%
+	\fi%
+	\pgfmath@processnext}
+
+% \pgfmath@processoperationsuntil
+%
+% Process operations in the stack, until the specified
+% operation/s is/are encountered. The overall result is 
+% at the top of the stack.
+%
+\def\pgfmath@processoperationsuntil#1{%
+	\expandafter\pgfmath@in@\pgfmath@stacknextoperator{#1\pgfmath@empty}%
+	\ifpgfmath@in@%
+		\let\pgfmath@processnext\pgfmath@processoperationsuntil@end%		
+	\else%
+		\pgfmath@stackpopoperation%
+		\let\pgfmath@processnext\pgfmath@processoperationsuntil%
+	\fi%
+	\pgfmath@processnext{#1}}
+\def\pgfmath@processoperationsuntil@end#1{}
+
+
+% OK. Now the operators are parsed.
+% These correspond to the + - / * ^ < > = operators and r (postfix) function.
+%
+\def\pgfmath@parseadd{%	
+	% If no operator has been assigned (i.e. + is the first operator scanned),
+	% do nothing, except add addition to the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Empty the process stack up to any inequalities.
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathadd@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsesubtract{%	
+	% If no operator has been assigned (i.e. - is the first operator scanned),
+	% do nothing, except add subtract to the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Empty the process stack up to any inequalities.
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathsubtract@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsemultiply{%
+	% If no operator has been assigned (i.e. * is the first operator scanned),
+	% do nothing, except push multiply onto the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Process all operations up to inequalites or addition/subtraction
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathmultiply@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsedivide{%
+	% If no operator has been assigned (i.e. / is the first operator scanned),
+	% do nothing, except push divide onto the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Process all operations up to inequalites or addition/subtraction
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathdivide@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parsegreaterthan{%
+	% On scanning an equality/inequality operator everything up to
+	% (but not including) the operator is evaluated... 
+	\pgfmath@processalloperations%
+	% ...and the operation pushed onto the stack.
+	\pgfmath@stackpushoperator{\pgfmathgreaterthan@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parselessthan{%
+	\pgfmath@processalloperations%
+	\pgfmath@stackpushoperator{\pgfmathlessthan@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parseequalto={%
+	\pgfmath@processalloperations%
+	\pgfmath@stackpushoperator{\pgfmathequalto@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parsepower{%
+	% Easy, just push power onto the stack.
+	\pgfmath@stackpushoperator{\pgfmathpow@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parseradians{%
+	% r is a post-fix function...
+	\ifx\pgfmath@primaryoperation\pgfmath@empty%
+	\else%
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%	
+	\pgfmath@stackpop{\pgfmath@temp}%
+	\pgfmathdeg@{\pgfmath@temp}%
+	% ...so processing returns to \pgfmath@parseoperator
+	\pgfmath@parseoperator}
+	
+\newcount\c@pgfmath@parsecounta
+\newcount\c@pgfmath@parsecountb
+\newcount\c@pgfmath@parsecountc
+\newdimen\pgfmath@parsex
+
+% \pgfmath@quickparseoperand
+%
+% An operand can *only* be a dimension.
+%
+\def\pgfmath@quickparseoperand{%
+	\afterassignment\pgfmath@quickparseoperand@%
+	\pgfmath@parsex\pgfmath@token}
+\def\pgfmath@quickparseoperand@{%
+	\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+	\pgfmath@parseoperator%
+}
+	
+% \pgfmath@parseoperand
+%
+% An operand can be an ASCII number (with or without dimensions, with
+% or without a decimal point), a TeX register (count, dimen or skip,
+% which may have expanded with \the), or a function e.g. sin(X).
+%
+% It is assumed that after \edef-ing, the only unexpanded tokens are registers. 
+%
+\def\pgfmath@parseoperand{%
+	\def\pgfmath@sign{}%
+	\expandafter\pgfmath@parseoperandsign\pgfmath@token}
+\def\pgfmath@parseoperandsign#1{%
+	\pgfmath@in@#1{-+}% 
+	\ifpgfmath@in@
+		% Gobble multiple signs.
+		\edef\pgfmath@sign{\pgfmath@sign#1}%
+		\expandafter\pgfmath@parseoperandsign%
+	\else%
+		\expandafter\pgfmath@parsenumberorfunction\expandafter#1%
+	\fi%
+}
+
+\newif\ifpgfmath@dimen@
+
+\def\pgfmath@ifregisterdimen@#1\pgfmath@{%
+	\pgfmath@in@{p}{#1}%
+	\ifpgfmath@in@%
+		\pgfmath@dimen@true%
+	\else%
+		\pgfmath@dimen@false%
+	\fi} 			
+
+\def\pgfmath@parsenumberorfunction#1{%
+  \let\pgfmath@parsenext\pgfmath@parsenumberorfunction@simple%
+  \ifx#1\wd\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \ifx#1\ht\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \ifx#1\dp\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \pgfmath@parsenext#1%
+}
+
+\def\pgfmath@boxdimen#1#2{%
+  \pgfmath@parsex=\pgfmath@sign#1#2%
+  \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+  \global\pgfmathunitsdeclaredtrue% a dimension has units 
+  \pgfmath@parseoperator%
+}
+
+\def\pgfmath@parsenumberorfunction@simple#1{%	
+	\expandafter\ifcat#1\relax%
+		% So, a TeX register.
+		\afterassignment\pgfmath@ifregisterdimen@%
+		\pgfmath@parsex\pgfmath@sign#1pt\relax\pgfmath@%
+		\ifpgfmath@dimen@% 
+			% A dimension! So stop scanning operand here.
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+         \global\pgfmathunitsdeclaredtrue% a dimension has units
+			\def\pgfmath@temp{}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+		\else%
+			% A count! Expand it, but carry on as usual as it might
+			% be immediately followed by a dimension.
+			\ifdim\pgfmath@parsex<0pt\relax%
+				\edef\pgfmath@sign{\pgfmath@sign-}%
+				\pgfmath@parsex-\pgfmath@parsex%
+			\fi%
+			\edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parsenumberorfunction@%
+		\fi%
+	\else%
+		% Could be a number or a function...?
+		\edef\pgfmath@temp{#1}%
+		\let\pgfmath@parsenext\pgfmath@parsenumberorfunction@%
+	\fi%
+	\expandafter\pgfmath@parsenext\pgfmath@temp%
+}%
+
+\def\pgfmath@parsenumberorfunction@#1{%
+	\ifx#1(% It might be a group e.g. -(1+2)...
+		\let\pgfmath@parsenext\pgfmath@parseoperandgroup%
+	\else%
+		\pgfmath@in@{#1}{.0123456789}% 
+		\ifpgfmath@in@% ... or a number...
+			\let\pgfmath@parsenext\pgfmath@parsenumber%
+		\else% ... or a function.
+			\let\pgfmath@parsenext\pgfmath@parsefunction%
+		\fi%
+	\fi%
+	\pgfmath@parsenext#1%
+}%
+
+\def\pgfmath@parseoperandgroup({%
+	\let\pgfmath@postparsegroup\pgfmath@@parseoperandgroup%
+	\pgfmath@startparsegroup%
+}
+
+\def\pgfmath@@parseoperandgroup{%
+	\let\pgfmath@postparsegroup\pgfmath@parseoperator%
+	\edef\pgfmathresult{\pgfmath@sign\pgfmathresult}%
+	\pgfmath@parseoperator%
+}
+
+\def\pgfmath@parsenumber{% 
+	% Consider the number 3.14159
+	% 3 is parsed by assignment to a, then '.' is absorbed and 14159
+	% parsed by assignement to b (actually b=114159, see below). 
+	\c@pgfmath@parsecountc0\relax%
+	\afterassignment\pgfmath@parsedecimalpoint%
+	\c@pgfmath@parsecounta0}
+
+\def\pgfmath@parsedecimalpoint#1{%
+	\ifx#1.% Is there a decimal point? If not, see if there are any units.
+		\let\pgfmath@parsenext\pgfmath@parsemantissa%
+	\else%
+		\c@pgfmath@parsecountb10\relax% The first digit of b is gobbled (see below). 
+		\let\pgfmath@parsenext\pgfmath@parseunits%
+	\fi%
+	\pgfmath@parsenext#1}
+
+
+
+% We would like to assign the following number (which is the mantisse)
+% to a number. However, for a very long mantisse as in 3.141592653589793238462643
+% this will fail since the number becomes too large.
+%
+% Because of this, we have to do some ``magic'': We scan 9 tokens and
+% then do an assignment with a guard after 9 tokens so that the
+% assigment cannot fail.
+%
+\def\pgfmath@parsemantissa.#1#2#3#4#5#6#7#8#9{%
+  \afterassignment\pgfmath@checkforguard%    
+  % Consider the number: 2.005
+  % 2 is assigned to a, but b will be assigned 5, which is *not right*. 
+  % So using 1 here hereresults in  b=1005. The first digit is then  
+  % gobbled later, when expanded with \the.
+  \c@pgfmath@parsecountb1#1#2#3#4#5#6#7#8#9\relax}%
+
+\def\pgfmath@checkforguard{%
+  \pgfmath@ifnextchar\relax%
+  {%
+    % Ok, this is a looong mantisse. Start gobbling all following
+    % numbers
+    \pgfmath@gobblemantisse%
+  }%
+  {%
+    \pgfmath@removeguard%
+  }%
+}
+
+\def\pgfmath@gobblemantisse\relax#1#2#3#4#5#6#7#8#9{%
+  \afterassignment\pgfmath@checkforguard%
+  \c@pgfmath@parsecountc0#1#2#3#4#5#6#7#8#9\relax% these digits are ignored
+}
+
+\def\pgfmath@removeguard#1\relax{\pgfmath@parseunits#1}
+
+ 
+\def\pgfmath@parseunits#1{%
+  % Here the extra first digit in b is gobbled. 
+  \edef\pgfmath@resulttemp{%
+    \pgfmath@sign\the\c@pgfmath@parsecounta.\expandafter\pgfmath@gobbleone\the\c@pgfmath@parsecountb}%
+  % Check whether #1 is a \dp, \wd, or \ht
+  \let\pgfmath@parsenext=\pgfmath@parseunits@simple%
+  \ifx#1\wd\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \ifx#1\ht\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \ifx#1\dp\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \pgfmath@parsenext#1%
+}
+
+\def\pgfmath@parseunits@boxdimen#1#2{%
+  \pgfmath@parsex=\pgfmath@sign#1#2%
+  \pgfmath@parsex\pgfmath@resulttemp\pgfmath@parsex%
+  \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+  \global\pgfmathunitsdeclaredtrue% a dimension has units 
+  \pgfmath@parseoperator%
+}
+
+\def\pgfmath@parseunits@simple#1{%
+	% Now check if #1 is actually a register.
+	\ifcat#1\relax%
+		\afterassignment\pgfmath@ifregisterdimen@%
+		\pgfmath@parsex#1pt\relax\pgfmath@%
+		\pgfmath@parsex\pgfmath@resulttemp\pgfmath@parsex%
+		\ifpgfmath@dimen@% If it's a dimen stop scanning operand here.
+      \global\pgfmathunitsdeclaredtrue% a dimension has units
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+		\else
+			\edef\pgfmath@resulttemp{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parseunits@%
+		\fi%
+		\expandafter\pgfmath@parsenext%
+	\else%
+		\expandafter\pgfmath@parseunits@\expandafter#1%
+	\fi}
+
+\def\pgfmath@parseunits@#1#2{%
+	% Check if #1 is an operator, or the character `@' indicating the end of the parse.
+	\pgfmath@in@#1{@+-*/^r<>=()}%
+	\ifpgfmath@in@%
+		\edef\pgfmath@tokens{#1#2}%
+		\edef\pgfmathresult{\pgfmath@resulttemp}%
+		\let\pgfmath@parsenext\pgfmath@parseoperator%
+	\else%
+		\pgfmath@in@#1{Ee}% e+0X
+		\ifpgfmath@in@%
+			% Oh no! It might be and em or an ex...
+			\pgfmath@in@#2{mx}%
+			\ifpgfmath@in@%
+				\global\pgfmathunitsdeclaredtrue%
+				\pgfmath@parsex\pgfmath@resulttemp#1#2\relax%
+				\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+				\edef\pgfmath@tokens{}%
+				\let\pgfmath@parsenext\pgfmath@parseoperator%
+			\else%
+				\edef\pgfmath@tokens{#2}%
+				\let\pgfmath@parsenext\pgfmath@parsescientific%
+			\fi%
+		\else
+			% Anything else *should* be a TeX unit.
+			\global\pgfmathunitsdeclaredtrue%
+			\pgfmath@parsex\pgfmath@resulttemp#1#2\relax%
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\edef\pgfmath@tokens{}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+	\fi\fi%
+	\expandafter\pgfmath@parsenext\pgfmath@tokens%
+}
+
+% Parse 'Scientific' notation in the form xEyy
+%
+\def\pgfmath@parsescientific{%
+	\afterassignment\pgfmath@parsescientific@%
+	\c@pgfmath@parsecounta}
+
+\def\pgfmath@parsescientific@{%
+	\edef\pgfmath@parsesci@temp{\pgfmath@resulttemp\the\c@pgfmath@parsecountc}%
+	\expandafter\pgfmathscientific\expandafter{\pgfmath@parsesci@temp}%
+		{\the\c@pgfmath@parsecounta}%
+	\edef\pgfmath@resulttemp{\pgfmathresult}%
+	\pgfmath@parseunits@}
+
+% Functions parsed (not calculated) here are:
+%
+% round(X)         'half-up' rounding.
