painful pgfplots update (14jun08)

git-svn-id: svn://tug.org/texlive/trunk@8751 c570f23f-e606-0410-a88d-b1316a301751

18 files changed, 11913 insertions, 4033 deletions

diff --git a/Master/texmf-dist/tex/context/pgfplots/t-pgfplots.tex b/Master/texmf-dist/tex/context/pgfplots/t-pgfplots.tex
new file mode 100644
index 00000000000..93324e1e5b0
--- /dev/null
+++ b/Master/texmf-dist/tex/context/pgfplots/t-pgfplots.tex
@@ -0,0 +1,61 @@
+%--------------------------------------------
+%
+% Package pgfplots
+%
+% Provides a user-friendly interface to create function plots (normal
+% plots, semi-logplots and double-logplots).
+% 
+% It is based on Till Tantau's PGF package.
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+
+\usemodule[tikz]
+\usetikzlibrary[plotmarks]
+
+\edef\tikzatcode{\the\catcode`\@}
+\edef\tikzbarcode{\the\catcode`\|}
+\edef\tikzexclaimcode{\the\catcode`\!}
+\catcode`\@=11
+\catcode`\|=12
+\catcode`\!=12
+
+\input pgfplots.code.tex
+
+\let\pgfplots@ORIG@tikz@installcommands@before@context=\tikz@installcommands
+
+\def\tikz@installcommands{%
+	\pgfplots@ORIG@tikz@installcommands@before@context
+	%
+	\let\startaxis=\pgfplots@environment@axis
+	\let\stopaxis=\endpgfplots@environment@axis
+	%
+	\let\startsemilogxaxis=\pgfplots@environment@semilogxaxis
+	\let\stopsemilogxaxis=\endpgfplots@environment@semilogxaxis
+	%
+	\let\startsemilogyaxis=\pgfplots@environment@semilogyaxis
+	\let\stopsemilogyaxis=\endpgfplots@environment@semilogyaxis
+	%
+	\let\startloglogaxis=\pgfplots@environment@loglogaxis
+	\let\stoploglogaxis=\endpgfplots@environment@loglogaxis
+}%
+
+\catcode`\@=\tikzatcode
+\catcode`\|=\tikzbarcode
+\catcode`\!=\tikzexclaimcode
+
+\endinput
diff --git a/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex b/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex
new file mode 100644
index 00000000000..16e4b539c02
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex
@@ -0,0 +1,202 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% This is a helper package with an elementary array datastructure,
+% featuring O(1) index access and O(N) creation, deletion, copy.
+%
+% The following macros are supplied:
+%
+% \pgfplotsarraynewempty
+% \pgfplotsarraynew
+% \pgfplotsarraycopy
+% \pgfplotsarraypushback
+% \pgfplotsarraysize
+% \pgfplotsarrayselect
+% \pgfplotsarrayletentry
+% \pgfplotsarraycheckempty
+% \pgfplotsarrayforeach
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newcount\c@pgfplotsarray@tmp
+\newif\ifpgfplotsarrayempty
+
+% Creates a new, empty array.
+\long\def\pgfplotsarraynewempty#1{%
+	\pgfplotsarray@@def{#1@size}{0}%
+}
+
+% Creates a new array with an abirtrary number of elements.
+% Arguments:
+% #1: the array's name (a macro name)
+% #2: the elements in the form 
+%     first\\second\\third\\ ...\\
+%     like in tabular with one column.
+%
+% Example:
+% \pgfplotsarraynew\fooarray{First Element\\Second Element\\Third Element\\}
+%
+% WARNING: do NOT forget the final '\\'!
+\long\def\pgfplotsarraynew#1#2{%
+	\pgfplotsarraynewempty{#1}%
+	\long\def\pgfplotsarraynew@impl@rest{#2}%
+	\loop
+	\ifx\pgfplotsarraynew@impl@rest\pgfutil@empty
+		\pgfplots@loop@CONTINUEfalse
+	\else
+		\pgfplots@loop@CONTINUEtrue
+	\fi
+	\ifpgfplots@loop@CONTINUE
+		\expandafter\pgfplotsarraynew@impl\pgfplotsarraynew@impl@rest\toarray#1\relax
+	\repeat
+}
+
+% helper macro for \pgfplotsarraynew
+\long\def\pgfplotsarraynew@impl#1\\#2\toarray#3{%
+	\pgfplotsarraypushback#1\to#3\relax%
+	\def\pgfplotsarraynew@impl@rest{#2}%
+}
+
+
+\def\pgfplotsarray@@let#1=#2{%
+	\def\pgfplotsarray@TMP@@{\expandafter\let\csname\string#1\endcsname}%
+	\expandafter\pgfplotsarray@TMP@@\expandafter=\csname\string#2\endcsname
+}%
+
+\def\pgfplotsarray@@def#1{%
+	\expandafter\def\csname\string#1\endcsname
+}%
+\def\pgfplotsarray@@edef#1{%
+	\expandafter\edef\csname\string#1\endcsname
+}%
+
+\def\pgfplotsarray@@getsizeto#1#2{%
+	\pgfplotsarraysize{#1}\to\c@pgfplotsarray@tmp
+	\edef#2{\the\c@pgfplotsarray@tmp}%
+}%
+
+% Copies array #1 to array #2.
+\def\pgfplotsarraycopy#1\to#2{%
+	\pgfplotsarray@@let{#2@size}={#1@size}%
+	\pgfplotsarray@@getsizeto{#1}{\pgfplotsarray@TMP}%
+	\c@pgfplotsarray@tmp=0
+	\loop
+	\ifnum\c@pgfplotsarray@tmp<\pgfplotsarray@TMP
+	\pgfplotsarray@@let{#2@\the\c@pgfplotsarray@tmp}={#1@\the\c@pgfplotsarray@tmp}%
+	\advance\c@pgfplotsarray@tmp by1
+	\repeat
+}
+
+
+
+% #1: the item to append
+% #2: the array as macro name
+% Example:
+% \pgfplotsarraypushback Next last element\to\fooarray
+\long\def\pgfplotsarraypushback#1\to#2{%
+	\pgfplotsarraysize{#2}\to\c@pgfplotsarray@tmp
+	\pgfplotsarray@@def{#2@\the\c@pgfplotsarray@tmp}{#1}%
+	\advance\c@pgfplotsarray@tmp by1
+	\pgfplotsarray@@edef{#2@size}{\the\c@pgfplotsarray@tmp}%
+}
+
+
+% Counts the number of elements in array #1, storing it into the count
+% register #2.
+% Example:
+% \pgfplotsarraysize\foo\to{\count0}%
+% \the\count0
+\long\def\pgfplotsarraysize#1\to#2{%
+	#2=\csname\string#1@size\endcsname\relax
+}
+
+% Returns the #1th element of array #2 into macro #3
+% Arguments:
+% #1: a count 0,...,N-1 where N is the array size.
+%     You may specify a number of a count.
+% #2: a array
+% #3: a macro name
+% Example:
+%   Element 0:
+%   \pgfplotsarrayselect0\of\foo\to\elem
+%   \elem
+%   Element \count1:
+%   \pgfplotsarrayselect\count1\of\foo\to\elem
+\long\def\pgfplotsarrayselect#1\of#2\to#3{%
+	\c@pgfplotsarray@tmp=#1\relax
+	\expandafter\let\expandafter#3\expandafter=\csname\string#2@\the\c@pgfplotsarray@tmp\endcsname%
+}
+\long\def\pgfplotsarrayletentry#1\of#2=#3{%
+	\c@pgfplotsarray@tmp=#1\relax
+	\expandafter\let\csname\string#2@\the\c@pgfplotsarray@tmp\endcsname=#3\relax
+}
+
+% Sets the boolean \ifpgfplotsarrayempty depending on whether array #1 is empty
+% or not.
+% Example:
+%
+% \pgfplotsarraycheckempty\fooarray
+% \ifpgfplotsarrayempty
+%    List fooarray is empty!
+% \else
+%    List is not empty.
+% \fi
+\def\pgfplotsarraycheckempty#1{%
+	\pgfplotsarraysize{#1}\to\c@pgfplotsarray@tmp
+	\ifnum\c@pgfplotsarray@tmp=0\relax
+		\pgfplotsarrayemptytrue
+	\else
+		\pgfplotsarrayemptyfalse
+	\fi
+}
+
+
+% Iterates through each array element, names it #2 and calls code #3.
+% Example:
+% \pgfplotsarraynew\fooarray{Eins\\Zwei\\Drei\\}%
+% \pgfplotsarrayforeach\fooarray\as\foo{Element \foo\par}%
+% results in
+%  Element Eins
+%  Element Zwei
+%  Element Drei
+% Each single element will be grouped with TeX groups.