+% floor(X)         floor function.
+% ciel(X)          ceiling function.
+% abs(X)           absolute function.
+%
+% exp(X)           e^X (0 <= X <~= 9.7).
+% ln(X)            logarithm of X.
+% pow(X,Y)         X^Y,
+%
+% sin(X)           sine function.
+% cos(X)           cosine function.
+% tan(X)           tan function.
+% asin(X)          arcsine of X (in radians)    -1 <= X <= 1
+% acos(X)          arccosine of X (in radians)  -1 <= X <= 1
+% atan(X)          arctangent of X (in radians) -1 <= X <= 1
+% veclen(X,Y)      the length Z where Z^2 = X^2 + Y^2
+% mod(X,Y)         X modulo Y
+% max(X,Y)         the maximum of X or Y
+% min(X,Y)         the minimum of X or Y
+%
+% NB veclen, mod, max, and min *cannot* be nested.
+%
+% deg(X)           converts X to degrees (X in radians)
+% rad(X)           converts X to radians (X in degrees)
+%
+% rnd              generate pseudo-random number X (0 <= X <= 1).
+% rand             generate pseudo-random number X (1 <= X <= -1).
+% sqrt(X)          square root.
+% 
+% pi               the constant PI.
+
+\def\pgfmath@parsefunction{%
+	\def\pgfmath@parsedfunctionname{}%
+	\futurelet\pgfmath@parsetoken\pgfmath@parsefunction@@}
+\def\pgfmath@parsefunction@@#1{%
+	\pgfmath@in@#1{()@+-*/^<>=}% A function name ends with one of these...
+	\ifpgfmath@in@%
+		\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@end%
+	\else%
+		\ifx\pgfmath@parsetoken\pgfmath@sptoken% ...or a space.
+			\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@end%
+		\else%
+			\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@continue%
+	\fi\fi%
+	\pgfmath@parsefunctionnext#1}
+
+\def\pgfmath@parsefunction@end#1{%
+	\expandafter\ifx\csname pgfmath@parsefunction@\pgfmath@parsedfunctionname\endcsname\relax%
+		\pgfmath@reportunknownfunction%
+		\let\pgfmath@parsefunctionnext\relax%
+	\else%
+		\let\pgfmath@parsefunctionnext\pgfmath@executeparsefunction@%
+	\fi%
+	\pgfmath@parsefunctionnext#1}
+
+\def\pgfmath@parsefunction@continue#1{%
+	\edef\pgfmath@parsedfunctionname{\pgfmath@parsedfunctionname#1}%
+	\futurelet\pgfmath@parsetoken\pgfmath@parsefunction@@}
+	
+\def\pgfmath@executeparsefunction@{\csname pgfmath@parsefunction@\pgfmath@parsedfunctionname\endcsname}
+		
+		
+\def\pgfmath@reportunknownfunction{%
+	\pgfmath@error{Unknown function `\pgfmath@parsedfunctionname'}{}%
+}
+
+% \pgfmath@postfunction
+% 
+% In scanning a function e.g. sin(40), we subvert the normal parsing 
+% group mechanism by messing around with \pgfmath@parsepostgroup, so 
+% that after scanning ), the parser doesn't scan for an operator, but 
+% returns to the macros scanning the function. 
+% Here the mechanism is restored, and the value of the function is 
+% stored along with the approprate sign, which was saved earlier.
+%
+\def\pgfmath@postfunction{%
+	\let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+	\edef\pgfmathresult{\pgfmath@sign\pgfmathresult}%
+	\pgfmath@parseoperator}
+	
+
+% \pgfmath@parsefunction@abs
+%
+\def\pgfmath@parsefunction@abs{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@abs@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@abs@{%	
+	\expandafter\pgfmathabs@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sqrt
+%
+\def\pgfmath@parsefunction@sqrt{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sqrt@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sqrt@{%	
+	\expandafter\pgfmathsqrt@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@round
+%
+\def\pgfmath@parsefunction@round{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@round@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@round@{%	
+	\expandafter\pgfmathround@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@floor
+%
+\def\pgfmath@parsefunction@floor{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@floor@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@floor@{%	
+	\expandafter\pgfmathfloor@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@ceil
+%
+\def\pgfmath@parsefunction@ceil{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@ceil@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@ceil@{%	
+	\expandafter\pgfmathceil@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sin
+%
+\def\pgfmath@parsefunction@sin{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sin@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sin@{%	
+	\expandafter\pgfmathsin@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cos
+%
+\def\pgfmath@parsefunction@cos{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cos@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cos@{%	
+	\expandafter\pgfmathcos@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@asin
+%
+\def\pgfmath@parsefunction@asin{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@asin@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@asin@{%	
+	\expandafter\pgfmathasin@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@acos
+%
+\def\pgfmath@parsefunction@acos{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@acos@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@acos@{%	
+	\expandafter\pgfmathacos@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@atan
+%
+\def\pgfmath@parsefunction@atan{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@atan@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@atan@{%	
+	\expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@tan
+%
+\def\pgfmath@parsefunction@tan{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@tan@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@tan@{%	
+	\expandafter\pgfmathtan@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cot
+%
+\def\pgfmath@parsefunction@cot{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cot@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cot@{%	
+	\expandafter\pgfmathcot@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sec
+%
+\def\pgfmath@parsefunction@sec{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sec@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sec@{%	
+	\expandafter\pgfmathsec@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cosec
+%
+\def\pgfmath@parsefunction@cosec{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cosec@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cosec@{%	
+	\expandafter\pgfmathcosec@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@rad
+%
+\def\pgfmath@parsefunction@rad{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@rad@%
+	\pgfmath@parse@}
+\def\pgfmath@parsefunction@rad@{%
+	\expandafter\pgfmathrad@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}%
+	
+% \pgfmath@parsefunction@rad
+%
+\def\pgfmath@parsefunction@deg{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@deg@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@deg@{%
+	\expandafter\pgfmathdeg@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}%
+	
+% \pgfmath@parsefunction@rnd
+%
+\def\pgfmath@parsefunction@rnd{%
+	\expandafter\pgfmathrnd%
+	\expandafter\pgfmath@postfunction}
+			
+% \pgfmath@parsefunction@rand
+%
+\def\pgfmath@parsefunction@rand{%
+	\expandafter\pgfmathrand%
+	\expandafter\pgfmath@postfunction}%
+			
+% \pgfmath@parsefunction@exp
+%
+\def\pgfmath@parsefunction@exp{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@exp@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@exp@{%	
+	\expandafter\pgfmathexp@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@ln
+%
+\def\pgfmath@parsefunction@ln{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@ln@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@ln@{%	
+	\expandafter\pgfmathln@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+	
+% \pgfmath@parsefunction@pi
+%
+\def\pgfmath@parsefunction@pi{%
+	\pgfmathpi%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@veclen
+%
+\def\pgfmath@parsefunction@veclen{%
+	\expandafter\pgfmath@parsefunction@veclen@}
+\def\pgfmath@parsefunction@veclen@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@veclen@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@veclen@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathveclen@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@mod 
+%
+\def\pgfmath@parsefunction@mod{%
+	\expandafter\pgfmath@parsefunction@mod@}
+\def\pgfmath@parsefunction@mod@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@mod@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@mod@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmod@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@max
+%
+\def\pgfmath@parsefunction@max{%
+	\expandafter\pgfmath@parsefunction@max@}
+\def\pgfmath@parsefunction@max@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@max@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@max@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmax@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}	
+
+% \pgfmath@parsefunction@min 
+%
+\def\pgfmath@parsefunction@min{%
+	\expandafter\pgfmath@parsefunction@min@}
+\def\pgfmath@parsefunction@min@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@min@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@min@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmin@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+	
+% \pgfmath@parsefunction@pow 
+%
+\def\pgfmath@parsefunction@pow{%
+	\expandafter\pgfmath@parsefunction@pow@}
+\def\pgfmath@parsefunction@pow@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@pow@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@pow@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathpow@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}	
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathrnd.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathrnd.code.tex
new file mode 100644
index 00000000000..ea8d5bb3092
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathrnd.code.tex
@@ -0,0 +1,212 @@
+% 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 pesudorandom numbers.
+%
+% Version 1.414213 29/9/2007
+
+% Pseudo-random number generation.
+%
+% See:
+% \book@{pressetal1992,
+%    author    = {William H. Press and Brian P. Flannery and Saul A. 
+%                 Teukolsky and William T. Vetterling}, 
+%    title     = {Numerical Recipies in C},
+%    edition   = {Second},
+%    publisher = {Cambridge University Press}
+% }
+%
+% See also, the documentation for the lcg package by Erich Janka:
+% (http://www.ctan.org/tex-archive/macros/latex/contrib/lcg/lcg.pdf)
+%
+\def\pgfmath@rnd@m{2147483647}% LaTeX Maximum.
+
+\begingroup
+\c@pgfmath@counta=\time%
+\multiply\c@pgfmath@counta by\year%
+\xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}% The seed. 
+\endgroup
+
+% \pgfmathsetseed
+%
+% Explictly set the seed for the generator
+%   
+% #1 -> the new seed.
+%
+\def\pgfmathsetseed#1{\pgfmathparse{#1}\expandafter\pgfmath@setseed\pgfmathresult\relax}%
+\def\pgfmath@setseed#1.#2\relax{\def\pgfmath@rnd@z{#1}}%  
+
+% Alternative paramaters - see Press et al (1992) p278-279, 
+% for discussion.
+%
+% a=16807 q=127773 r=2836
+% a=48271 q=4488   r=3399
+%
+\def\pgfmath@rnd@a{69621}
+\def\pgfmath@rnd@r{23902}
+\def\pgfmath@rnd@q{30845}
+
+% \pgfmathgeneratepseudorandomnumber
+% 
+% A linear congruency generator for generating
+% pseudo-random numbers. Generates numbers in
+% the range 1 - 2^31-1.
+%
+\def\pgfmathgeneratepseudorandomnumber{%
+	\begingroup%
+		\c@pgfmath@counta=\pgfmath@rnd@z%
+		\c@pgfmath@countb=\pgfmath@rnd@z%
+		\c@pgfmath@countc=\pgfmath@rnd@q%
+		\divide\c@pgfmath@counta by\c@pgfmath@countc%
+		\multiply\c@pgfmath@counta by-\c@pgfmath@countc%
+		\advance\c@pgfmath@counta by\c@pgfmath@countb
+		\c@pgfmath@countc=\pgfmath@rnd@a%
+		\multiply\c@pgfmath@counta by\c@pgfmath@countc%
+		\c@pgfmath@countc=\pgfmath@rnd@q%
+		\divide\c@pgfmath@countb by\c@pgfmath@countc%
+		\c@pgfmath@countc=\pgfmath@rnd@r%
+		\multiply\c@pgfmath@countb by\c@pgfmath@countc%
+		\advance\c@pgfmath@counta by-\c@pgfmath@countb%
+		\ifnum\c@pgfmath@counta<0\relax%
+			\c@pgfmath@countb=\pgfmath@rnd@m%
+			\advance\c@pgfmath@counta by\c@pgfmath@countb%
+		\fi%
+		\xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}%
+	\endgroup%
+	\edef\pgfmathresult{\pgfmath@rnd@z}%
+}
+
+% \pgfmathrnd
+%
+% Generates a pseudo-random number between 0 and 1.
+%
+\def\pgfmathrnd{%
+	\begingroup%
+		\pgfmathgeneratepseudorandomnumber%
+		\c@pgfmath@counta\pgfmathresult%
+		\c@pgfmath@countb\c@pgfmath@counta%
+		\divide\c@pgfmath@countb100001\relax% To get one.
+		\multiply\c@pgfmath@countb-100001\relax%
+		\advance\c@pgfmath@countb\c@pgfmath@counta%
+		\advance\c@pgfmath@countb1000000\relax%
+		\expandafter\pgfmathrnd@\the\c@pgfmath@countb\pgfmath@%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}%
+
+\def\pgfmathrnd@#1#2#3\pgfmath@{%
+	\edef\pgfmath@temp{#2.#3}%
+	\pgfmath@x=\pgfmath@temp pt\relax%
+}%
+
+% \pgfmathrand
+%
+% Generates a pseudo-random number between -1 and 1.
+%
+\def\pgfmathrand{%
+	\begingroup%
+		\pgfmathgeneratepseudorandomnumber%
+		\c@pgfmath@counta\pgfmathresult%
+		\c@pgfmath@countb\c@pgfmath@counta%
+		\divide\c@pgfmath@countb200001\relax%
+		\multiply\c@pgfmath@countb-200001\relax%
+		\advance\c@pgfmath@countb\c@pgfmath@counta%
+		\advance\c@pgfmath@countb-100000\relax%
+		\ifnum\c@pgfmath@countb<0\relax%
+			\advance\c@pgfmath@countb-1000000\relax%
+		\else%
+			\advance\c@pgfmath@countb1000000\relax%
+		\fi%
+		\expandafter\pgfmathrand@\the\c@pgfmath@countb\pgfmath@%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}%
+
+\def\pgfmathrand@#1#2#3#4\pgfmath@{%
+	\ifx#1-%
+		\edef\pgfmath@temp{-#3.#4}%
+	\else%
+		\edef\pgfmath@temp{#2.#3#4}%
+	\fi%
+	\pgfmath@x=\pgfmath@temp pt\relax%
+}%
+
+% \pgfmathrandominteger
+%
+% Return a 'randomly' selected integer in the range #2 - #3 (inclusive).
+%
+% #1 - a macro to store the integer (not a count register).
+% #2 - the lower limit of the range.
+% #3 - the upper limit of the range.
+%
+\def\pgfmathrandominteger#1#2#3{%
+	\begingroup%
+		\pgfmathgeneratepseudorandomnumber%
+		\c@pgfmath@counta#2\relax%
+		\c@pgfmath@countb#3\relax%
+		\c@pgfmath@countc\c@pgfmath@countb%
+		% OK. Maybe #2 > #3.
+		\ifnum\c@pgfmath@counta>\c@pgfmath@countb\relax%
+			\c@pgfmath@countc\c@pgfmath@countb%
+			\c@pgfmath@countb\c@pgfmath@counta%
+			\c@pgfmath@counta\c@pgfmath@countc%
+		\fi%
+		\advance\c@pgfmath@countc1\relax%
+		\advance\c@pgfmath@countc-\c@pgfmath@counta%
+		\c@pgfmath@counta\pgfmathresult\relax%
+		\c@pgfmath@countb\c@pgfmath@counta%
+		\divide\c@pgfmath@countb\c@pgfmath@countc%
+		\multiply\c@pgfmath@countb-\c@pgfmath@countc%
+		\advance\c@pgfmath@counta\c@pgfmath@countb%
+		\advance\c@pgfmath@counta#2\relax%
+		\edef\pgfmathresult{\the\c@pgfmath@counta}%
+		\pgfmath@smuggleone{\pgfmathresult}%
+	\endgroup%
+	\edef#1{\pgfmathresult}%
+}
+
+% \pgfmathdeclarerandomlist
+%
+% Create a list to be used with \pgfmathrandomelement.
+%
+% #1 - the name of the list
+% #2 - a list of comma separated elements.
+%
+\def\pgfmathdeclarerandomlist#1#2{%
+	\def\pgfmath@randomlistname{#1}%
+	\begingroup%
+		\c@pgfmath@counta=1\relax%
+		% {} is a possible random element so (locally) 
+		% redefine \pgfmath@empty.
+		\def\pgfmath@empty{pgfmath@empty}% 
+		\expandafter\pgfmath@scanrandomlist#2{pgfmath@empty}}
+\def\pgfmath@scanrandomlist#1{%
+	\def\pgfmath@scanneditem{#1}%
+	\ifx\pgfmath@scanneditem\pgfmath@empty%
+		\advance\c@pgfmath@counta-1\relax%
+		\expandafter\xdef\csname pgfmath@randomlist@\pgfmath@randomlistname\endcsname{\the\c@pgfmath@counta}%
+		\endgroup%	
+	\else%
+		\expandafter\gdef\csname pgfmath@randomlist@\pgfmath@randomlistname @\the\c@pgfmath@counta\endcsname{#1}%
+		\advance\c@pgfmath@counta1\relax%
+		\expandafter\pgfmath@scanrandomlist%
+	\fi}
+
+% \pgfmathrandomitem
+%
+% Return a 'randomly' selected element from a list.
+%
+% #1 - a macro to store the item.
+% #2 - the name of the list.
+%
+\def\pgfmathrandomitem#1#2{%
+	\pgfmath@ifundefined{pgfmath@randomlist@#2}{\pgfmath@error{Unknown random list `#2'}}{%
+		\edef\pgfmath@randomlistlength{\csname pgfmath@randomlist@#2\endcsname}%
+		\pgfmathrandominteger{\pgfmath@randomtemp}{1}{\pgfmath@randomlistlength}%
+		\def#1{\csname pgfmath@randomlist@#2@\pgfmath@randomtemp\endcsname}}}
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathtrig.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathtrig.code.tex
new file mode 100644
index 00000000000..20d86dd8bdf
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathtrig.code.tex
@@ -0,0 +1,1496 @@
+% 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 trigonometric functions/operations.
+%
+% Much of this file is based on ideas and code (particularly 
+% the old \pgfcoremath.code.tex) due to Till Tantau.
+%
+% Version 1.414213 29/9/2007
+
+% \pgfmathpi
+%
+\def\pgfmathpi{\edef\pgfmathresult{\pgfmath@pi}}
+\def\pgfmath@pi{3.14159}
+
+% \pgfmathradians 
+% (for comptability with 1.18 beta, will be deprecated)
+% 
+% Convert #1 from radians to degrees (accurate to 1 deg).
+%
+\def\pgfmathradians#1{%
+	\pgfmathparse{#1}%
+	\pgfmathradians@{\pgfmathresult}}
+\def\pgfmathradians@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}%
+
+% \pgfmathdeg
+% 
+% Convert #1 from radians to degrees.
+%
+\def\pgfmathdeg#1{%
+	\pgfmathparse{#1}%
+	\pgfmathdeg@{\pgfmathresult}}
+\def\pgfmathdeg@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}%
+
+% \pgfmathrad
+% 
+% Convert #1 from degrees to radians.
+%
+\def\pgfmathrad#1{%
+	\pgfmathparse{#1}%
+	\pgfmathrad@{\pgfmathresult}}
+\def\pgfmathrad@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@x3.14159\pgfmath@x% 
+		\divide\pgfmath@x180\relax%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}%
+
+% \pgfmathsin
+% 
+% Calculate the sine of #1 (in degrees).
+%
+\def\pgfmathsin#1{%
+	\pgfmathparse{#1}%
+	\pgfmathsin@{\pgfmathresult}}
+\def\pgfmathsin@#1{%
+	% Let #1 = a.b
+	% Then sin(#1) \approx (1-b)*sin(a) + b*sin(a+1)
+	%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\advance\pgfmath@x-90pt\relax%
+		\afterassignment\pgfmath@gobbletilpgfmath@
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@
+		\divide\c@pgfmath@counta360\relax%
+		\multiply\c@pgfmath@counta-360\relax%
+		\advance\pgfmath@x\c@pgfmath@counta pt\relax%
+		\ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
+		\ifdim\pgfmath@x<180pt\relax%
+		\else
+			\pgfmath@x-\pgfmath@x%
+			\advance\pgfmath@x360pt\relax%
+		\fi%
+		% Now 0 <= x < 179. So split x into integer and decimal...
+		%
+		\afterassignment\pgfmath@xa%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+		%
+		% ...if #1 is an integer, don't do anything fancy.
+		\ifdim\pgfmath@xa=0pt%
+			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax%
+		\else%
+			\pgfmath@x-\pgfmath@xa%
+			\advance\pgfmath@x1pt\relax%
+			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
+			\advance\c@pgfmath@counta1\relax%
+			\expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
+		\fi%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup
+}
+
+% \pgfmathcos
+% 
+% Calculate the cosine of #1 (in degrees).
+%
+\def\pgfmathcos#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathcos@\expandafter{\pgfmathresult}}
+\def\pgfmathcos@#1{%
+	% Let x = a.b
+	% Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
+	%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\afterassignment\pgfmath@gobbletilpgfmath@%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% 
+		\divide\c@pgfmath@counta360\relax%
+		\multiply\c@pgfmath@counta-360\relax%
+		\advance\pgfmath@x\c@pgfmath@counta pt\relax%
+		\ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
+		\ifdim\pgfmath@x<180pt\relax%
+		\else%
+			\pgfmath@x-\pgfmath@x%
+			\advance\pgfmath@x360pt\relax%
+		\fi%
+		% Now 0 <= x < 179. So split x into integer and decimal...
+		%
+		\afterassignment\pgfmath@xa%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+		%
+		% ...if #1 is an integer, don't do anything fancy.
+		\ifdim\pgfmath@xa=0pt%
+			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt%
+		\else%
+			\pgfmath@x-\pgfmath@xa%
+			\advance\pgfmath@x1pt\relax%
+			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
+			\advance\c@pgfmath@counta1\relax%
+			\ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
+			\expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
+		\fi%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+% \pgfmathsincos
+% 
+% Calculate the sin and cosine of #1 (in degrees).
+%
+\def\pgfmathsincos#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathsincos@\expandafter{\pgfmathresult}}
+\def\pgfmathsincos@#1{%
+	\edef\pgfmath@temparg{#1}%
+	\pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}%
+	\pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}%
+}
+
+% \pgfmathtan
+% 
+% Calculate the tangent of #1 (in degrees).
+%
+\def\pgfmathtan#1{%
+	\pgfmathparse{#1}%
+	\pgfmathtan@{\pgfmathresult}}
+\def\pgfmathtan@#1{%
+	\begingroup%
+		\edef\pgfmath@temparg{#1}%
+		\pgfmathcos@{\pgfmath@temparg}%
+		\expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
+		\edef\pgfmath@tantemp{\pgfmathresult}%
+		\pgfmathsin@{\pgfmath@temparg}%
+		\pgfmath@x\pgfmathresult pt\relax%
+		\pgfmath@x\pgfmath@tantemp\pgfmath@x%
+		\ifdim\pgfmath@x<0pt\relax%
+			\c@pgfmath@countb-1\relax%
+		\else%
+			\c@pgfmath@countb1\relax%
+		\fi%
+		% Adjust to 4 decimal places. This gets rid of some annoyingly tiny errors.
+		\afterassignment\pgfmath@x%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+		\ifdim\pgfmath@x<.0001pt\relax%
+			\pgfmath@x0pt\relax%
+		\fi%
+		\advance\pgfmath@x\c@pgfmath@counta pt%
+		\multiply\pgfmath@x\c@pgfmath@countb%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+% \pgfmathcosec
+% 
+% Calculate the cosec of #1 (in degrees).
+%
+\def\pgfmathcosec#1{%
+	\pgfmathparse{#1}%
+	\pgfmathcosec@{\pgfmathresult}}
+\def\pgfmathcosec@#1{%
+	\expandafter\pgfmathsin@\expandafter{#1}%
+	\pgfmathreciprocal@{\pgfmathresult}%
+}
+
+% \pgfmathsec
+% 
+% Calculate the sec of #1 (in degrees).
+%
+\def\pgfmathsec#1{%
+	\pgfmathparse{#1}%
+	\pgfmathsec@{\pgfmathresult}}
+\def\pgfmathsec@#1{%
+	\expandafter\pgfmathcos@\expandafter{#1}%
+	\pgfmathreciprocal@{\pgfmathresult}%
+}
+
+% \pgfmathcot
+% 
+% Calculate the cotangent of #1 (in degrees).
+%
+\def\pgfmathcot#1{%
+	\pgfmathparse{#1}%
+	\pgfmathcot@{\pgfmathresult}}
+\def\pgfmathcot@#1{%
+	\begingroup%
+		\edef\pgfmath@temparg{#1}%
+		\pgfmathsin@{\pgfmath@temparg}%
+		\expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
+		\edef\pgfmath@tantemp{\pgfmathresult}%
+		\pgfmathcos@{\pgfmath@temparg}%
+		\pgfmath@x\pgfmathresult pt\relax%
+		\pgfmath@x\pgfmath@tantemp\pgfmath@x%
+		\ifdim\pgfmath@x<0pt\relax%
+			\c@pgfmath@countb-1\relax%
+		\else%
+			\c@pgfmath@countb1\relax%
+		\fi%
+		% Adjust to 4 decimal places. This gets rid of some annoyingly tiny errors.