+\long\def\pgfplotsarrayforeach#1\as#2#3{%
+	\pgfplotsarray@@getsizeto{#1}{\pgfplotsarray@TMP}%
+	\c@pgfplotsarray@tmp=0\relax
+	\loop
+	\ifnum\c@pgfplotsarray@tmp<\pgfplotsarray@TMP\relax
+	\begingroup
+	\expandafter\let\expandafter#2\expandafter=\csname\string#1@\the\c@pgfplotsarray@tmp\endcsname%
+	#3%
+	\endgroup
+	\advance\c@pgfplotsarray@tmp by1
+	\repeat
+}
+
+% The same but without groups around #3.
+\long\def\pgfplotsarrayforeachungrouped#1\as#2#3{%
+	\pgfplotsarray@@getsizeto{#1}{\pgfplotsarray@TMP}%
+	\c@pgfplotsarray@tmp=0\relax
+	\loop
+	\ifnum\c@pgfplotsarray@tmp<\pgfplotsarray@TMP\relax
+	\expandafter\let\expandafter#2\expandafter=\csname\string#1@\the\c@pgfplotsarray@tmp\endcsname%
+	#3%
+	\advance\c@pgfplotsarray@tmp by1
+	\repeat
+}
diff --git a/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex b/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex
new file mode 100644
index 00000000000..48fd19a890c
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex
@@ -0,0 +1,256 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% This is a helper package with an elementary list datastructure.
+%
+% Its implementation is based on Knuth's list macros in "The TeXbook".
+%
+% The following macros are supplied:
+%
+% \pgfplotslistnewempty
+% \pgfplotslistnew
+% \pgfplotslistcopy
+% \pgfplotslistpopfront
+% \pgfplotslistpushback
+% \pgfplotslistpushfront
+% \pgfplotslistsize
+% \pgfplotslistselect
+% \pgfplotslistcheckempty
+% \pgfplotslistforeach
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newtoks\pgfplotslist@TOK@a
+\newtoks\pgfplotslist@TOK@b
+\newif\ifpgfplotslistempty
+
+
+\newif\ifpgfplots@loop@CONTINUE
+\newif\ifpgfplotslist@is@backslash@terminated
+
+% Creates a new, empty list.
+\long\def\pgfplotslistnewempty#1{\let#1=\pgfutil@empty}
+
+% Creates a new list with an abirtrary number of elements.
+% Arguments:
+% #1: the list's name (a macro name)
+% #2: the elements in the form 
+%     first\\second\\third\\ ...\\
+%     like in tabular with one column.
+%     You can also use comma-separated lists
+%     first,second,third
+%
+% Example:
+% 1.
+%  \pgfplotslistnew\foolist{First Element\\Second Element\\Third Element\\}
+%   WARNING: do NOT forget the final '\\'!
+%
+% 2.
+% \pgfplotslistnew\foolist{First Element,Second Element,Third Element}
+%
+% Use braces '{}' to use '\\' or ',' as arguments.
+%
+\long\def\pgfplotslistnew#1#2{%
+	\pgfplotslistnewempty{#1}%
+	\long\def\pgfplotslistnew@impl@rest{#2}%
+	\pgfplotslist@check@backslash@list #2\\\pgfplotslist@EOI
+	\ifpgfplotslist@is@backslash@terminated
+	\else
+		\expandafter\def\expandafter\pgfplotslistnew@impl@rest\expandafter{\pgfplotslistnew@impl@rest,}%
+	\fi
+	\loop
+	\ifx\pgfplotslistnew@impl@rest\pgfutil@empty
+		\pgfplots@loop@CONTINUEfalse
+	\else
+		\pgfplots@loop@CONTINUEtrue
+	\fi
+	\ifpgfplots@loop@CONTINUE
+		\ifpgfplotslist@is@backslash@terminated
+			\expandafter\pgfplotslistnew@impl\pgfplotslistnew@impl@rest\tolist#1\relax
+		\else
+			\expandafter\pgfplotslistnew@impl@comma\pgfplotslistnew@impl@rest\tolist#1\relax
+		\fi
+	\repeat
+}
+\def\pgfplotslist@EOI{\pgfplotslist@EOI}
+
+\def\pgfplotslist@check@backslash@list#1\\#2\pgfplotslist@EOI{%
+	\def\pgfplotslist@TMPB{#2}%
+	\ifx\pgfplotslist@TMPB\pgfutil@empty
+		\pgfplotslist@is@backslash@terminatedfalse
+	\else
+		\pgfplotslist@is@backslash@terminatedtrue
+	\fi
+}%
+
+% Copies list #1 to list #2.
+\def\pgfplotslistcopy#1\to#2{\let#2=#1}
+
+
+% helper macro for \pgfplotslistnew
+\long\def\pgfplotslistnew@impl#1\\#2\tolist#3{%
+	\pgfplotslistpushback#1\to#3\relax%
+	\def\pgfplotslistnew@impl@rest{#2}%
+}
+\long\def\pgfplotslistnew@impl@comma#1,#2\tolist#3{%
+	\pgfplotslistpushback#1\to#3\relax%
+	\def\pgfplotslistnew@impl@rest{#2}%
+}
+
+
+% #1: the item to prepend
+% #2: the list as macro name
+% Example:
+% \pgfplotslistpushfront Next first Element\to\foolist
+\long\def\pgfplotslistpushfront#1\to#2{%
+	\pgfplotslist@TOK@a={\pgfplotslist@sep{#1}}%
+	\pgfplotslist@TOK@b=\expandafter{#2}%
+  	\edef#2{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+}
+
+% #1: the item to append
+% #2: the list as macro name
+% Example:
+% \pgfplotslistpushback Next last element\to\foolist
+\long\def\pgfplotslistpushback#1\to#2{%
+	\pgfplotslist@TOK@a={\pgfplotslist@sep{#1}}%
+	\ifx#2\pgfutil@empty
+		\pgfplotslist@TOK@b={}%
+	\else
+		\pgfplotslist@TOK@b=\expandafter{#2}%
+	\fi
+ 	\edef#2{\the\pgfplotslist@TOK@b\the\pgfplotslist@TOK@a}%
+}
+
+% Concatenates two lists #2 and #3 into #1
+% Example:
+% \pgfplotslistconcat\result=\foolist&\bar
+\long\def\pgfplotslistconcat#1=#2&#3{%
+	\pgfplotslist@TOK@a=\expandafter{#2}%
+	\pgfplotslist@TOK@b=\expandafter{#3}%
+	\edef#1{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+}
+
+% implements #2 := pop_front(#1)
+% Example:
+% \pgfplotslistpopfront\foolist\to\poppedfirstelem
+\long\def\pgfplotslistpopfront#1\to#2{%
+	\pgfplotslistcheckempty#1\relax
+	\ifpgfplotslistempty
+		\pgfplots@error{ERROR: \string\pgfplotslistpopfront\ from \string#1\ although list is EMPTY}%
+	\else
+		\expandafter\pgfplotslistpopfront@impl#1\pgfplotslistpopfront@macronames#1#2%
+	\fi
+}
+
+% implementation helper for listpopfront
+\long\def\pgfplotslistpopfront@impl\pgfplotslist@sep#1#2\pgfplotslistpopfront@macronames#3#4{%
+	\def#4{#1}%
+	\def#3{#2}%
+}
+
+% Counts the number of elements in list #1, storing it into the count
+% register #2.
+% Example:
+% \pgfplotslistsize\foo\to{\count0}%
+% \the\count0
+\long\def\pgfplotslistsize#1\to#2{%
+	#2=0%
+	\long\def\pgfplotslist@sep##1{\advance#2 by 1 }%
+	#1%
+}
+
+% Returns the #1th element of list #2 into macro #3
+% Arguments:
+% #1: a count 0,...,N-1 where N is the list size.
+%     You may specify a number of a count.
+% #2: a list
+% #3: a macro name
+% Example:
+%   Element 0:
+%   \pgfplotslistselect0\of\foo\to\elem
+%   \elem
+%   Element \count1:
+%   \pgfplotslistselect\count1\of\foo\to\elem
+\long\def\pgfplotslistselect#1\of#2\to#3{%
+	\global\def\pgfplotslistselect@tmp{\def#3{\pgfplots@error{The requested item #1 of \string#2 is OUT OF RANGE.}}}%
+	\begingroup
+	\count0=#1\relax
+ 	\long\def\pgfplotslist@sep##1{%
+		\advance\count0-1\relax
+		\ifnum\count0=-1\relax
+			\global\def\pgfplotslistselect@tmp{\def#3{##1}}%
+		\fi%
+	}%
+	#2%
+	\endgroup
+	\pgfplotslistselect@tmp
+}
+
+% Sets the boolean \ifpgfplotslistempty depending on whether list #1 is empty
+% or not.
+% Example:
+%
+% \pgfplotslistcheckempty\foolist
+% \ifpgfplotslistempty
+%    List foolist is empty!
+% \else
+%    List is not empty.