+		\afterassignment\pgfmath@x%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+		\ifdim\pgfmath@x<.0001pt\relax%
+			\pgfmath@x0pt\relax%
+		\fi%
+		\advance\pgfmath@x\c@pgfmath@counta pt%
+		\multiply\pgfmath@x\c@pgfmath@countb%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+% \pgfmathasin
+%
+% The asin of #1
+%
+\def\pgfmathasin#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathasin@\expandafter{\pgfmathresult}}
+\def\pgfmathasin@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@xa\pgfmath@x%
+		\ifdim\pgfmath@x<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@x1000\pgfmath@x%
+		\afterassignment\pgfmath@gobbletilpgfmath@%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
+		\pgfmath@x-\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
+		\advance\pgfmath@x90pt\relax%
+		\ifdim\pgfmath@xa<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+% \pgfmathacos
+%
+% The acos of #1
+%	
+\def\pgfmathacos#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathacos@\expandafter{\pgfmathresult}}
+\def\pgfmathacos@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@xa\pgfmath@x%
+		\ifdim\pgfmath@x<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@x1000\pgfmath@x%
+		\afterassignment\pgfmath@gobbletilpgfmath@%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
+		\expandafter\pgfmath@x\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
+		\ifdim\pgfmath@xa<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+% \pgfmathasin
+%
+% The atan of #1
+%
+\def\pgfmathatan#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathatan@\expandafter{\pgfmathresult}}
+\def\pgfmathatan@#1{%
+	\begingroup%
+		\expandafter\pgfmath@x#1pt\relax%
+		\pgfmath@xa\pgfmath@x%
+		\ifdim\pgfmath@x<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@xb\pgfmath@x%
+		\ifdim\pgfmath@x>1pt\relax%
+			\edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
+			\pgfmathreciprocal@{\pgfmath@temp}%
+			\pgfmath@x\pgfmathresult pt\relax%
+		\fi%
+		\pgfmath@x1000\pgfmath@x%
+		\afterassignment\pgfmath@gobbletilpgfmath@%
+		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
+		\ifdim\pgfmath@xb>1pt\relax%
+			\expandafter\pgfmath@x\expandafter-\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
+			\advance\pgfmath@x90pt%
+		\else%
+			\expandafter\pgfmath@x\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
+		\fi%
+		\ifdim\pgfmath@xa<0pt\relax%
+			\pgfmath@x-\pgfmath@x%
+		\fi%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+}
+
+	
+\def\pgfmath@def#1#2#3{\expandafter\def\csname pgfmath@#1@#2\endcsname{#3}}
+\pgfmath@def{cos}{0}{1.00000}		\pgfmath@def{cos}{1}{0.99985}
+\pgfmath@def{cos}{2}{0.99939}		\pgfmath@def{cos}{3}{0.99863}
+\pgfmath@def{cos}{4}{0.99756}		\pgfmath@def{cos}{5}{0.99619}
+\pgfmath@def{cos}{6}{0.99452}		\pgfmath@def{cos}{7}{0.99255}
+\pgfmath@def{cos}{8}{0.99027}		\pgfmath@def{cos}{9}{0.98769}
+\pgfmath@def{cos}{10}{0.98481}		\pgfmath@def{cos}{11}{0.98163}
+\pgfmath@def{cos}{12}{0.97815}		\pgfmath@def{cos}{13}{0.97437}
+\pgfmath@def{cos}{14}{0.97030}		\pgfmath@def{cos}{15}{0.96593}
+\pgfmath@def{cos}{16}{0.96126}		\pgfmath@def{cos}{17}{0.95630}
+\pgfmath@def{cos}{18}{0.95106}		\pgfmath@def{cos}{19}{0.94552}
+\pgfmath@def{cos}{20}{0.93969}		\pgfmath@def{cos}{21}{0.93358}
+\pgfmath@def{cos}{22}{0.92718}		\pgfmath@def{cos}{23}{0.92050}
+\pgfmath@def{cos}{24}{0.91355}		\pgfmath@def{cos}{25}{0.90631}
+\pgfmath@def{cos}{26}{0.89879}		\pgfmath@def{cos}{27}{0.89101}
+\pgfmath@def{cos}{28}{0.88295}		\pgfmath@def{cos}{29}{0.87462}
+\pgfmath@def{cos}{30}{0.86603}		\pgfmath@def{cos}{31}{0.85717}
+\pgfmath@def{cos}{32}{0.84805}		\pgfmath@def{cos}{33}{0.83867}
+\pgfmath@def{cos}{34}{0.82904}		\pgfmath@def{cos}{35}{0.81915}
+\pgfmath@def{cos}{36}{0.80902}		\pgfmath@def{cos}{37}{0.79864}
+\pgfmath@def{cos}{38}{0.78801}		\pgfmath@def{cos}{39}{0.77715}
+\pgfmath@def{cos}{40}{0.76604}		\pgfmath@def{cos}{41}{0.75471}
+\pgfmath@def{cos}{42}{0.74314}		\pgfmath@def{cos}{43}{0.73135}
+\pgfmath@def{cos}{44}{0.71934}		\pgfmath@def{cos}{45}{0.70711}
+\pgfmath@def{cos}{46}{0.69466}		\pgfmath@def{cos}{47}{0.68200}
+\pgfmath@def{cos}{48}{0.66913}		\pgfmath@def{cos}{49}{0.65606}
+\pgfmath@def{cos}{50}{0.64279}		\pgfmath@def{cos}{51}{0.62932}
+\pgfmath@def{cos}{52}{0.61566}		\pgfmath@def{cos}{53}{0.60182}
+\pgfmath@def{cos}{54}{0.58779}		\pgfmath@def{cos}{55}{0.57358}
+\pgfmath@def{cos}{56}{0.55919}		\pgfmath@def{cos}{57}{0.54464}
+\pgfmath@def{cos}{58}{0.52992}		\pgfmath@def{cos}{59}{0.51504}
+\pgfmath@def{cos}{60}{0.50000}		\pgfmath@def{cos}{61}{0.48481}
+\pgfmath@def{cos}{62}{0.46947}		\pgfmath@def{cos}{63}{0.45399}
+\pgfmath@def{cos}{64}{0.43837}		\pgfmath@def{cos}{65}{0.42262}
+\pgfmath@def{cos}{66}{0.40674}		\pgfmath@def{cos}{67}{0.39073}
+\pgfmath@def{cos}{68}{0.37461}		\pgfmath@def{cos}{69}{0.35837}
+\pgfmath@def{cos}{70}{0.34202}		\pgfmath@def{cos}{71}{0.32557}
+\pgfmath@def{cos}{72}{0.30902}		\pgfmath@def{cos}{73}{0.29237}
+\pgfmath@def{cos}{74}{0.27564}		\pgfmath@def{cos}{75}{0.25882}
+\pgfmath@def{cos}{76}{0.24192}		\pgfmath@def{cos}{77}{0.22495}
+\pgfmath@def{cos}{78}{0.20791}		\pgfmath@def{cos}{79}{0.19081}
+\pgfmath@def{cos}{80}{0.17365}		\pgfmath@def{cos}{81}{0.15643}
+\pgfmath@def{cos}{82}{0.13917}		\pgfmath@def{cos}{83}{0.12187}
+\pgfmath@def{cos}{84}{0.10453}		\pgfmath@def{cos}{85}{0.08716}
+\pgfmath@def{cos}{86}{0.06976}		\pgfmath@def{cos}{87}{0.05234}
+\pgfmath@def{cos}{88}{0.03490}		\pgfmath@def{cos}{89}{0.01745}
+\pgfmath@def{cos}{90}{0.00000}		\pgfmath@def{cos}{91}{-0.01745}
+\pgfmath@def{cos}{92}{-0.03490}		\pgfmath@def{cos}{93}{-0.05234}
+\pgfmath@def{cos}{94}{-0.06976}		\pgfmath@def{cos}{95}{-0.08716}
+\pgfmath@def{cos}{96}{-0.10453}		\pgfmath@def{cos}{97}{-0.12187}
+\pgfmath@def{cos}{98}{-0.13917}		\pgfmath@def{cos}{99}{-0.15643}
+\pgfmath@def{cos}{100}{-0.17365}		\pgfmath@def{cos}{101}{-0.19081}
+\pgfmath@def{cos}{102}{-0.20791}		\pgfmath@def{cos}{103}{-0.22495}
+\pgfmath@def{cos}{104}{-0.24192}		\pgfmath@def{cos}{105}{-0.25882}
+\pgfmath@def{cos}{106}{-0.27564}		\pgfmath@def{cos}{107}{-0.29237}
+\pgfmath@def{cos}{108}{-0.30902}		\pgfmath@def{cos}{109}{-0.32557}
+\pgfmath@def{cos}{110}{-0.34202}		\pgfmath@def{cos}{111}{-0.35837}
+\pgfmath@def{cos}{112}{-0.37461}		\pgfmath@def{cos}{113}{-0.39073}
+\pgfmath@def{cos}{114}{-0.40674}		\pgfmath@def{cos}{115}{-0.42262}
+\pgfmath@def{cos}{116}{-0.43837}		\pgfmath@def{cos}{117}{-0.45399}
+\pgfmath@def{cos}{118}{-0.46947}		\pgfmath@def{cos}{119}{-0.48481}
+\pgfmath@def{cos}{120}{-0.50000}		\pgfmath@def{cos}{121}{-0.51504}
+\pgfmath@def{cos}{122}{-0.52992}		\pgfmath@def{cos}{123}{-0.54464}
+\pgfmath@def{cos}{124}{-0.55919}		\pgfmath@def{cos}{125}{-0.57358}
+\pgfmath@def{cos}{126}{-0.58779}		\pgfmath@def{cos}{127}{-0.60182}
+\pgfmath@def{cos}{128}{-0.61566}		\pgfmath@def{cos}{129}{-0.62932}
+\pgfmath@def{cos}{130}{-0.64279}		\pgfmath@def{cos}{131}{-0.65606}
+\pgfmath@def{cos}{132}{-0.66913}		\pgfmath@def{cos}{133}{-0.68200}
+\pgfmath@def{cos}{134}{-0.69466}		\pgfmath@def{cos}{135}{-0.70711}
+\pgfmath@def{cos}{136}{-0.71934}		\pgfmath@def{cos}{137}{-0.73135}
+\pgfmath@def{cos}{138}{-0.74314}		\pgfmath@def{cos}{139}{-0.75471}
+\pgfmath@def{cos}{140}{-0.76604}		\pgfmath@def{cos}{141}{-0.77715}
+\pgfmath@def{cos}{142}{-0.78801}		\pgfmath@def{cos}{143}{-0.79864}
+\pgfmath@def{cos}{144}{-0.80902}		\pgfmath@def{cos}{145}{-0.81915}
+\pgfmath@def{cos}{146}{-0.82904}		\pgfmath@def{cos}{147}{-0.83867}
+\pgfmath@def{cos}{148}{-0.84805}		\pgfmath@def{cos}{149}{-0.85717}
+\pgfmath@def{cos}{150}{-0.86603}		\pgfmath@def{cos}{151}{-0.87462}
+\pgfmath@def{cos}{152}{-0.88295}		\pgfmath@def{cos}{153}{-0.89101}
+\pgfmath@def{cos}{154}{-0.89879}		\pgfmath@def{cos}{155}{-0.90631}
+\pgfmath@def{cos}{156}{-0.91355}		\pgfmath@def{cos}{157}{-0.92050}
+\pgfmath@def{cos}{158}{-0.92718}		\pgfmath@def{cos}{159}{-0.93358}
+\pgfmath@def{cos}{160}{-0.93969}		\pgfmath@def{cos}{161}{-0.94552}
+\pgfmath@def{cos}{162}{-0.95106}		\pgfmath@def{cos}{163}{-0.95630}
+\pgfmath@def{cos}{164}{-0.96126}		\pgfmath@def{cos}{165}{-0.96593}
+\pgfmath@def{cos}{166}{-0.97030}		\pgfmath@def{cos}{167}{-0.97437}
+\pgfmath@def{cos}{168}{-0.97815}		\pgfmath@def{cos}{169}{-0.98163}
+\pgfmath@def{cos}{170}{-0.98481}		\pgfmath@def{cos}{171}{-0.98769}
+\pgfmath@def{cos}{172}{-0.99027}		\pgfmath@def{cos}{173}{-0.99255}
+\pgfmath@def{cos}{174}{-0.99452}		\pgfmath@def{cos}{175}{-0.99619}
+\pgfmath@def{cos}{176}{-0.99756}		\pgfmath@def{cos}{177}{-0.99863}
+\pgfmath@def{cos}{178}{-0.99939}		\pgfmath@def{cos}{179}{-0.99985}
+\pgfmath@def{cos}{180}{-1.00000}	   \pgfmath@def{cos}{181}{-0.99985}
+
+\pgfmath@def{cosfrac}{0}{1.00000}		\pgfmath@def{cosfrac}{1}{0.99995}
+\pgfmath@def{cosfrac}{2}{0.99980}		\pgfmath@def{cosfrac}{3}{0.99955}
+\pgfmath@def{cosfrac}{4}{0.99920}		\pgfmath@def{cosfrac}{5}{0.99875}
+\pgfmath@def{cosfrac}{6}{0.99820}		\pgfmath@def{cosfrac}{7}{0.99755}
+\pgfmath@def{cosfrac}{8}{0.99681}		\pgfmath@def{cosfrac}{9}{0.99597}
+\pgfmath@def{cosfrac}{10}{0.99503}		\pgfmath@def{cosfrac}{11}{0.99400}
+\pgfmath@def{cosfrac}{12}{0.99287}		\pgfmath@def{cosfrac}{13}{0.99165}
+\pgfmath@def{cosfrac}{14}{0.99034}		\pgfmath@def{cosfrac}{15}{0.98893}
+\pgfmath@def{cosfrac}{16}{0.98744}		\pgfmath@def{cosfrac}{17}{0.98585}
+\pgfmath@def{cosfrac}{18}{0.98418}		\pgfmath@def{cosfrac}{19}{0.98242}
+\pgfmath@def{cosfrac}{20}{0.98058}		\pgfmath@def{cosfrac}{21}{0.97865}
+\pgfmath@def{cosfrac}{22}{0.97664}		\pgfmath@def{cosfrac}{23}{0.97455}
+\pgfmath@def{cosfrac}{24}{0.97238}		\pgfmath@def{cosfrac}{25}{0.97014}
+\pgfmath@def{cosfrac}{26}{0.96782}		\pgfmath@def{cosfrac}{27}{0.96542}
+\pgfmath@def{cosfrac}{28}{0.96296}		\pgfmath@def{cosfrac}{29}{0.96042}
+\pgfmath@def{cosfrac}{30}{0.95782}		\pgfmath@def{cosfrac}{31}{0.95515}
+\pgfmath@def{cosfrac}{32}{0.95242}		\pgfmath@def{cosfrac}{33}{0.94962}
+\pgfmath@def{cosfrac}{34}{0.94677}		\pgfmath@def{cosfrac}{35}{0.94385}
+\pgfmath@def{cosfrac}{36}{0.94088}		\pgfmath@def{cosfrac}{37}{0.93786}
+\pgfmath@def{cosfrac}{38}{0.93478}		\pgfmath@def{cosfrac}{39}{0.93165}
+\pgfmath@def{cosfrac}{40}{0.92847}		\pgfmath@def{cosfrac}{41}{0.92525}
+\pgfmath@def{cosfrac}{42}{0.92198}		\pgfmath@def{cosfrac}{43}{0.91866}
+\pgfmath@def{cosfrac}{44}{0.91531}		\pgfmath@def{cosfrac}{45}{0.91192}
+\pgfmath@def{cosfrac}{46}{0.90849}		\pgfmath@def{cosfrac}{47}{0.90502}
+\pgfmath@def{cosfrac}{48}{0.90152}		\pgfmath@def{cosfrac}{49}{0.89799}
+\pgfmath@def{cosfrac}{50}{0.89442}		\pgfmath@def{cosfrac}{51}{0.89083}
+\pgfmath@def{cosfrac}{52}{0.88721}		\pgfmath@def{cosfrac}{53}{0.88357}
+\pgfmath@def{cosfrac}{54}{0.87990}		\pgfmath@def{cosfrac}{55}{0.87621}
+\pgfmath@def{cosfrac}{56}{0.87250}		\pgfmath@def{cosfrac}{57}{0.86877}
+\pgfmath@def{cosfrac}{58}{0.86503}		\pgfmath@def{cosfrac}{59}{0.86126}
+\pgfmath@def{cosfrac}{60}{0.85749}		\pgfmath@def{cosfrac}{61}{0.85370}
+\pgfmath@def{cosfrac}{62}{0.84990}		\pgfmath@def{cosfrac}{63}{0.84609}
+\pgfmath@def{cosfrac}{64}{0.84227}		\pgfmath@def{cosfrac}{65}{0.83844}
+\pgfmath@def{cosfrac}{66}{0.83460}		\pgfmath@def{cosfrac}{67}{0.83077}
+\pgfmath@def{cosfrac}{68}{0.82692}		\pgfmath@def{cosfrac}{69}{0.82308}
+\pgfmath@def{cosfrac}{70}{0.81923}		\pgfmath@def{cosfrac}{71}{0.81538}
+\pgfmath@def{cosfrac}{72}{0.81153}		\pgfmath@def{cosfrac}{73}{0.80768}
+\pgfmath@def{cosfrac}{74}{0.80384}		\pgfmath@def{cosfrac}{75}{0.80000}
+\pgfmath@def{cosfrac}{76}{0.79616}		\pgfmath@def{cosfrac}{77}{0.79232}
+\pgfmath@def{cosfrac}{78}{0.78850}		\pgfmath@def{cosfrac}{79}{0.78468}
+\pgfmath@def{cosfrac}{80}{0.78086}		\pgfmath@def{cosfrac}{81}{0.77706}
+\pgfmath@def{cosfrac}{82}{0.77326}		\pgfmath@def{cosfrac}{83}{0.76948}
+\pgfmath@def{cosfrac}{84}{0.76570}		\pgfmath@def{cosfrac}{85}{0.76193}
+\pgfmath@def{cosfrac}{86}{0.75818}		\pgfmath@def{cosfrac}{87}{0.75444}
+\pgfmath@def{cosfrac}{88}{0.75071}		\pgfmath@def{cosfrac}{89}{0.74699}
+\pgfmath@def{cosfrac}{90}{0.74329}		\pgfmath@def{cosfrac}{91}{0.73960}
+\pgfmath@def{cosfrac}{92}{0.73593}		\pgfmath@def{cosfrac}{93}{0.73227}
+\pgfmath@def{cosfrac}{94}{0.72862}		\pgfmath@def{cosfrac}{95}{0.72499}
+\pgfmath@def{cosfrac}{96}{0.72138}		\pgfmath@def{cosfrac}{97}{0.71779}
+\pgfmath@def{cosfrac}{98}{0.71421}		\pgfmath@def{cosfrac}{99}{0.71065}
+\pgfmath@def{cosfrac}{100}{0.70710}	
+
+% Oh No! Some really loooooong tables.