+% \fi
+\def\pgfplotslistcheckempty#1{%
+	\ifx#1\pgfutil@empty
+		\pgfplotslistemptytrue
+	\else
+		\pgfplotslistemptyfalse
+	\fi
+}
+
+
+% Iterates through each list element, names it #2 and calls code #3.
+% Example:
+% \pgfplotslistnew\foolist{Eins\\Zwei\\Drei\\}%
+% \pgfplotslistforeach\foolist\as\foo{Element \foo\par}%
+% results in
+%  Element Eins
+%  Element Zwei
+%  Element Drei
+% Each single element will be grouped with TeX groups.
+\long\def\pgfplotslistforeach#1\as#2#3{%
+	\begingroup
+	\long\def\pgfplotslist@sep##1{\def#2{##1}%
+		\begingroup
+		#3
+		\endgroup}%
+	#1\relax
+	\endgroup
+}
+
+\newif\ifpgfplotslistforeachungroupedrunning
+
+% The same but without groups around #3.
+\long\def\pgfplotslistforeachungrouped#1\as#2#3{%
+	\ifpgfplotslistforeachungroupedrunning
+		\pgfplots@error{Sorry, you can't nest pgfplotslistforeachungrouped.}%
+	\else
+		\pgfplotslistforeachungroupedrunningtrue
+		\long\def\pgfplotslist@sep##1{\def#2{##1}#3}%
+		#1\relax
+		\pgfplotslistforeachungroupedrunningfalse
+	\fi
+}
diff --git a/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.code.tex b/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.code.tex
new file mode 100644
index 00000000000..82e27215bf4
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.code.tex
@@ -0,0 +1,1007 @@
+%--------------------------------------------
+%
+% Package numtable
+%
+% Provides support to read and work with abstact numeric tables of the
+% form
+%
+% COLUMN1	COLUMN2 COLUMN3
+% 1 		2		3
+% 4			4		552
+% 1e124		0.00001	1.2345e-12
+% ...
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+
+% This file relies on
+% - pgfplotsliststructure.code.tex
+% - pgfplotsarraystructure.code.tex
+% - a (quite!) recent PGF.
+%
+% and needs some token registers. It does not use more of pgfplots.
+%
+\newif\ifpgfplotstable@search@header
+\newcount\c@pgfplotstable@counta
+\newwrite\pgfplotstable@outfile
+\newif\ifpgfplotstabletypesetdebug
+\newif\ifpgfplotstableuserow
+
+% should always be false; use only in grouped internal macros
+\newif\ifpgfplots@table@options@areset
+
+\input pgfplotstable.coltype.code.tex
+
+\pgfkeys{%
+	/pgfplots/table/header/.is if=pgfplotstable@search@header,
+	/pgfplots/table/header=true,
+	/pgfplots/table/x index/.store in=\pgfplots@plot@tbl@xindex,
+	/pgfplots/table/x index=0,
+	/pgfplots/table/x/.store in=\pgfplots@plot@tbl@x,
+	/pgfplots/table/x=,
+	/pgfplots/table/y index/.store in=\pgfplots@plot@tbl@yindex,
+	/pgfplots/table/y index=1,
+	/pgfplots/table/y/.store in=\pgfplots@plot@tbl@y,
+	/pgfplots/table/y=,
+	/pgfplots/table/x error index/.initial=,
+	/pgfplots/table/y error index/.initial=,
+	/pgfplots/table/x error/.initial=,
+	/pgfplots/table/y error/.initial=,
+	/pgfplots/table/row predicate/.code={},
+	/pgfplots/table/skip rows between index/.style 2 args={%
+		/pgfplots/table/row predicate/.append code={%
+			\ifnum##1<#1\relax
+			\else
+				\ifnum##1<#2\relax
+					\pgfplotstableuserowfalse
+				\fi
+			\fi}
+	},
+	/pgfplots/table/col sep/.is choice,
+	/pgfplots/table/col sep/space/.code		= {\def\pgfplotstableread@COLSEP@CASE{0}},
+	/pgfplots/table/col sep/comma/.code		= {\def\pgfplotstableread@COLSEP@CASE{1}},
+	/pgfplots/table/col sep/semicolon/.code	= {\def\pgfplotstableread@COLSEP@CASE{2}},
+	/pgfplots/table/col sep/colon/.code		= {\def\pgfplotstableread@COLSEP@CASE{3}},
+	/pgfplots/table/col sep/braces/.code	= {\def\pgfplotstableread@COLSEP@CASE{4}},
+	/pgfplots/table/col sep=space,
+	% columns={name1,name2}
+	% or
+	% columns={[index]2,name2,name3,[index]5}
+	/pgfplots/table/columns/.initial=,
+	/pgfplots/table/column name/.initial=\pgfkeysnovalue,
+	%
+	% this thing here allows to MODIFY 'column name'.
+	%
+	% Argument #1 is the current column name, that means after
+	% evaluating 'column name'. If this key changes anything, it
+	% should write its result back into 'column name'.
+	%
+	% That means you can use 'column name' to assign the name as such
+	% and 'assign column name' to generate final TeX code (for example
+	% to insert \multicolumn{1}{c}{#1} or so).
+	% default is empty which means no change.
+	%/pgfplots/table/assign column name/.code={
+	%	\pgfkeyssetvalue{/pgfplots/table/column name}{#1}%
+	%},
+	%
+	%
+	%
+	% A style which inserts \multicolumn{1}{#1}{<column name>} for
+	% each column name.
+	% The column name as such can be set with the 'column name' option.
+	/pgfplots/table/multicolumn names/.style={%
+		/pgfplots/table/assign column name/.code={%
+			\pgfkeyssetvalue{/pgfplots/table/column name}{\multicolumn{1}{#1}{##1}}%
+		}%
+	},
+	/pgfplots/table/multicolumn names/.default=c,
+	/pgfplots/table/dec sep align/.style={%
+		/pgf/number format/assume math mode,
+		/pgf/number format/set decimal separator/.add={&}{},
+		/pgfplots/table/assign column name/.code={%
+			\pgfkeyssetvalue{/pgfplots/table/column name}{\multicolumn{2}{#1}{##1}}%
+		},%
+		/pgfplots/table/column type={>{$}r<{$}@{}>{$}l<{$}},
+		/pgfplots/table/assign cell content/.code={%
+			\pgfmathprintnumberto{##1}\pgfmathresult%
+			\expandafter\pgfutil@in@\expandafter&\expandafter{\pgfmathresult}%
+			\ifpgfutil@in@
+			\else
+				\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult&}%
+			\fi
+			\pgfkeyslet{/pgfplots/table/@cell content}\pgfmathresult
+		},
+	},
+	/pgfplots/table/dec sep align/.default=c,
+	%
+	% A style which can be used together with the 'dcolumn' package by
+	% David Carlisle.
+	% #1: the dcolumn type, defaults to 'D{.}{.}{2}'
+	% #2: the column name type, defaults to 'c'
+	/pgfplots/table/dcolumn/.style 2 args={%
+		/pgf/number format/assume math mode,
+		column type={#1},
+		multicolumn names=#2,
+	},
+	/pgfplots/table/dcolumn/.default={D{.}{.}{2}}{c},
+	/pgfplots/table/column type/.initial={c},
+	/pgfplots/table/every table/.style={},
+	/pgfplots/table/every even row/.style={},
+	/pgfplots/table/every odd row/.style={},
+	/pgfplots/table/every last row/.style={},
+	/pgfplots/table/every first row/.style={},
+	/pgfplots/table/every head row/.style={},
+	/pgfplots/table/every first column/.style={},
+	/pgfplots/table/every last column/.style={},
+	/pgfplots/table/every even column/.style={},
+	/pgfplots/table/every odd column/.style={},
+	/pgfplots/table/before row/.initial=,
+	/pgfplots/table/after row/.initial=,
+	/pgfplots/table/begin table/.initial={\begin{tabular}},
+	/pgfplots/table/end table/.initial={\end{tabular}},
+	/pgfplots/table/outfile/.initial=,
+	/pgfplots/table/debug/.is if=pgfplotstabletypesetdebug,
+	%
+	% will be redefined by |assign cell content| for every cell:
+	/pgfplots/table/@cell content/.initial=,
+	%
+	% #1: the cells content as it has been found in the input table
+	% this command key should somehow fill |cell content|.
+	/pgfplots/table/assign cell content/.code={%
+		\pgfmathprintnumberto{#1}\pgfmathresult%
+		\pgfkeyslet{/pgfplots/table/@cell content}\pgfmathresult
+	},
+	%
+	% this here is the default formatting. It uses
+	% \pgfmathprintnumber.
+	/pgfplots/table/assign cell content as number/.code={%
+		\pgfmathprintnumberto{#1}\pgfmathresult%
+		\pgfkeyslet{/pgfplots/table/@cell content}\pgfmathresult
+	},
+	/pgfplots/table/string type/.style={%
+		/pgfplots/table/assign cell content/.style={%
+			/pgfplots/table/@cell content={##1}%
+		}%
+	},%
+	/pgfplots/table/font/.initial=,
+	/pgfplots/table/.unknown/.code={%
+		\pgfqkeys{/pgf/number format}{\pgfkeyscurrentname=#1}%
+	}%
+}
+
+% \pgfplotstableread[OPTIONS] {FILE} to \name
+%
+% This method reads a table from FILE to macro \name.
+%
+% FILE is something like
+% G	Basis	dof	L2	A	Lmax	cgiter	maxlevel	eps
+% 5	5	5	8.31160034e-02	0.00000000e+00	1.80007647e-01	2	2	-1
+% 17	17	17	2.54685628e-02	0.00000000e+00	3.75580565e-02	5	3	-1
+% ...
+%
+% A number format line is also understood:
+% G	Basis	dof	L2	A	Lmax	cgiter	maxlevel	eps
+% $flags int	int	int	sci:8	sci:8	sci:8	int	int	std:8
+% 5	5	5	8.31160034e-02	0.00000000e+00	1.80007647e-01	2	2	-1
+%
+% or a three-column-gnuplot file with 2 comment headers like
+% #Curve 0, 20 points
+% #x y type
+% 0.00000 0.00000 i
+% 0.52632 0.50235 i
+%
+% The table data is stored columnwise in lists and can be accessed
+% with the other methods of this package.
+\def\pgfplotstableread{%
+	\pgfutil@ifnextchar[{%
+		\pgfplotstableread@impl
+	}{%
+		\pgfplotstableread@impl[]%
+	}%
+}
+
+% BACKWARDS COMPATIBILITY
+\let\pgfnumtableread=\pgfplotstableread
+
+\def\pgfplotstablegetcolumnlist#1\to#2{%
+	\let#2=#1
+}
+
+\def\pgfplotstablegetcolumnbyname#1\of#2\to#3{%
+	\pgfutil@ifundefined{\string#2@#1}{%
+		\pgfplots@error{Sorry, could not retrieve column '#1' from table...}%
+	}{%
+		\expandafter\let\expandafter#3\csname\string#2@#1\endcsname
+	}%
+}
+
+\def\pgfplotstablegetcolumnnamebyindex#1\of#2\to#3{%
+	\pgfplotslistselect#1\of#2\to#3\relax
+}%
+\def\pgfplotstablegetcolumnbyindex#1\of#2\to#3{%
+	\pgfplotslistselect#1\of#2\to#3\relax
+	\expandafter\pgfplotstablegetcolumnbyname#3\of#2\to{#3}%
+}
+
+\def\pgfplotstablecopy#1\to#2{%
+	\let#2=#1%
+	\pgfplotslistforeachungrouped#1\as\pgfplotstable@TMP{%
+		\def\pgfplotstable@TMPB{%
+			\expandafter\let\csname\string#2@\pgfplotstable@TMP\endcsname}%
+		\expandafter\pgfplotstable@TMPB\csname\string#1@\pgfplotstable@TMP\endcsname
+	}%
+}
+
+% Typesets a table.
+%
+% \pgfplotstabletypeset[<options>]<\tablestructure>
+%
+% If you do not select any columns, the complete table is drawn.
+%
+% There are several options and styles which are available in
+% <options>, see the declaration above.
+%
+% ATTENTION: the default implementation employs
+% \begin{tabular}...\end{tabular} and is therefor only usable with
+% LaTeX!
+%
+% You will need to reconfigure the tables.
+%
+% Inside of \pgfplotstabletypeset, the macros \pgfplotstablecol and
+% \pgfplotstablerow will expand to the current column index and row
+% index.
+\def\pgfplotstabletypeset{%
+	\pgfutil@ifnextchar[{%	
+		\pgfplotstabletypeset@opt
+	}{%
+		\pgfplotstabletypeset@opt[]%
+	}%
+}
+
+% Like \pgfplotstabletypeset, but the first argument is a file name.
+\def\pgfplotstabletypesetfile{%
+	\pgfutil@ifnextchar[{%	
+		\pgfplotstabletypesetfile@opt
+	}{%
+		\pgfplotstabletypesetfile@opt[]%
+	}%
+}
+\def\pgfplotstabletypesetfile@opt[#1]#2{%
+	\begingroup
+	\ifpgfplots@table@options@areset
+	\else
+		\pgfplots@table@options@aresettrue
+		\pgfplotstableset{/pgfplots/table/every table,#1}%
+	\fi
+	\pgfplotstableread{#2}\pgfplotstabletypesetfile@opt@@
+	\pgfplotstabletypeset\pgfplotstabletypesetfile@opt@@
+	\endgroup
+}%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% IMPLEMENTATION
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newif\ifpgfplotstableread@curline@contains@colnames
+\newif\ifpgfplotstableread@foundcolnames
+\newif\ifpgfplotstableread@skipline
+\def\pgfplotstableread@impl[#1]#2{%
+	\pgfutil@ifnextchar t{%
+		\pgfplotstableread@impl@@{#1}{#2}%
+	}{%
+		\pgfplotstableread@impl@{#1}{#2}%
+	}%
+}%
+
+% I don't know why; but I started with 
+% >> \pgfplotstableread[]{file} to \macro
+% That ' to ' is really ugly. This here is for backwards
+% compatibility:
+\def\pgfplotstableread@impl@@#1#2to #3{%
+	\pgfplotstableread@impl@{#1}{#2}{#3}%
+}%
+
+\def\pgfplotstableread@impl@#1#2#3{%
+	\begingroup
+	\ifpgfplots@table@options@areset
+	\else
+		\pgfplotstableset{/pgfplots/table/every table,#1}%
+	\fi
+%\pgfplots@message{ATTEMPTING TO READ #2}%
+	\openin1=#2\relax
+	\def\pgfplotstableread@filename{#2}%
+	\let\pgfplotstableread@lineno=\c@pgf@counta
+	\let\pgfplotstableread@numcols=\c@pgf@countb
+	\let\pgfplotstableread@curcol=\c@pgf@countc
+	\let\pgfplotstableread@usablelineno=\c@pgf@countd
+	\pgfplotstableread@lineno=0
+	\pgfplotstableread@usablelineno=0
+	\pgfplotstableread@numcols=0
+	\pgfplotslistnewempty\pgfplotstable@colnames
+	\ifeof1
+		\pgfplotstable@error{Could not read table file '#2'.}%
+	\fi
+	%
+	\pgfplotstableread@loop@over@lines
+	%
+	\ifpgfplotstableread@foundcolnames
+	\else
+		\pgfplotstableread@create@column@names@with@numbers
+	\fi
+	% Well, now write the identified data to #3:
+	%
+	% make all temporaries global:
+	\global\let\pgfplotstable@colnames=\pgfplotstable@colnames
+	\pgfplotstableread@curcol=0\relax
+	\loop
+	\ifnum\pgfplotstableread@curcol<\pgfplotstableread@numcols
+%\pgfplots@message{ASSIGNING COLUMN NO \the\pgfplotstableread@curcol / \the\pgfplotstableread@numcols}%
+		% numtable@TMP := column list content
+		\expandafter\global\expandafter\let\expandafter\pgfplotstable@TMP\csname numtable@col@\the\pgfplotstableread@curcol\endcsname
+		% global := numtable@TMP
+		\expandafter\global\expandafter\let\csname numtable@col@\the\pgfplotstableread@curcol\endcsname=\pgfplotstable@TMP
+		\advance\pgfplotstableread@curcol by1\relax
+	\repeat
+	\closein1
+	\endgroup
+	% Now, we can access the global variables!
+	% copy them to #3.