+\pgfmath@def{atan}{0}{0.00000}		\pgfmath@def{atan}{1}{0.05729}
+\pgfmath@def{atan}{2}{0.11459}		\pgfmath@def{atan}{3}{0.17188}
+\pgfmath@def{atan}{4}{0.22918}		\pgfmath@def{atan}{5}{0.28647}
+\pgfmath@def{atan}{6}{0.34377}		\pgfmath@def{atan}{7}{0.40106}
+\pgfmath@def{atan}{8}{0.45835}		\pgfmath@def{atan}{9}{0.51564}
+\pgfmath@def{atan}{10}{0.57293}		\pgfmath@def{atan}{11}{0.63022}
+\pgfmath@def{atan}{12}{0.68751}		\pgfmath@def{atan}{13}{0.74480}
+\pgfmath@def{atan}{14}{0.80208}		\pgfmath@def{atan}{15}{0.85937}
+\pgfmath@def{atan}{16}{0.91665}		\pgfmath@def{atan}{17}{0.97393}
+\pgfmath@def{atan}{18}{1.03121}		\pgfmath@def{atan}{19}{1.08848}
+\pgfmath@def{atan}{20}{1.14576}		\pgfmath@def{atan}{21}{1.20303}
+\pgfmath@def{atan}{22}{1.26030}		\pgfmath@def{atan}{23}{1.31757}
+\pgfmath@def{atan}{24}{1.37483}		\pgfmath@def{atan}{25}{1.43209}
+\pgfmath@def{atan}{26}{1.48935}		\pgfmath@def{atan}{27}{1.54661}
+\pgfmath@def{atan}{28}{1.60386}		\pgfmath@def{atan}{29}{1.66111}
+\pgfmath@def{atan}{30}{1.71835}		\pgfmath@def{atan}{31}{1.77560}
+\pgfmath@def{atan}{32}{1.83284}		\pgfmath@def{atan}{33}{1.89007}
+\pgfmath@def{atan}{34}{1.94730}		\pgfmath@def{atan}{35}{2.00453}
+\pgfmath@def{atan}{36}{2.06175}		\pgfmath@def{atan}{37}{2.11897}
+\pgfmath@def{atan}{38}{2.17619}		\pgfmath@def{atan}{39}{2.23340}
+\pgfmath@def{atan}{40}{2.29061}		\pgfmath@def{atan}{41}{2.34781}
+\pgfmath@def{atan}{42}{2.40500}		\pgfmath@def{atan}{43}{2.46220}
+\pgfmath@def{atan}{44}{2.51938}		\pgfmath@def{atan}{45}{2.57657}
+\pgfmath@def{atan}{46}{2.63374}		\pgfmath@def{atan}{47}{2.69092}
+\pgfmath@def{atan}{48}{2.74808}		\pgfmath@def{atan}{49}{2.80524}
+\pgfmath@def{atan}{50}{2.86240}		\pgfmath@def{atan}{51}{2.91955}
+\pgfmath@def{atan}{52}{2.97669}		\pgfmath@def{atan}{53}{3.03383}
+\pgfmath@def{atan}{54}{3.09097}		\pgfmath@def{atan}{55}{3.14809}
+\pgfmath@def{atan}{56}{3.20521}		\pgfmath@def{atan}{57}{3.26232}
+\pgfmath@def{atan}{58}{3.31943}		\pgfmath@def{atan}{59}{3.37653}
+\pgfmath@def{atan}{60}{3.43363}		\pgfmath@def{atan}{61}{3.49071}
+\pgfmath@def{atan}{62}{3.54779}		\pgfmath@def{atan}{63}{3.60487}
+\pgfmath@def{atan}{64}{3.66193}		\pgfmath@def{atan}{65}{3.71899}
+\pgfmath@def{atan}{66}{3.77604}		\pgfmath@def{atan}{67}{3.83308}
+\pgfmath@def{atan}{68}{3.89012}		\pgfmath@def{atan}{69}{3.94715}
+\pgfmath@def{atan}{70}{4.00417}		\pgfmath@def{atan}{71}{4.06118}
+\pgfmath@def{atan}{72}{4.11819}		\pgfmath@def{atan}{73}{4.17518}
+\pgfmath@def{atan}{74}{4.23217}		\pgfmath@def{atan}{75}{4.28915}
+\pgfmath@def{atan}{76}{4.34612}		\pgfmath@def{atan}{77}{4.40308}
+\pgfmath@def{atan}{78}{4.46004}		\pgfmath@def{atan}{79}{4.51698}
+\pgfmath@def{atan}{80}{4.57392}		\pgfmath@def{atan}{81}{4.63084}
+\pgfmath@def{atan}{82}{4.68776}		\pgfmath@def{atan}{83}{4.74467}
+\pgfmath@def{atan}{84}{4.80157}		\pgfmath@def{atan}{85}{4.85846}
+\pgfmath@def{atan}{86}{4.91534}		\pgfmath@def{atan}{87}{4.97221}
+\pgfmath@def{atan}{88}{5.02907}		\pgfmath@def{atan}{89}{5.08592}
+\pgfmath@def{atan}{90}{5.14276}		\pgfmath@def{atan}{91}{5.19959}
+\pgfmath@def{atan}{92}{5.25641}		\pgfmath@def{atan}{93}{5.31322}
+\pgfmath@def{atan}{94}{5.37002}		\pgfmath@def{atan}{95}{5.42681}
+\pgfmath@def{atan}{96}{5.48359}		\pgfmath@def{atan}{97}{5.54035}
+\pgfmath@def{atan}{98}{5.59711}		\pgfmath@def{atan}{99}{5.65385}
+\pgfmath@def{atan}{100}{5.71059}		\pgfmath@def{atan}{101}{5.76731}
+\pgfmath@def{atan}{102}{5.82402}		\pgfmath@def{atan}{103}{5.88072}
+\pgfmath@def{atan}{104}{5.93741}		\pgfmath@def{atan}{105}{5.99409}
+\pgfmath@def{atan}{106}{6.05075}		\pgfmath@def{atan}{107}{6.10741}
+\pgfmath@def{atan}{108}{6.16405}		\pgfmath@def{atan}{109}{6.22068}
+\pgfmath@def{atan}{110}{6.27729}		\pgfmath@def{atan}{111}{6.33390}
+\pgfmath@def{atan}{112}{6.39049}		\pgfmath@def{atan}{113}{6.44707}
+\pgfmath@def{atan}{114}{6.50364}		\pgfmath@def{atan}{115}{6.56019}
+\pgfmath@def{atan}{116}{6.61673}		\pgfmath@def{atan}{117}{6.67326}
+\pgfmath@def{atan}{118}{6.72978}		\pgfmath@def{atan}{119}{6.78628}
+\pgfmath@def{atan}{120}{6.84277}		\pgfmath@def{atan}{121}{6.89924}
+\pgfmath@def{atan}{122}{6.95571}		\pgfmath@def{atan}{123}{7.01216}
+\pgfmath@def{atan}{124}{7.06859}		\pgfmath@def{atan}{125}{7.12501}
+\pgfmath@def{atan}{126}{7.18142}		\pgfmath@def{atan}{127}{7.23781}
+\pgfmath@def{atan}{128}{7.29419}		\pgfmath@def{atan}{129}{7.35056}
+\pgfmath@def{atan}{130}{7.40691}		\pgfmath@def{atan}{131}{7.46324}
+\pgfmath@def{atan}{132}{7.51957}		\pgfmath@def{atan}{133}{7.57587}
+\pgfmath@def{atan}{134}{7.63217}		\pgfmath@def{atan}{135}{7.68844}
+\pgfmath@def{atan}{136}{7.74471}		\pgfmath@def{atan}{137}{7.80095}
+\pgfmath@def{atan}{138}{7.85719}		\pgfmath@def{atan}{139}{7.91340}
+\pgfmath@def{atan}{140}{7.96961}		\pgfmath@def{atan}{141}{8.02579}
+\pgfmath@def{atan}{142}{8.08196}		\pgfmath@def{atan}{143}{8.13812}
+\pgfmath@def{atan}{144}{8.19426}		\pgfmath@def{atan}{145}{8.25038}
+\pgfmath@def{atan}{146}{8.30649}		\pgfmath@def{atan}{147}{8.36258}
+\pgfmath@def{atan}{148}{8.41866}		\pgfmath@def{atan}{149}{8.47472}
+\pgfmath@def{atan}{150}{8.53076}		\pgfmath@def{atan}{151}{8.58679}
+\pgfmath@def{atan}{152}{8.64280}		\pgfmath@def{atan}{153}{8.69879}
+\pgfmath@def{atan}{154}{8.75477}		\pgfmath@def{atan}{155}{8.81073}
+\pgfmath@def{atan}{156}{8.86667}		\pgfmath@def{atan}{157}{8.92260}
+\pgfmath@def{atan}{158}{8.97851}		\pgfmath@def{atan}{159}{9.03440}
+\pgfmath@def{atan}{160}{9.09027}		\pgfmath@def{atan}{161}{9.14613}
+\pgfmath@def{atan}{162}{9.20197}		\pgfmath@def{atan}{163}{9.25779}
+\pgfmath@def{atan}{164}{9.31359}		\pgfmath@def{atan}{165}{9.36938}
+\pgfmath@def{atan}{166}{9.42515}		\pgfmath@def{atan}{167}{9.48090}
+\pgfmath@def{atan}{168}{9.53663}		\pgfmath@def{atan}{169}{9.59235}
+\pgfmath@def{atan}{170}{9.64804}		\pgfmath@def{atan}{171}{9.70372}
+\pgfmath@def{atan}{172}{9.75938}		\pgfmath@def{atan}{173}{9.81502}
+\pgfmath@def{atan}{174}{9.87064}		\pgfmath@def{atan}{175}{9.92624}
+\pgfmath@def{atan}{176}{9.98182}		\pgfmath@def{atan}{177}{10.03739}
+\pgfmath@def{atan}{178}{10.09294}		\pgfmath@def{atan}{179}{10.14846}
+\pgfmath@def{atan}{180}{10.20397}		\pgfmath@def{atan}{181}{10.25946}
+\pgfmath@def{atan}{182}{10.31493}		\pgfmath@def{atan}{183}{10.37037}
+\pgfmath@def{atan}{184}{10.42580}		\pgfmath@def{atan}{185}{10.48121}
+\pgfmath@def{atan}{186}{10.53660}		\pgfmath@def{atan}{187}{10.59197}
+\pgfmath@def{atan}{188}{10.64732}		\pgfmath@def{atan}{189}{10.70265}
+\pgfmath@def{atan}{190}{10.75796}		\pgfmath@def{atan}{191}{10.81325}
+\pgfmath@def{atan}{192}{10.86852}		\pgfmath@def{atan}{193}{10.92377}
+\pgfmath@def{atan}{194}{10.97900}		\pgfmath@def{atan}{195}{11.03420}
+\pgfmath@def{atan}{196}{11.08939}		\pgfmath@def{atan}{197}{11.14456}
+\pgfmath@def{atan}{198}{11.19970}		\pgfmath@def{atan}{199}{11.25483}
+\pgfmath@def{atan}{200}{11.30993}		\pgfmath@def{atan}{201}{11.36501}
+\pgfmath@def{atan}{202}{11.42007}		\pgfmath@def{atan}{203}{11.47511}
+\pgfmath@def{atan}{204}{11.53013}		\pgfmath@def{atan}{205}{11.58512}
+\pgfmath@def{atan}{206}{11.64010}		\pgfmath@def{atan}{207}{11.69505}
+\pgfmath@def{atan}{208}{11.74998}		\pgfmath@def{atan}{209}{11.80489}
+\pgfmath@def{atan}{210}{11.85977}		\pgfmath@def{atan}{211}{11.91464}
+\pgfmath@def{atan}{212}{11.96948}		\pgfmath@def{atan}{213}{12.02430}
+\pgfmath@def{atan}{214}{12.07910}		\pgfmath@def{atan}{215}{12.13388}
+\pgfmath@def{atan}{216}{12.18863}		\pgfmath@def{atan}{217}{12.24336}
+\pgfmath@def{atan}{218}{12.29807}		\pgfmath@def{atan}{219}{12.35275}
+\pgfmath@def{atan}{220}{12.40741}		\pgfmath@def{atan}{221}{12.46205}
+\pgfmath@def{atan}{222}{12.51667}		\pgfmath@def{atan}{223}{12.57126}
+\pgfmath@def{atan}{224}{12.62583}		\pgfmath@def{atan}{225}{12.68038}
+\pgfmath@def{atan}{226}{12.73490}		\pgfmath@def{atan}{227}{12.78940}
+\pgfmath@def{atan}{228}{12.84388}		\pgfmath@def{atan}{229}{12.89833}
+\pgfmath@def{atan}{230}{12.95276}		\pgfmath@def{atan}{231}{13.00717}
+\pgfmath@def{atan}{232}{13.06155}		\pgfmath@def{atan}{233}{13.11590}
+\pgfmath@def{atan}{234}{13.17024}		\pgfmath@def{atan}{235}{13.22455}
+\pgfmath@def{atan}{236}{13.27883}		\pgfmath@def{atan}{237}{13.33309}
+\pgfmath@def{atan}{238}{13.38733}		\pgfmath@def{atan}{239}{13.44154}
+\pgfmath@def{atan}{240}{13.49573}		\pgfmath@def{atan}{241}{13.54989}
+\pgfmath@def{atan}{242}{13.60403}		\pgfmath@def{atan}{243}{13.65814}