+	\let#3=\pgfplotstable@colnames
+	\c@pgfplotstable@counta=0\relax%
+	\pgfplotslistforeachungrouped\pgfplotstable@colnames\as\pgfplotstable@TMP{%
+		\def\pgfplotstable@TMPB{%
+			\expandafter\let\csname\string#3@\pgfplotstable@TMP\endcsname}%
+		\expandafter\pgfplotstable@TMPB\csname numtable@col@\the\c@pgfplotstable@counta\endcsname
+%\message{Column '\pgfplotstable@TMP' has entries: \expandafter\meaning\csname numtable@col@\the\c@pgfplotstable@counta\endcsname}%
+		\expandafter\global\expandafter\let\csname numtable@col@\the\c@pgfplotstable@counta\endcsname=\pgfutil@empty
+		\advance\c@pgfplotstable@counta by1\relax
+	}%
+	\global\let\pgfplotstable@colnames=\pgfutil@empty
+}
+
+\def\pgfplotstableread@loop@over@lines{%
+	\ifeof1
+%\pgfplots@message{EOF}%
+	\else
+		\read1 to\pgfplotstable@LINE
+		\ifeof1
+		\else
+		\expandafter\pgfplotstableread@checkspecial@line\pgfplotstable@LINE\pgfplotstable@EOI
+		\ifpgfplotstableread@skipline
+		\else
+			%--------------------------------------------------
+			% \ifnum\pgfplotstableread@lineno=0
+			% 	\let\pgfplotstable@firstline=\pgfplotstable@LINE
+			% \fi
+			%-------------------------------------------------- 
+%\pgfplots@message{READING LINE \the\pgfplotstableread@lineno: '\meaning\pgfplotstable@LINE'.}%
+			\ifnum\pgfplotstableread@numcols=0\relax
+				\pgfplotstableread@curcol=0\relax
+				\pgfplotstableread@curline@contains@colnamesfalse
+				\pgfplotstableread@impl@DO\pgfplotstableread@impl@countcols@and@identifynames@NEXT\pgfplotstable@LINE
+				%\expandafter\pgfplotstableread@impl@countcols@and@identifynames@ITERATE\pgfplotstable@LINE\pgfplotstable@EOI
+				\pgfplotstableread@numcols=\pgfplotstableread@curcol
+				\pgfplotstableread@curcol=0\relax
+				% Create empty column lists:
+				\pgfplotstableread@create@column@lists
+				%
+				\ifnum\pgfplotstableread@usablelineno=0\relax
+				\ifnum\pgfplotstableread@lineno=2\relax
+				\ifnum\pgfplotstableread@numcols=3\relax
+					% The file started with
+					% #...
+					% #...
+					% X Y i
+					% -> thats a gnuplot file!
+					\pgfplotstableread@curline@contains@colnamesfalse
+				\fi
+				\fi
+				\fi
+				% Now, read the first line.
+				% It contains either
+				% - column names,
+				% - numerical data,
+				% - nothing (comments).
+				\ifpgfplotstableread@curline@contains@colnames
+					\pgfplotstableread@foundcolnamestrue
+					\pgfplotstableread@curcol=0\relax
+					\pgfplotstableread@impl@DO\pgfplotstableread@impl@collectcolnames@NEXT\pgfplotstable@LINE
+					%\expandafter\pgfplotstableread@impl@collectcolnames@ITERATE\pgfplotstable@LINE\pgfplotstable@EOI
+				\else
+					\pgfplotstableread@foundcolnamesfalse
+					\pgfplotstableread@curcol=0\relax
+					% Leave column name lists empty...
+					\pgfplotstableread@impl@DO\pgfplotstableread@impl@nextrow@NEXT\pgfplotstable@LINE
+					%\expandafter\pgfplotstableread@impl@nextrow@ITERATE\pgfplotstable@LINE\pgfplotstable@EOI
+				\fi
+%\pgfplots@message{After reading first row: found '\the\pgfplotstableread@numcols' columns; column name list='\meaning\pgfplotstable@colnames'}%
+			\else
+				\pgfplotstableread@curcol=0\relax
+				\pgfplotstableread@impl@DO\pgfplotstableread@impl@nextrow@NEXT\pgfplotstable@LINE
+				%\expandafter\pgfplotstableread@impl@nextrow@ITERATE\pgfplotstable@LINE\pgfplotstable@EOI
+			\fi
+			\ifnum\pgfplotstableread@curcol=\pgfplotstableread@numcols
+			\else
+				\pgfplotstable@error{ERROR: the input table has an unexpected number of columns in row '\the\pgfplotstableread@lineno'. Expected: '\the\pgfplotstableread@numcols'; got '\the\pgfplotstableread@curcol. Maybe the input table is corrupted?}%
+			\fi
+			\advance\pgfplotstableread@usablelineno by1\relax
+		\fi
+		\fi
+		\advance\pgfplotstableread@lineno by1\relax
+		\pgfplotstableread@loop@over@lines
+	\fi
+}
+
+\def\pgfplotstableread@checkspecial@line{%
+	\pgfutil@ifnextchar##{%
+		\pgfplotstableread@skiplinetrue
+		\pgfplotstableread@impl@gobble
+	}{%
+		\pgfutil@ifnextchar${%
+			\pgfplotstableread@process@flags@line
+		}{%
+			\pgfutil@ifnextchar\pgfplotstable@EOI{%
+				\pgfplotstableread@skiplinetrue
+				\pgfplotstableread@impl@gobble
+			}{%
+				\pgfutil@ifnextchar\par{%
+					\pgfplotstableread@skiplinetrue
+					\pgfplotstableread@impl@gobble
+				}{%
+					\pgfplotstableread@skiplinefalse
+					\pgfplotstableread@impl@gobble
+				}%
+			}%
+		}%
+	}%
+}
+
+\long\def\pgfplotstableread@process@flags@line$flags {%
+%\pgfplots@message{Ignoring flags line ...}%
+	\pgfplotstableread@skiplinetrue
+	\pgfplotstableread@impl@gobble
+}
+
+\def\pgfplotstableread@create@column@lists{%
+	\loop
+	\ifnum\pgfplotstableread@curcol<\pgfplotstableread@numcols
+		\expandafter\pgfplotslistnewempty\csname numtable@col@\the\pgfplotstableread@curcol\endcsname
+		\advance\pgfplotstableread@curcol by1\relax
+	\repeat
+}
+
+\def\pgfplotstableread@create@column@names@with@numbers{%
+	\pgfplotstableread@curcol=0\relax
+	\loop
+	\ifnum\pgfplotstableread@curcol<\pgfplotstableread@numcols
+		\expandafter\pgfplotslistpushback\the\pgfplotstableread@curcol\to\pgfplotstable@colnames
+		\advance\pgfplotstableread@curcol by1\relax
+	\repeat
+}
+
+\long\def\pgfplotstableread@impl@gobble#1\pgfplotstable@EOI{}%
+
+\def\pgfplotstable@EOI{\pgfplotstable@EOI}%
+
+%%%%%%%%%%%%%%%
+
+% A loop command which processes every single entry in a raw data row #2 
+% and invokes the macro #1{<arg>}  for each found column entry.
+%
+% Columns are separated by the /pgfplots/table/col sep character.
+%
+% #1: a command which takes precisely one argument. It will be called
+% for each found column entry
+%
+% #2: a macro containing a raw data line with <col sep> separated
+% entries.
+\def\pgfplotstableread@impl@DO#1#2{%
+	\let\pgfplotstableread@impl@ITERATE@NEXT@=#1\relax
+	\ifcase\pgfplotstableread@COLSEP@CASE\relax
+		% SPACE:
+		\expandafter\pgfplotstableread@impl@ITERATE#2\pgfplotstable@EOI
+	\or
+		% COMMA:
+		\let\pgfplotstableread@impl@ITERATE@NEXT=\pgfplotstableread@impl@ITERATE@NEXT@COMMA
+		\expandafter\pgfplotstableread@impl@ITERATE#2,\pgfplotstable@EOI
+	\or
+		% SEMICOLON:
+		\let\pgfplotstableread@impl@ITERATE@NEXT=\pgfplotstableread@impl@ITERATE@NEXT@SEMICOLON
+		\expandafter\pgfplotstableread@impl@ITERATE#2;\pgfplotstable@EOI
+	\or
+		% COLON:
+		\let\pgfplotstableread@impl@ITERATE@NEXT=\pgfplotstableread@impl@ITERATE@NEXT@COLON
+		\expandafter\pgfplotstableread@impl@ITERATE#2:\pgfplotstable@EOI
+	\or
+		% BRACE:
+		\let\pgfplotstableread@impl@ITERATE@NEXT=\pgfplotstableread@impl@ITERATE@NEXT@BRACE
+		\expandafter\pgfplotstableread@impl@ITERATE#2\pgfplotstable@EOI
+	\fi
+}%
+\def\pgfplotstableread@impl@ITERATE{%
+	\pgfutil@ifnextchar\pgfplotstable@EOI{%
+		\pgfplotstableread@impl@gobble
+	}{%
+		\pgfplotstableread@impl@ITERATE@NEXT
+	}%
+}%
+\def\pgfplotstableread@impl@ITERATE@NEXT#1 {%
+	\pgfplotstableread@impl@ITERATE@NEXT@{#1}%
+	\pgfplotstableread@impl@ITERATE
+}%
+\def\pgfplotstableread@impl@ITERATE@NEXT@COMMA#1,{%
+	\pgfplotstableread@impl@ITERATE@NEXT@{#1}%
+	\pgfplotstableread@impl@ITERATE
+}%
+\def\pgfplotstableread@impl@ITERATE@NEXT@SEMICOLON#1;{%
+	\pgfplotstableread@impl@ITERATE@NEXT@{#1}%
+	\pgfplotstableread@impl@ITERATE
+}%
+\def\pgfplotstableread@impl@ITERATE@NEXT@COLON#1:{%
+	\pgfplotstableread@impl@ITERATE@NEXT@{#1}%
+	\pgfplotstableread@impl@ITERATE
+}%
+\def\pgfplotstableread@impl@ITERATE@NEXT@BRACE#1{%
+	\pgfplotstableread@impl@ITERATE@NEXT@{#1}%
+	\pgfplotstableread@impl@ITERATE
+}%
+%%%%%%%%%%%%
+
+
+\long\def\pgfplotstableread@impl@nextrow@NEXT#1{%
+%\pgfplots@message{Inserting '#1' at (\the\pgfplotstableread@lineno, \the\pgfplotstableread@curcol).}%
+	\def\pgfplotstableread@TMP{\pgfplotslistpushback#1\to}%
+	\expandafter\pgfplotstableread@TMP\csname numtable@col@\the\pgfplotstableread@curcol\endcsname
+	\advance\pgfplotstableread@curcol by1\relax
+}
+
+
+
+\long\def\pgfplotstableread@impl@collectcolnames@NEXT#1{%
+%\pgfplots@message{Got column name no \the\pgfplotstableread@curcol\ as '#1'}%
+	\pgfutil@ifundefined{pgfplotstableread@impl@COLNAME@#1}{%
+		\def\pgfplotstable@TMP{#1}%
+	}{% generate unique column names
+		\pgfplots@warning{Warning: table '\pgfplotstableread@filename' has non-unique column name '#1'. Only the first occurence can be accessed via column names.}%
+		\edef\pgfplotstable@TMP{#1--index\the\pgfplotstableread@curcol}%
+	}%
+	\expandafter\def\csname pgfplotstableread@impl@COLNAME@#1\endcsname{foo}% remember this name.