+\pgfmath@def{atan}{244}{13.71223}		\pgfmath@def{atan}{245}{13.76630}
+\pgfmath@def{atan}{246}{13.82034}		\pgfmath@def{atan}{247}{13.87435}
+\pgfmath@def{atan}{248}{13.92834}		\pgfmath@def{atan}{249}{13.98230}
+\pgfmath@def{atan}{250}{14.03624}		\pgfmath@def{atan}{251}{14.09015}
+\pgfmath@def{atan}{252}{14.14404}		\pgfmath@def{atan}{253}{14.19790}
+\pgfmath@def{atan}{254}{14.25174}		\pgfmath@def{atan}{255}{14.30555}
+\pgfmath@def{atan}{256}{14.35933}		\pgfmath@def{atan}{257}{14.41309}
+\pgfmath@def{atan}{258}{14.46682}		\pgfmath@def{atan}{259}{14.52053}
+\pgfmath@def{atan}{260}{14.57421}		\pgfmath@def{atan}{261}{14.62787}
+\pgfmath@def{atan}{262}{14.68149}		\pgfmath@def{atan}{263}{14.73510}
+\pgfmath@def{atan}{264}{14.78867}		\pgfmath@def{atan}{265}{14.84222}
+\pgfmath@def{atan}{266}{14.89575}		\pgfmath@def{atan}{267}{14.94924}
+\pgfmath@def{atan}{268}{15.00271}		\pgfmath@def{atan}{269}{15.05615}
+\pgfmath@def{atan}{270}{15.10957}		\pgfmath@def{atan}{271}{15.16296}
+\pgfmath@def{atan}{272}{15.21632}		\pgfmath@def{atan}{273}{15.26966}
+\pgfmath@def{atan}{274}{15.32297}		\pgfmath@def{atan}{275}{15.37625}
+\pgfmath@def{atan}{276}{15.42950}		\pgfmath@def{atan}{277}{15.48273}
+\pgfmath@def{atan}{278}{15.53593}		\pgfmath@def{atan}{279}{15.58910}
+\pgfmath@def{atan}{280}{15.64224}		\pgfmath@def{atan}{281}{15.69536}
+\pgfmath@def{atan}{282}{15.74845}		\pgfmath@def{atan}{283}{15.80151}
+\pgfmath@def{atan}{284}{15.85454}		\pgfmath@def{atan}{285}{15.90755}
+\pgfmath@def{atan}{286}{15.96052}		\pgfmath@def{atan}{287}{16.01347}
+\pgfmath@def{atan}{288}{16.06640}		\pgfmath@def{atan}{289}{16.11929}
+\pgfmath@def{atan}{290}{16.17215}		\pgfmath@def{atan}{291}{16.22499}
+\pgfmath@def{atan}{292}{16.27780}		\pgfmath@def{atan}{293}{16.33058}
+\pgfmath@def{atan}{294}{16.38333}		\pgfmath@def{atan}{295}{16.43605}
+\pgfmath@def{atan}{296}{16.48875}		\pgfmath@def{atan}{297}{16.54142}
+\pgfmath@def{atan}{298}{16.59405}		\pgfmath@def{atan}{299}{16.64666}
+\pgfmath@def{atan}{300}{16.69924}		\pgfmath@def{atan}{301}{16.75179}
+\pgfmath@def{atan}{302}{16.80431}		\pgfmath@def{atan}{303}{16.85680}
+\pgfmath@def{atan}{304}{16.90927}		\pgfmath@def{atan}{305}{16.96170}
+\pgfmath@def{atan}{306}{17.01411}		\pgfmath@def{atan}{307}{17.06648}
+\pgfmath@def{atan}{308}{17.11883}		\pgfmath@def{atan}{309}{17.17114}
+\pgfmath@def{atan}{310}{17.22343}		\pgfmath@def{atan}{311}{17.27569}
+\pgfmath@def{atan}{312}{17.32792}		\pgfmath@def{atan}{313}{17.38012}
+\pgfmath@def{atan}{314}{17.43228}		\pgfmath@def{atan}{315}{17.48442}
+\pgfmath@def{atan}{316}{17.53653}		\pgfmath@def{atan}{317}{17.58861}
+\pgfmath@def{atan}{318}{17.64066}		\pgfmath@def{atan}{319}{17.69268}
+\pgfmath@def{atan}{320}{17.74467}		\pgfmath@def{atan}{321}{17.79663}
+\pgfmath@def{atan}{322}{17.84855}		\pgfmath@def{atan}{323}{17.90045}
+\pgfmath@def{atan}{324}{17.95232}		\pgfmath@def{atan}{325}{18.00416}
+\pgfmath@def{atan}{326}{18.05596}		\pgfmath@def{atan}{327}{18.10774}
+\pgfmath@def{atan}{328}{18.15949}		\pgfmath@def{atan}{329}{18.21120}
+\pgfmath@def{atan}{330}{18.26289}		\pgfmath@def{atan}{331}{18.31454}
+\pgfmath@def{atan}{332}{18.36616}		\pgfmath@def{atan}{333}{18.41775}
+\pgfmath@def{atan}{334}{18.46931}		\pgfmath@def{atan}{335}{18.52084}
+\pgfmath@def{atan}{336}{18.57234}		\pgfmath@def{atan}{337}{18.62381}
+\pgfmath@def{atan}{338}{18.67525}		\pgfmath@def{atan}{339}{18.72665}
+\pgfmath@def{atan}{340}{18.77803}		\pgfmath@def{atan}{341}{18.82937}
+\pgfmath@def{atan}{342}{18.88068}		\pgfmath@def{atan}{343}{18.93196}
+\pgfmath@def{atan}{344}{18.98321}		\pgfmath@def{atan}{345}{19.03443}
+\pgfmath@def{atan}{346}{19.08562}		\pgfmath@def{atan}{347}{19.13677}
+\pgfmath@def{atan}{348}{19.18789}		\pgfmath@def{atan}{349}{19.23898}
+\pgfmath@def{atan}{350}{19.29004}		\pgfmath@def{atan}{351}{19.34107}
+\pgfmath@def{atan}{352}{19.39206}		\pgfmath@def{atan}{353}{19.44303}
+\pgfmath@def{atan}{354}{19.49396}		\pgfmath@def{atan}{355}{19.54486}
+\pgfmath@def{atan}{356}{19.59572}		\pgfmath@def{atan}{357}{19.64656}
+\pgfmath@def{atan}{358}{19.69736}		\pgfmath@def{atan}{359}{19.74813}
+\pgfmath@def{atan}{360}{19.79887}		\pgfmath@def{atan}{361}{19.84958}
+\pgfmath@def{atan}{362}{19.90025}		\pgfmath@def{atan}{363}{19.95089}
+\pgfmath@def{atan}{364}{20.00150}		\pgfmath@def{atan}{365}{20.05208}
+\pgfmath@def{atan}{366}{20.10262}		\pgfmath@def{atan}{367}{20.15313}
+\pgfmath@def{atan}{368}{20.20361}		\pgfmath@def{atan}{369}{20.25406}
+\pgfmath@def{atan}{370}{20.30447}		\pgfmath@def{atan}{371}{20.35485}
+\pgfmath@def{atan}{372}{20.40520}		\pgfmath@def{atan}{373}{20.45551}
+\pgfmath@def{atan}{374}{20.50579}		\pgfmath@def{atan}{375}{20.55604}
+\pgfmath@def{atan}{376}{20.60626}		\pgfmath@def{atan}{377}{20.65644}
+\pgfmath@def{atan}{378}{20.70659}		\pgfmath@def{atan}{379}{20.75670}
+\pgfmath@def{atan}{380}{20.80679}		\pgfmath@def{atan}{381}{20.85684}
+\pgfmath@def{atan}{382}{20.90685}		\pgfmath@def{atan}{383}{20.95684}
+\pgfmath@def{atan}{384}{21.00678}		\pgfmath@def{atan}{385}{21.05670}
+\pgfmath@def{atan}{386}{21.10658}		\pgfmath@def{atan}{387}{21.15643}
+\pgfmath@def{atan}{388}{21.20625}		\pgfmath@def{atan}{389}{21.25603}
+\pgfmath@def{atan}{390}{21.30578}		\pgfmath@def{atan}{391}{21.35549}
+\pgfmath@def{atan}{392}{21.40517}		\pgfmath@def{atan}{393}{21.45482}
+\pgfmath@def{atan}{394}{21.50444}		\pgfmath@def{atan}{395}{21.55402}
+\pgfmath@def{atan}{396}{21.60356}		\pgfmath@def{atan}{397}{21.65307}
+\pgfmath@def{atan}{398}{21.70255}		\pgfmath@def{atan}{399}{21.75200}
+\pgfmath@def{atan}{400}{21.80140}		\pgfmath@def{atan}{401}{21.85078}
+\pgfmath@def{atan}{402}{21.90012}		\pgfmath@def{atan}{403}{21.94943}
+\pgfmath@def{atan}{404}{21.99870}		\pgfmath@def{atan}{405}{22.04794}
+\pgfmath@def{atan}{406}{22.09715}		\pgfmath@def{atan}{407}{22.14632}
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+\pgfmath@def{acos}{708}{44.92757}		\pgfmath@def{acos}{709}{44.84638}
+\pgfmath@def{acos}{710}{44.76508}		\pgfmath@def{acos}{711}{44.68366}
+\pgfmath@def{acos}{712}{44.60212}		\pgfmath@def{acos}{713}{44.52046}
+\pgfmath@def{acos}{714}{44.43869}		\pgfmath@def{acos}{715}{44.35680}
+\pgfmath@def{acos}{716}{44.27478}		\pgfmath@def{acos}{717}{44.19265}
+\pgfmath@def{acos}{718}{44.11039}		\pgfmath@def{acos}{719}{44.02802}
+\pgfmath@def{acos}{720}{43.94552}		\pgfmath@def{acos}{721}{43.86289}
+\pgfmath@def{acos}{722}{43.78014}		\pgfmath@def{acos}{723}{43.69727}
+\pgfmath@def{acos}{724}{43.61427}		\pgfmath@def{acos}{725}{43.53115}
+\pgfmath@def{acos}{726}{43.44790}		\pgfmath@def{acos}{727}{43.36452}
+\pgfmath@def{acos}{728}{43.28101}		\pgfmath@def{acos}{729}{43.19737}
+\pgfmath@def{acos}{730}{43.11360}		\pgfmath@def{acos}{731}{43.02970}
+\pgfmath@def{acos}{732}{42.94567}		\pgfmath@def{acos}{733}{42.86151}
+\pgfmath@def{acos}{734}{42.77721}		\pgfmath@def{acos}{735}{42.69278}
+\pgfmath@def{acos}{736}{42.60821}		\pgfmath@def{acos}{737}{42.52351}
+\pgfmath@def{acos}{738}{42.43867}		\pgfmath@def{acos}{739}{42.35370}
+\pgfmath@def{acos}{740}{42.26858}		\pgfmath@def{acos}{741}{42.18333}
+\pgfmath@def{acos}{742}{42.09793}		\pgfmath@def{acos}{743}{42.01240}
+\pgfmath@def{acos}{744}{41.92672}		\pgfmath@def{acos}{745}{41.84090}
+\pgfmath@def{acos}{746}{41.75493}		\pgfmath@def{acos}{747}{41.66882}
+\pgfmath@def{acos}{748}{41.58257}		\pgfmath@def{acos}{749}{41.49617}
+\pgfmath@def{acos}{750}{41.40962}		\pgfmath@def{acos}{751}{41.32292}
+\pgfmath@def{acos}{752}{41.23607}		\pgfmath@def{acos}{753}{41.14908}
+\pgfmath@def{acos}{754}{41.06193}		\pgfmath@def{acos}{755}{40.97463}
+\pgfmath@def{acos}{756}{40.88717}		\pgfmath@def{acos}{757}{40.79956}
+\pgfmath@def{acos}{758}{40.71180}		\pgfmath@def{acos}{759}{40.62388}
+\pgfmath@def{acos}{760}{40.53580}		\pgfmath@def{acos}{761}{40.44756}
+\pgfmath@def{acos}{762}{40.35916}		\pgfmath@def{acos}{763}{40.27061}
+\pgfmath@def{acos}{764}{40.18189}		\pgfmath@def{acos}{765}{40.09300}
+\pgfmath@def{acos}{766}{40.00396}		\pgfmath@def{acos}{767}{39.91474}
+\pgfmath@def{acos}{768}{39.82537}		\pgfmath@def{acos}{769}{39.73582}
+\pgfmath@def{acos}{770}{39.64611}		\pgfmath@def{acos}{771}{39.55622}
+\pgfmath@def{acos}{772}{39.46617}		\pgfmath@def{acos}{773}{39.37594}
+\pgfmath@def{acos}{774}{39.28554}		\pgfmath@def{acos}{775}{39.19496}
+\pgfmath@def{acos}{776}{39.10421}		\pgfmath@def{acos}{777}{39.01328}
+\pgfmath@def{acos}{778}{38.92218}		\pgfmath@def{acos}{779}{38.83089}
+\pgfmath@def{acos}{780}{38.73942}		\pgfmath@def{acos}{781}{38.64777}
+\pgfmath@def{acos}{782}{38.55594}		\pgfmath@def{acos}{783}{38.46392}
+\pgfmath@def{acos}{784}{38.37171}		\pgfmath@def{acos}{785}{38.27932}
+\pgfmath@def{acos}{786}{38.18673}		\pgfmath@def{acos}{787}{38.09396}
+\pgfmath@def{acos}{788}{38.00100}		\pgfmath@def{acos}{789}{37.90784}
+\pgfmath@def{acos}{790}{37.81448}		\pgfmath@def{acos}{791}{37.72093}
+\pgfmath@def{acos}{792}{37.62719}		\pgfmath@def{acos}{793}{37.53324}
+\pgfmath@def{acos}{794}{37.43909}		\pgfmath@def{acos}{795}{37.34474}
+\pgfmath@def{acos}{796}{37.25019}		\pgfmath@def{acos}{797}{37.15542}
+\pgfmath@def{acos}{798}{37.06046}		\pgfmath@def{acos}{799}{36.96528}
+\pgfmath@def{acos}{800}{36.86989}		\pgfmath@def{acos}{801}{36.77429}
+\pgfmath@def{acos}{802}{36.67848}		\pgfmath@def{acos}{803}{36.58245}
+\pgfmath@def{acos}{804}{36.48621}		\pgfmath@def{acos}{805}{36.38974}
+\pgfmath@def{acos}{806}{36.29305}		\pgfmath@def{acos}{807}{36.19615}
+\pgfmath@def{acos}{808}{36.09901}		\pgfmath@def{acos}{809}{36.00165}
+\pgfmath@def{acos}{810}{35.90406}		\pgfmath@def{acos}{811}{35.80625}
+\pgfmath@def{acos}{812}{35.70820}		\pgfmath@def{acos}{813}{35.60991}
+\pgfmath@def{acos}{814}{35.51139}		\pgfmath@def{acos}{815}{35.41263}
+\pgfmath@def{acos}{816}{35.31364}		\pgfmath@def{acos}{817}{35.21440}
+\pgfmath@def{acos}{818}{35.11491}		\pgfmath@def{acos}{819}{35.01518}
+\pgfmath@def{acos}{820}{34.91520}		\pgfmath@def{acos}{821}{34.81497}
+\pgfmath@def{acos}{822}{34.71449}		\pgfmath@def{acos}{823}{34.61375}
+\pgfmath@def{acos}{824}{34.51276}		\pgfmath@def{acos}{825}{34.41150}
+\pgfmath@def{acos}{826}{34.30999}		\pgfmath@def{acos}{827}{34.20821}
+\pgfmath@def{acos}{828}{34.10616}		\pgfmath@def{acos}{829}{34.00385}
+\pgfmath@def{acos}{830}{33.90126}		\pgfmath@def{acos}{831}{33.79840}
+\pgfmath@def{acos}{832}{33.69526}		\pgfmath@def{acos}{833}{33.59184}
+\pgfmath@def{acos}{834}{33.48814}		\pgfmath@def{acos}{835}{33.38416}
+\pgfmath@def{acos}{836}{33.27989}		\pgfmath@def{acos}{837}{33.17533}
+\pgfmath@def{acos}{838}{33.07047}		\pgfmath@def{acos}{839}{32.96532}
+\pgfmath@def{acos}{840}{32.85988}		\pgfmath@def{acos}{841}{32.75413}
+\pgfmath@def{acos}{842}{32.64807}		\pgfmath@def{acos}{843}{32.54171}
+\pgfmath@def{acos}{844}{32.43504}		\pgfmath@def{acos}{845}{32.32806}
+\pgfmath@def{acos}{846}{32.22076}		\pgfmath@def{acos}{847}{32.11314}
+\pgfmath@def{acos}{848}{32.00520}		\pgfmath@def{acos}{849}{31.89693}
+\pgfmath@def{acos}{850}{31.78833}		\pgfmath@def{acos}{851}{31.67939}
+\pgfmath@def{acos}{852}{31.57012}		\pgfmath@def{acos}{853}{31.46051}
+\pgfmath@def{acos}{854}{31.35056}		\pgfmath@def{acos}{855}{31.24026}
+\pgfmath@def{acos}{856}{31.12961}		\pgfmath@def{acos}{857}{31.01860}
+\pgfmath@def{acos}{858}{30.90724}		\pgfmath@def{acos}{859}{30.79551}
+\pgfmath@def{acos}{860}{30.68341}		\pgfmath@def{acos}{861}{30.57095}
+\pgfmath@def{acos}{862}{30.45811}		\pgfmath@def{acos}{863}{30.34489}
+\pgfmath@def{acos}{864}{30.23128}		\pgfmath@def{acos}{865}{30.11729}
+\pgfmath@def{acos}{866}{30.00291}		\pgfmath@def{acos}{867}{29.88813}
+\pgfmath@def{acos}{868}{29.77294}		\pgfmath@def{acos}{869}{29.65736}
+\pgfmath@def{acos}{870}{29.54136}		\pgfmath@def{acos}{871}{29.42494}
+\pgfmath@def{acos}{872}{29.30810}		\pgfmath@def{acos}{873}{29.19084}
+\pgfmath@def{acos}{874}{29.07315}		\pgfmath@def{acos}{875}{28.95502}
+\pgfmath@def{acos}{876}{28.83645}		\pgfmath@def{acos}{877}{28.71743}
+\pgfmath@def{acos}{878}{28.59796}		\pgfmath@def{acos}{879}{28.47803}
+\pgfmath@def{acos}{880}{28.35763}		\pgfmath@def{acos}{881}{28.23677}
+\pgfmath@def{acos}{882}{28.11542}		\pgfmath@def{acos}{883}{27.99360}
+\pgfmath@def{acos}{884}{27.87128}		\pgfmath@def{acos}{885}{27.74847}
+\pgfmath@def{acos}{886}{27.62516}		\pgfmath@def{acos}{887}{27.50134}
+\pgfmath@def{acos}{888}{27.37700}		\pgfmath@def{acos}{889}{27.25214}
+\pgfmath@def{acos}{890}{27.12675}		\pgfmath@def{acos}{891}{27.00082}
+\pgfmath@def{acos}{892}{26.87434}		\pgfmath@def{acos}{893}{26.74731}
+\pgfmath@def{acos}{894}{26.61973}		\pgfmath@def{acos}{895}{26.49157}
+\pgfmath@def{acos}{896}{26.36283}		\pgfmath@def{acos}{897}{26.23351}
+\pgfmath@def{acos}{898}{26.10359}		\pgfmath@def{acos}{899}{25.97306}
+\pgfmath@def{acos}{900}{25.84193}		\pgfmath@def{acos}{901}{25.71017}
+\pgfmath@def{acos}{902}{25.57778}		\pgfmath@def{acos}{903}{25.44475}
+\pgfmath@def{acos}{904}{25.31106}		\pgfmath@def{acos}{905}{25.17671}
+\pgfmath@def{acos}{906}{25.04169}		\pgfmath@def{acos}{907}{24.90598}
+\pgfmath@def{acos}{908}{24.76958}		\pgfmath@def{acos}{909}{24.63247}
+\pgfmath@def{acos}{910}{24.49464}		\pgfmath@def{acos}{911}{24.35608}
+\pgfmath@def{acos}{912}{24.21678}		\pgfmath@def{acos}{913}{24.07672}
+\pgfmath@def{acos}{914}{23.93588}		\pgfmath@def{acos}{915}{23.79427}
+\pgfmath@def{acos}{916}{23.65185}		\pgfmath@def{acos}{917}{23.50863}
+\pgfmath@def{acos}{918}{23.36457}		\pgfmath@def{acos}{919}{23.21967}
+\pgfmath@def{acos}{920}{23.07391}		\pgfmath@def{acos}{921}{22.92728}
+\pgfmath@def{acos}{922}{22.77975}		\pgfmath@def{acos}{923}{22.63132}
+\pgfmath@def{acos}{924}{22.48195}		\pgfmath@def{acos}{925}{22.33164}
+\pgfmath@def{acos}{926}{22.18036}		\pgfmath@def{acos}{927}{22.02810}
+\pgfmath@def{acos}{928}{21.87483}		\pgfmath@def{acos}{929}{21.72053}
+\pgfmath@def{acos}{930}{21.56518}		\pgfmath@def{acos}{931}{21.40876}
+\pgfmath@def{acos}{932}{21.25124}		\pgfmath@def{acos}{933}{21.09260}
+\pgfmath@def{acos}{934}{20.93281}		\pgfmath@def{acos}{935}{20.77185}
+\pgfmath@def{acos}{936}{20.60969}		\pgfmath@def{acos}{937}{20.44630}
+\pgfmath@def{acos}{938}{20.28165}		\pgfmath@def{acos}{939}{20.11570}
+\pgfmath@def{acos}{940}{19.94844}		\pgfmath@def{acos}{941}{19.77982}
+\pgfmath@def{acos}{942}{19.60981}		\pgfmath@def{acos}{943}{19.43837}
+\pgfmath@def{acos}{944}{19.26546}		\pgfmath@def{acos}{945}{19.09105}
+\pgfmath@def{acos}{946}{18.91509}		\pgfmath@def{acos}{947}{18.73754}
+\pgfmath@def{acos}{948}{18.55835}		\pgfmath@def{acos}{949}{18.37748}
+\pgfmath@def{acos}{950}{18.19487}		\pgfmath@def{acos}{951}{18.01047}
+\pgfmath@def{acos}{952}{17.82423}		\pgfmath@def{acos}{953}{17.63609}
+\pgfmath@def{acos}{954}{17.44598}		\pgfmath@def{acos}{955}{17.25385}
+\pgfmath@def{acos}{956}{17.05962}		\pgfmath@def{acos}{957}{16.86322}
+\pgfmath@def{acos}{958}{16.66457}		\pgfmath@def{acos}{959}{16.46359}
+\pgfmath@def{acos}{960}{16.26020}		\pgfmath@def{acos}{961}{16.05430}
+\pgfmath@def{acos}{962}{15.84580}		\pgfmath@def{acos}{963}{15.63459}
+\pgfmath@def{acos}{964}{15.42057}		\pgfmath@def{acos}{965}{15.20360}
+\pgfmath@def{acos}{966}{14.98357}		\pgfmath@def{acos}{967}{14.76033}
+\pgfmath@def{acos}{968}{14.53374}		\pgfmath@def{acos}{969}{14.30364}
+\pgfmath@def{acos}{970}{14.06986}		\pgfmath@def{acos}{971}{13.83221}
+\pgfmath@def{acos}{972}{13.59049}		\pgfmath@def{acos}{973}{13.34447}
+\pgfmath@def{acos}{974}{13.09392}		\pgfmath@def{acos}{975}{12.83856}
+\pgfmath@def{acos}{976}{12.57811}		\pgfmath@def{acos}{977}{12.31225}
+\pgfmath@def{acos}{978}{12.04060}		\pgfmath@def{acos}{979}{11.76278}
+\pgfmath@def{acos}{980}{11.47834}		\pgfmath@def{acos}{981}{11.18676}
+\pgfmath@def{acos}{982}{10.88748}		\pgfmath@def{acos}{983}{10.57984}
+\pgfmath@def{acos}{984}{10.26309}		\pgfmath@def{acos}{985}{9.93636}
+\pgfmath@def{acos}{986}{9.59863}		\pgfmath@def{acos}{987}{9.24870}
+\pgfmath@def{acos}{988}{8.88512}		\pgfmath@def{acos}{989}{8.50614}
+\pgfmath@def{acos}{990}{8.10961}		\pgfmath@def{acos}{991}{7.69281}
+\pgfmath@def{acos}{992}{7.25224}		\pgfmath@def{acos}{993}{6.78328}
+\pgfmath@def{acos}{994}{6.27958}		\pgfmath@def{acos}{995}{5.73196}
+\pgfmath@def{acos}{996}{5.12640}		\pgfmath@def{acos}{997}{4.43922}
+\pgfmath@def{acos}{998}{3.62430}		\pgfmath@def{acos}{999}{2.56255}
+\pgfmath@def{acos}{1000}{0.00000}
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex
new file mode 100644
index 00000000000..db2c38fa350
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex
@@ -0,0 +1,265 @@
+% Copyright 2007 Mark Wibrow
+%
+% but subject to the LaTeX Project Public License 
+% (http://www.latex-project.org/lppl.txt)
+%
+% and the GNU Public License 
+% (http://www.gnu.org/licenses/gpl.txt)
+%
+
+% This file defines utilities common to the \pgfmath files.