+	\expandafter\pgfplotslistpushback\expandafter{\pgfplotstable@TMP}\to\pgfplotstable@colnames
+	\advance\pgfplotstableread@curcol by1\relax
+}
+
+
+
+
+\long\def\pgfplotstableread@impl@countcols@and@identifynames@NEXT#1{%
+	\advance\pgfplotstableread@curcol by1\relax
+	\ifpgfplotstable@search@header
+		\ifpgfplotstableread@curline@contains@colnames
+		\else
+			\pgfplotstableread@isnumber@ITERATE#1\pgfplotstable@EOI
+%\ifpgfplotstableread@curline@contains@colnames\pgfplots@message{'#1' is a column name!}\else\pgfplots@message{'#1' is NO column name!}\fi
+		\fi
+	\fi
+}
+\def\pgfplotstableread@isnumber@plus{+}
+\def\pgfplotstableread@isnumber@minus{-}
+\def\pgfplotstableread@isnumber@zero{0}
+\def\pgfplotstableread@isnumber@one{1}
+\def\pgfplotstableread@isnumber@two{2}
+\def\pgfplotstableread@isnumber@three{3}
+\def\pgfplotstableread@isnumber@four{4}
+\def\pgfplotstableread@isnumber@five{5}
+\def\pgfplotstableread@isnumber@six{6}
+\def\pgfplotstableread@isnumber@seven{7}
+\def\pgfplotstableread@isnumber@eight{8}
+\def\pgfplotstableread@isnumber@nine{9}
+\def\pgfplotstableread@isnumber@e{e}
+\def\pgfplotstableread@isnumber@E{E}
+\def\pgfplotstableread@isnumber@period{.}
+
+\def\pgfplotstableread@isnumber@ITERATE#1{%
+	\def\pgfplotstableread@CURTOK{#1}%
+	\ifx\pgfplotstableread@CURTOK\pgfplotstable@EOI
+		\def\pgfplotstableread@NEXT{}%
+	\else
+		\def\pgfplotstableread@NEXT{\pgfplotstableread@isnumber@ITERATE}%
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@plus
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@minus
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@zero
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@one
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@two
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@three
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@four
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@five
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@six
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@seven
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@eight
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@nine
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@e
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@E
+		\else
+		\ifx\pgfplotstableread@CURTOK\pgfplotstableread@isnumber@period
+		\else
+%\message{NO ITS NOT!  Token: '\meaning\pgfplotstableread@CURTOK'}%
+			% it's no number, so it is a column name.
+			\pgfplotstableread@curline@contains@colnamestrue
+			\def\pgfplotstableread@NEXT{\pgfplotstableread@impl@gobble}%
+		\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+	\fi
+	\pgfplotstableread@NEXT
+}
+
+\def\pgfplotstable@error#1{\PackageError{numtable}{#1}{Please refer to the manual for further information.}}%
+
+
+\def\pgfplotstableset{%
+	\pgfqkeys{/pgfplots/table}%
+}%
+
+% Accepts a macro #1 which contains an argument denoting a column
+% name.
+%
+% It checks whether #1 starts with '#', indicating that it is actually
+% a column INDEX. If that is the case,
+% \ifpgfplotstableread@foundcolnames is set to false and the index is
+% returned into #1.
+%
+% Otherwise, \ifpgfplotstableread@foundcolnames is set to true.
+\def\pgfplotstabletypeset@is@colname#1{%
+	\expandafter\pgfplotstabletypeset@is@colname@#1\pgfplotstable@EOI
+	\ifpgfplotstableread@foundcolnames
+	\else
+		\let#1=\pgfplotstable@TMP
+	\fi
+}%
+\def\pgfplotstabletypeset@is@colname@{%
+	\pgfutil@ifnextchar[{%
+		\pgfplotstabletypeset@is@colname@index
+	}{%
+		\pgfplotstableread@foundcolnamestrue
+		\pgfplotstabletypeset@is@colname@name
+	}%
+}
+\def\pgfplotstabletypeset@is@colname@index@@{index}%
+\def\pgfplotstabletypeset@is@colname@index[#1]#2\pgfplotstable@EOI{%
+	\def\pgfplotstable@TMP{#1}%
+	\ifx\pgfplotstable@TMP\pgfplotstabletypeset@is@colname@index@@
+		\pgfplotstableread@foundcolnamesfalse
+		\def\pgfplotstable@TMP{#2}%
+	\else
+		\pgfplotstableread@foundcolnamestrue
+	\fi
+}%
+\def\pgfplotstabletypeset@is@colname@name#1\pgfplotstable@EOI{}%
+\def\pgfplotstabletypeset@getfinalentry#1#2{%
+	\pgfkeysvalueof{/pgfplots/table/assign cell content/.@cmd}#1\pgfeov
+	\pgfkeysgetvalue{/pgfplots/table/@cell content}{#2}%
+}%
+
+% processes the option 'assign column name'
+\def\pgfplotstabletypeset@assign@final@colname#1#2{%
+	\pgfkeysifdefined{/pgfplots/table/assign column name/.@cmd}{%
+		\pgfkeysvalueof{/pgfplots/table/assign column name/.@cmd}#1\pgfeov
+		\pgfkeysgetvalue{/pgfplots/table/column name}{#2}%
+	}{}%
+}
+\def\pgfplotstabletypeset@nocolname{\pgfkeysnovalue}
+
+% checks if #1 contains invalid chars for pgfkeys and sets
+% \ifpgfutil@in@ to true if that is the case.
+\def\pgfplotstable@checkspecialchars@pgfkeys#1\pgfplotstable@EOI{%
+	\pgfutil@in@/{#1}%
+	\ifpgfutil@in@
+	\else
+		\pgfutil@in@={#1}%
+		\ifpgfutil@in@
+		\else
+			\pgfutil@in@,{#1}%
+		\fi
+	\fi
+
+}%
+
+% TODO
+% - replace grouped list foreach by popfront-loop and use arrays
+%   directly -> group only the pgfkeys eval
+\def\pgfplotstabletypeset@opt[#1]#2{%
+	\begingroup
+	\def\pgfplotstablecol{\the\c@pgfplotstable@colindex}%
+	\def\pgfplotstablerow{\the\c@pgfplotstable@rowindex}%
+%	\def\pgfplotstablecols{\the\c@pgfplotstable@numcols}%
+%	\def\pgfplotstablerows{\the\c@pgfplotstable@numrows}%
+	\ifpgfplots@table@options@areset
+	\else
+		\pgfplotstableset{/pgfplots/table/every table,#1}%
+	\fi
+	\pgfkeysgetvalue{/pgfplots/table/columns}{\pgfplotstable@colnames}%
+	\ifx\pgfplotstable@colnames\pgfutil@empty
+		\pgfplotstablegetcolumnlist#2\to\pgfplotstable@colnames
+	\else
+		\expandafter\pgfplotslistnew\expandafter\pgfplotstable@colnames\expandafter{\pgfplotstable@colnames}%
+	\fi
+	\global\pgfplotslistnewempty\pgfplotstabletypeset@final@colnames
+	\global\pgfplotslistnewempty\pgfplotstabletypeset@final@coltypes
+	\global\pgfplotslistnewempty\pgfplotstabletypeset@final@cols
+	\let\c@pgfplotstable@numcols=\c@pgf@counta
+	\let\c@pgfplotstable@numrows=\c@pgf@countd
+	\let\c@pgfplotstable@rowindex=\c@pgf@countc
+	\let\c@pgfplotstable@colindex=\c@pgf@countb
+	\pgfplotslistsize\pgfplotstable@colnames\to\c@pgfplotstable@numcols
+	\c@pgfplotstable@colindex=0\relax
+	\pgfplotslistforeach\pgfplotstable@colnames\as\pgfplotstable@colname{%
+		\c@pgfplotstable@rowindex=0\relax
+		\pgfplotstabletypeset@is@colname\pgfplotstable@colname
+		\ifpgfplotstableread@foundcolnames
+		\else
+			\pgfplotstablegetcolumnnamebyindex\pgfplotstable@colname\of#2\to\pgfplotstable@colname
+		\fi
+		\pgfplotstablegetcolumnbyname\pgfplotstable@colname\of#2\to\pgfplotstable@col
+		%
+		% Set keys for columns!
+		\ifodd\c@pgfplotstable@colindex
+			\pgfplotslist@TOK@a={every odd column}%
+		\else
+			\pgfplotslist@TOK@a={every even column}%
+		\fi
+		\ifnum\c@pgfplotstable@colindex=0\relax
+			\pgfplotslist@TOK@a=\expandafter{\the\pgfplotslist@TOK@a,every first column}%
+		\fi
+		\global\advance\c@pgfplotstable@colindex by1\relax
+		\ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numcols
+			\pgfplotslist@TOK@a=\expandafter{\the\pgfplotslist@TOK@a,every last column}%
+		\fi
+		\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@colname}%
+		\expandafter\pgfplotstable@checkspecialchars@pgfkeys\the\pgfplotslist@TOK@b\pgfplotstable@EOI
+		\ifpgfutil@in@
+			\edef\pgfplotstable@TMP{\the\pgfplotslist@TOK@a,columns/{\the\pgfplotslist@TOK@b}/.try}%
+		\else
+			\edef\pgfplotstable@TMP{\the\pgfplotslist@TOK@a,columns/\the\pgfplotslist@TOK@b/.try}%
+		\fi
+		\expandafter\pgfplotstableset\expandafter{\pgfplotstable@TMP}%
+		%
+		\pgfkeysgetvalue{/pgfplots/table/column name}{\pgfplotstable@colname@out}%
+		\ifx\pgfplotstable@colname@out\pgfplotstabletypeset@nocolname
+			\let\pgfplotstable@colname@out=\pgfplotstable@colname
+		\fi
+		\expandafter\pgfplotstabletypeset@assign@final@colname\expandafter{\pgfplotstable@colname@out}\pgfplotstable@colname@out
+		{\globaldefs=1
+		\expandafter\pgfplotslistpushback\pgfplotstable@colname@out\to\pgfplotstabletypeset@final@colnames
+		}%
+		\pgfkeysgetvalue{/pgfplots/table/column type}{\pgfplotstable@coltype}%
+		{\globaldefs=1
+		\expandafter\pgfplotslistpushback\pgfplotstable@coltype\to\pgfplotstabletypeset@final@coltypes
+		}%
+		%
+		\pgfplotslistnewempty\pgfplotstable@col@processed
+		\pgfplotslistforeachungrouped\pgfplotstable@col\as\pgfplotstable@entry{%
+			\pgfplotstableuserowtrue
+			\edef\pgfplotstable@TMP{\noexpand\pgfkeysvalueof{/pgfplots/table/row predicate/.@cmd}\the\c@pgfplotstable@rowindex}%
+			\pgfplotstable@TMP\pgfeov
+			\ifpgfplotstableuserow
+				\expandafter\pgfplotstabletypeset@getfinalentry\expandafter{\pgfplotstable@entry}{\pgfplotstable@entry}%
+				\expandafter\pgfplotslistpushback\pgfplotstable@entry\to\pgfplotstable@col@processed
+			\fi
+			\advance\c@pgfplotstable@rowindex by1\relax
+		}%
+		{\globaldefs=1
+		\expandafter\pgfplotslistpushback\expandafter{\pgfplotstable@col@processed}\to\pgfplotstabletypeset@final@cols
+		}%
+	}%
+	%
+	% Ok, I have now everything which will come into the final table.
+	%
+	% But I have it column-oriented; I need to transpose the storage.
+	%
+	% The following code assembles a
+	% \begin{tabular}{}
+	% ...
+	% \end{tabular}
+	% statement piece after piece.
+	%
+%\message{I have now \meaning\pgfplotstabletypeset@final@colnames, and \meaning\pgfplotstabletypeset@final@cols.}%
+	% Step 1: column names.
+	\c@pgfplotstable@colindex=0\relax
+	% STEP 1.1: collect column types:
+	\def\pgfplotstable@resulttypes{}%
+	\pgfplotslistforeachungrouped\pgfplotstabletypeset@final@coltypes\as\pgfplotstable@coltype{%
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@resulttypes}%
+		\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@coltype}%
+		\edef\pgfplotstable@resulttypes{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+	}%
+	\pgfkeysgetvalue{/pgfplots/table/begin table}{\pgfplotstable@entry}%
+	\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@entry}%
+	\ifx\pgfplotstable@resulttypes\pgfutil@empty
+		\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a}%
+	\else
+		\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@resulttypes}%
+		\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a{\the\pgfplotslist@TOK@b}}%
+	\fi
+	%
+	\pgfkeysgetvalue{/pgfplots/table/font}{\pgfplotstable@font}%
+	\ifx\pgfplotstable@font\pgfutil@empty
+	\else
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@font}%
+		\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@result}%
+		\edef\pgfplotstable@result{\noexpand\begingroup\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+	\fi
+	%
+
+	% Step 1.2: Collect FIRST ROW (column names)
+	\begingroup
+	\pgfplotstableset{every head row}%
+	\pgfkeysgetvalue{/pgfplots/table/before row}{\pgfplotstable@before}%
+	\pgfkeysgetvalue{/pgfplots/table/after row}{\pgfplotstable@after}%
+	\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@before}%
+	\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@after}%
+	\xdef\pgfplotstable@TMP{%
+		\noexpand\def\noexpand\pgfplotstable@before{\the\pgfplotslist@TOK@a}%
+		\noexpand\def\noexpand\pgfplotstable@after{\the\pgfplotslist@TOK@b}%
+	}%
+	\endgroup
+	\pgfplotstable@TMP
+	% insert 'before row' here:
+	\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@before}%
+	\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@result}%
+	\edef\pgfplotstable@result{\the\pgfplotslist@TOK@b\the\pgfplotslist@TOK@a}%
+	%
+	\pgfplotslistforeachungrouped\pgfplotstabletypeset@final@colnames\as\pgfplotstable@colname@out{%
+		\advance\c@pgfplotstable@colindex by1\relax
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+		\ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numcols\relax
+			\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@colname@out \\}%
+		\else
+			\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@colname@out &}%
+		\fi
+		\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+	}%
+	% insert 'after row' here:
+	\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+	\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@after}%
+	\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+	%
+%\message{I have now \meaning\pgfplotstable@result.}%
+	% Step 2: column contents.
+	% I will first convert \pgfplotstabletypeset@final@cols into an array.
+	\c@pgfplotstable@colindex=0\relax
+	\pgfplotsarraynewempty\pgfplotstabletypeset@final@cols@array
+	\pgfplotslistforeachungrouped\pgfplotstabletypeset@final@cols\as\pgfplotstable@col@processed{%
+		\expandafter\pgfplotsarraypushback\expandafter{\pgfplotstable@col@processed}\to\pgfplotstabletypeset@final@cols@array
+	}%
+	% init numrows:
+	\pgfplotsarrayselect\c@pgfplotstable@colindex\of\pgfplotstabletypeset@final@cols@array\to\pgfplotstable@col@processed
+	\pgfplotslistsize\pgfplotstable@col@processed\to\c@pgfplotstable@numrows
+	%
+	% Now, we loop over every column as long as there are still rows
+	% left. We assemble rows while we go.
+	%
+	\c@pgfplotstable@rowindex=0\relax
+	\ifnum\c@pgfplotstable@colindex<\c@pgfplotstable@numcols
+		\pgfplots@loop@CONTINUEtrue
+	\else
+		\pgfplots@loop@CONTINUEfalse
+	\fi
+	\loop
+	\ifpgfplots@loop@CONTINUE
+		\pgfplotsarrayselect\c@pgfplotstable@colindex\of\pgfplotstabletypeset@final@cols@array\to\pgfplotstable@col@processed
+		\pgfplotslistcheckempty\pgfplotstable@col@processed
+		\ifpgfplotslistempty
+			\pgfplots@loop@CONTINUEfalse
+		\else
+			\ifnum\c@pgfplotstable@colindex=0\relax
+				% Install styles for the next row.