+%
+% Version 1.414213 29/9/2007
+
+\def\pgfmathincluded{}
+
+% \pgfmath@ensureregister
+%
+% Ensure a control sequence exists as a TeX count/dimen register.
+%
+% #1 - count or dimen.
+% #2 - a control sequence.
+%
+\newbox\pgfmath@box%
+\def\pgfmath@ensureregister#1#2{%
+	\setbox\pgfmath@box\hbox\bgroup% In case #2 is a defined macro. Unlikely, but you never know...
+		\afterassignment\pgfmath@@ensureregister%
+		\noexpand#20.0pt\let\pgfmath@temp\relax\relax\pgfmath@#2#1\pgfmath@}
+
+\def\pgfmath@@ensureregister#1#2\pgfmath@#3#4#5\pgfmath@{%
+	\egroup%
+	\ifx#4c% 
+		\ifx#1.% Already a count register.
+		\else%
+			\csname newcount\endcsname#3% This gets round \outer in plain TeX.
+		\fi%
+	\else%
+		\ifx#4d% 
+			\ifx\let#1% Already a dimen register.
+			\else%
+				\csname newdimen\endcsname#3%
+			\fi%
+		\fi%
+	\fi%
+}
+
+% Check registers exist. If not, create them. 
+%
+\pgfmath@ensureregister{dimen}{\pgf@x}
+\pgfmath@ensureregister{dimen}{\pgf@xa}
+\pgfmath@ensureregister{dimen}{\pgf@xb}
+\pgfmath@ensureregister{dimen}{\pgf@xc}
+
+\pgfmath@ensureregister{dimen}{\pgf@y}
+\pgfmath@ensureregister{dimen}{\pgf@ya}
+\pgfmath@ensureregister{dimen}{\pgf@yb}
+\pgfmath@ensureregister{dimen}{\pgf@yc}
+
+\pgfmath@ensureregister{dimen}{\pgfutil@tempdima}
+\pgfmath@ensureregister{dimen}{\pgfutil@tempdimb}
+
+\pgfmath@ensureregister{count}{\c@pgf@counta}
+\pgfmath@ensureregister{count}{\c@pgf@countb}
+\pgfmath@ensureregister{count}{\c@pgf@countc}
+\pgfmath@ensureregister{count}{\c@pgf@countd}
+
+\pgfmath@ensureregister{count}{\pgfutil@tempcnta}
+\pgfmath@ensureregister{count}{\pgfutil@tempcntb}
+
+% Alias for \pgfmath.
+%
+\let\pgfmath@x\pgf@x
+\let\pgfmath@xa\pgf@xa
+\let\pgfmath@xb\pgf@xb
+\let\pgfmath@xc\pgf@xc
+
+\let\pgfmath@y\pgf@y
+\let\pgfmath@ya\pgf@ya
+\let\pgfmath@yb\pgf@yb
+\let\pgfmath@yc\pgf@yc
+
+\let\pgfmath@tempdima\pgfutil@tempdima
+\let\pgfmath@tempdima\pgfutil@tempdima
+
+\let\c@pgfmath@counta\c@pgf@counta
+\let\c@pgfmath@countb\c@pgf@countb
+\let\c@pgfmath@countc\c@pgf@countc
+\let\c@pgfmath@countd\c@pgf@countd
+
+\let\pgfmath@tempcnta\pgfutil@tempcnta
+\let\pgfmath@tempcntb\pgfutil@tempcntb
+
+% Now check if pgfutil and pgf@sys stuff exists. If it does, fine.
+% Just \let pgfmath versions. If not, define pgfmath versions (Arghhh). 
+%
+
+% \...ifnextchar
+%
+\ifx\pgfutil@ifnextchar\pgfmath@undefined%
+	\long\def\pgfmath@ifnextchar#1#2#3{%
+  \let\pgfmath@reserved@d#1%
+  \def\pgfmath@reserved@a{#2}%
+  \def\pgfmath@reserved@b{#3}%
+  \futurelet\pgfmath@let@token\pgfmath@ifnch}
+	\def\pgfmath@ifnch{%
+	  \ifx\pgfmath@let@token\pgfmath@sptoken%
+	    \let\pgfmath@reserved@c\pgfmath@xifnch%
+	  \else%
+	    \ifx\pgfmath@let@token\pgfmath@reserved@d%
+	      \let\pgfmath@reserved@c\pgfmath@reserved@a%
+	    \else%
+	      \let\pgfmath@reserved@c\pgfmath@reserved@b%
+	    \fi%
+	  \fi%
+	  \pgfmath@reserved@c}
+	{%
+	  \def\:{\global\let\pgfmath@sptoken= } \:
+	  \def\:{\pgfmath@xifnch} \expandafter\gdef\: {\futurelet\pgfmath@let@token\pgfmath@ifnch}
+	}%
+\else%
+	\let\pgfmath@ifnextchar\pgfutil@ifnextchar%
+	% Still need to define \pgfmath@sptoken (cannot \let).
+	{%
+		\def\:{\global\let\pgfmath@sptoken= } \:
+	}%
+\fi%
+
+% \...ifundefined
+%
+\ifx\pgfutil@ifundefined\pgfmath@undefined%
+	\long\def\pgfmath@ifundefined#1{%
+	  \expandafter\ifx\csname#1\endcsname\relax%
+	    \expandafter\pgfmath@firstoftwo%
+	  \else%
+	    \expandafter\pgfmath@secondoftwo%
+	  \fi}%
+\else%
+	\let\pgfmath@ifundefined\pgfutil@ifundefined%
+\fi%
+
+% \...selectfont
+%
+\ifx\pgfutil@selectfont\pgfmath@undefined%
+	\ifx\selectfont\pgfmath@undefined%
+		\let\pgfmath@selectfont\rm% Plain TeX and ConTeXt.
+	\else%
+		\let\pgfmath@selectfont\selectfont% LaTeX.
+	\fi%
+\else%
+	\let\pgfmath@selectfont\pgfutil@selectfont%
+\fi%
+
+% New definition easier than fussing around with let.
+%
+\newif\ifpgfmath@in@
+\def\pgfmath@in@#1#2{%
+ \def\pgfmath@in@@##1#1##2##3\pgfmath@in@@{%
+  \ifx\pgfmath@in@##2\pgfmath@in@false\else\pgfmath@in@true\fi}%
+ \pgfmath@in@@#2#1\pgfmath@in@\pgfmath@in@@}
+
+
+% \...tonumber
+%
+\ifx\pgf@sys@tonumber\pgfmath@undefined%
+  {\catcode`\p=12\catcode`\t=12\gdef\Pgf@geT#1pt{#1}}
+	\def\pgfmath@tonumber#1{\expandafter\Pgf@geT\the#1}
+\else%
+	\let\pgfmath@tonumber\pgf@sys@tonumber%
+\fi%
+
+
+% \PackageWarning and \PackageError
+%
+\ifx\PackageWarning\pgfmath@undefined
+	\def\pgfmath@PackageWarning#1#2{\immediate\write-1{Package #1: Warning! #2.}}%
+\else%
+	\let\pgfmath@PackageWarning\PackageWarning%
+\fi%
+\ifx\PackageError\pgfmath@undefined
+	\def\pgfmath@PackageError#1#2#3{\immediate\write-1{Package #1: Error! #2.}}%
+\else%
+	\let\pgfmath@PackageError\PackageError%
+\fi%
+
+\def\pgfmath@error#1#2{\pgfmath@PackageError{PGF Math}{#1}{#2}}
+\def\pgfmath@warning#1{\pgfmath@PackageWarning{PGF Math}{#1}}
+
+% \pgfmath@pt
+%
+% Needed to test for 'pt' resulting from expansion using \the.
+%
+{\catcode`\p=12\catcode`\t=12\gdef\PgfmaTh@PT{pt}}		
+\edef\pgfmath@pt{\PgfmaTh@PT}%
+
+% \pgfmath@empty
+%
+% A handy macro.
+%
+\def\pgfmath@empty{}
+
+\def\pgfmath@firstoftwo#1#2{#1}
+\def\pgfmath@secondoftwo#1#2{#2}
+
+% \pgfmath@gobbletilpgfmath@
+%
+% Gobble stream until \pgfmath@ {which is undefined}.
+% 
+\def\pgfmath@gobbletilpgfmath@#1\pgfmath@{}
+\def\pgfmath@gobbleone#1{}%
+
+
+% \pgfmathloop
+%
+% A version of the standard TeX and LaTeX
+% \loop, with an additional macro \pgfmathcounter
+% (which is *not* a TeX counter) which keeps
+% track of the iterations.
+%
+\newif\ifpgfmathcontinueloop
+\def\pgfmathloop#1\repeatpgfmathloop{%
+	\def\pgfmathcounter{1}%
+	\def\pgfmath@iterate{%
+		#1\relax%
+		{% Do this inside a group, just in case...
+			\c@pgfmath@counta\pgfmathcounter%
+			\advance\c@pgfmath@counta1\relax%
+			\xdef\pgfmathloop@temp{\the\c@pgfmath@counta}%
+		}%	
+		\edef\pgfmathcounter{\pgfmathloop@temp}%
+		\expandafter\pgfmath@iterate\fi}%
+	\pgfmath@iterate\let\pgfmath@iterate\relax}
+\let\repeatpgfmathloop\fi
+\def\pgfmathbreakloop{\let\pgfmath@iterate\relax}%
+
+% \pgfmath@returnone
+%
+% \edef \pfgmathresult to the value of #1 after the end
+% of a group, which *must directly follow*.
+%
+% #1 - a dimension representing a number or dimension.
+%
+% Changed by TT: made faster and simpler since it is used
+% *heavily*. #1 must be something that can be assigned to a
+% dimension. 
+%
+\def\pgfmath@returnone#1\endgroup{%
+  \pgfmath@x#1%
+  \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
+  \expandafter\endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@temp}%
+}
+
+
+% \pgfmath@returntwo
+%
+% Removed by TT: not used.
+
+
+% \pgfmath@smuggleone
+%
+% Smuggle a macro outside a group.
+%
+% Changed by TT: Speedup by insisting, that smuggleone is directly
+% followed by \endgroup
+%
+\def\pgfmath@smuggleone#1\endgroup{%
+  \expandafter\endgroup\expandafter\def\expandafter#1\expandafter{#1}}