+				\begingroup
+				\ifodd\c@pgfplotstable@rowindex
+					\pgfplotslist@TOK@a={every odd row}%
+				\else
+					\pgfplotslist@TOK@a={every even row}%
+				\fi
+				\ifnum\c@pgfplotstable@rowindex=0\relax
+					\pgfplotslist@TOK@a=\expandafter{\the\pgfplotslist@TOK@a,every first row}%
+				\fi
+				% misuse as temporary variable:
+				\c@pgfplotstable@colindex=\c@pgfplotstable@rowindex
+				\advance\c@pgfplotstable@colindex by1\relax
+				\ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numrows
+					\edef\pgfplotstable@TMP{\the\pgfplotslist@TOK@a,every row no \the\c@pgfplotstable@rowindex/.try,every last row}%
+				\else
+					\edef\pgfplotstable@TMP{\the\pgfplotslist@TOK@a,every row no \the\c@pgfplotstable@rowindex/.try}%
+				\fi
+				\expandafter\pgfplotstableset\expandafter{\pgfplotstable@TMP}%
+				\pgfkeysgetvalue{/pgfplots/table/before row}{\pgfplotstable@before}%
+				\pgfkeysgetvalue{/pgfplots/table/after row}{\pgfplotstable@after}%
+				\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@before}%
+				\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@after}%
+				\xdef\pgfplotstable@TMP{%
+					\noexpand\def\noexpand\pgfplotstable@before{\the\pgfplotslist@TOK@a}%
+					\noexpand\def\noexpand\pgfplotstable@after{\the\pgfplotslist@TOK@b}%
+				}%
+				\endgroup
+				\pgfplotstable@TMP
+				% insert 'before row' here:
+				\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@before}%
+				\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@result}%
+				\edef\pgfplotstable@result{\the\pgfplotslist@TOK@b\the\pgfplotslist@TOK@a}%
+			\fi
+			%
+			%
+			\pgfplotslistpopfront\pgfplotstable@col@processed\to\pgfplotstable@entry
+			\pgfplotsarrayletentry\c@pgfplotstable@colindex\of\pgfplotstabletypeset@final@cols@array=\pgfplotstable@col@processed
+			\advance\c@pgfplotstable@colindex by1\relax
+			\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+			\ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numcols\relax
+				\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@entry \\}%
+			\else
+				\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@entry &}%
+			\fi
+			\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+			\ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numcols\relax
+				\c@pgfplotstable@colindex=0\relax
+				% insert 'after row' here:
+				\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+				\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@after}%
+				\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+				\advance\c@pgfplotstable@rowindex by1\relax
+			\fi
+%\message{I have now \meaning\pgfplotstable@result.}%
+		\fi
+	\repeat
+	\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+	\pgfkeysgetvalue{/pgfplots/table/end table}{\pgfplotstable@entry}%
+	\pgfplotslist@TOK@b=\expandafter{\pgfplotstable@entry}%
+	\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a\the\pgfplotslist@TOK@b}%
+	\ifx\pgfplotstable@font\pgfutil@empty
+	\else
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result\endgroup}%
+		\edef\pgfplotstable@result{\the\pgfplotslist@TOK@a}%
+	\fi
+	\ifpgfplotstabletypesetdebug
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+		\immediate\write16{------- PGFPLOTSTABLE DEBUG MODE: --------}%
+		\immediate\write16{{\the\pgfplotslist@TOK@a}}%
+	\fi
+	\pgfkeysgetvalue{/pgfplots/table/outfile}{\pgfplotstable@entry}%
+	\ifx\pgfplotstable@entry\pgfutil@empty
+	\else
+		\begingroup
+		\immediate\openout\pgfplotstable@outfile=\pgfplotstable@entry\relax
+		\pgfplotslist@TOK@a=\expandafter{\pgfplotstable@result}%
+		\immediate\write\pgfplotstable@outfile{\the\pgfplotslist@TOK@a}%
+		\immediate\closeout\pgfplotstable@outfile
+		\endgroup
+	\fi
+	\pgfplotstable@result
+	\endgroup
+}%
+
+
+\endinput
diff --git a/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.coltype.code.tex b/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.coltype.code.tex
new file mode 100644
index 00000000000..b56d65147fc
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.coltype.code.tex
@@ -0,0 +1,85 @@
+%--------------------------------------------
+%
+% Package numtable.
+%
+% This file provides support for column types in LaTeX tabular
+% environments, i.e.
+%
+%\begin{tabular}{>{\pgfplotstablecoltype}c<{\endpgfplotstablecoltype}}
+%	1 \\
+%	2 \\
+%	3 \\
+%\end{tabular}
+%
+%
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+
+
+
+% If I did not get it wrong, the tabular package, initialised with a
+% column type like
+% >{\pgfplotstablecoltype}c<{\endpgfplotstablecoltype}
+% yields
+%
+% \pgfplotstablecoltype \ignorespaces <content> \unskip \endpgfplotstablecoltype
+% OR
+% \pgfplotstablecoltype \ignorespaces <content> \\ \endpgfplotstablecoltype
+%
+% So, I define \pgfplotstablecoltype to skip \ignorespaces and \unskip and simply
+% get <content>.
+\def\pgfplotstablecoltype{%
+	\begingroup
+	\let\pgfplotstablecoltype@content=\empty
+	\pgfutil@ifnextchar[{%
+		\pgfplotstablecoltype@
+	}{%
+		\pgfplotstablecoltype@until@end@start
+	}%
+}%
+\def\pgfplotstablecoltype@[#1]{%
+	\pgfqkeys{/pgf/number format}{#1}%
+	\pgfplotstablecoltype@until@end@start
+}%
+
+\def\pgfplotstablecoltype@until@end@start\ignorespaces{%
+	\pgfplotstablecoltype@until@end
+}%
+\def\pgfplotstablecoltype@until@end{%
+	\pgfutil@ifnextchar\\{%
+		\pgfplotstablecoltype@finish%
+	}{%
+		\pgfutil@ifnextchar{\unskip}{%
+			\pgfplotstablecoltype@finish%
+		}{%
+			\pgfplotstablecoltype@next
+		}%
+	}%
+}
+\def\pgfplotstablecoltype@next#1{%
+	\expandafter\def\expandafter\pgfplotstablecoltype@content\expandafter{\pgfplotstablecoltype@content#1}%
+	\pgfplotstablecoltype@until@end
+}
+\def\pgfplotstablecoltype@finish{%
+%\message{COLLECTED \meaning\pgfplotstablecoltype@content}%
+	\pgfmathprintnumber{\pgfplotstablecoltype@content}%
+	\endgroup
+}%
+
+%\def\pgfplotstablecoltype{\message{COLLECT}}%
+\def\endpgfplotstablecoltype{}%
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex
new file mode 100644
index 00000000000..628fc7f374e
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex
@@ -0,0 +1,12 @@
+\pgfkeysifdefined{/pgf/number format/1000 sep/.@cmd}{\endinput}{}
+%--------------------------------------------------
+% \pgfutil@ifundefined{pgfplothandlerybarinterval}
+% 	{}%
+% 	{\endinput}%
+%-------------------------------------------------- 
+
+\immediate\write16{Package pgfplots: loading support code for older PGF versions...}
+\input pgfplotsoldpgfsupp_misc.code.tex
+\input pgfplotsoldpgfsupp_pgfkeysfiltered.code.tex
+\input pgfplotsoldpgfsupp_pgfmathfloat.code.tex
+\input pgfplotsoldpgfsupp_pgflibraryplothandlers.code.tex
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_misc.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_misc.code.tex
new file mode 100644
index 00000000000..9e037470f6e
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_misc.code.tex
@@ -0,0 +1,96 @@
+
+% ======================================================
+% compatibility with PGF 2.0
+\def\pgfkeysaddvalue#1#2#3{%
+  {%
+    \toks0{#2}%
+    \pgfkeysifdefined{#1}
+    {\pgfkeys@temptoks\expandafter\expandafter\expandafter{\csname pgfk@#1\endcsname}}%
+    {\pgfkeys@temptoks{}}%
+    \toks1{#3}%
+    \xdef\pgfkeys@global@temp{\the\toks0 \the\pgfkeys@temptoks \the\toks1}% believe or don't: the spaces are important
+  }%
+  \pgfkeyslet{#1}\pgfkeys@global@temp%
+}
+
+\def\pgfkeys@try{%
+  \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}%
+  {%
+    \pgfkeysgetvalue{\pgfkeyscurrentpath/.@cmd}{\pgfkeys@code}%
+    \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% Hmm... no value
+      \pgfkeysifdefined{\pgfkeyscurrentpath/.@def}%
+      {\pgfkeysgetvalue{\pgfkeyscurrentpath/.@def}{\pgfkeyscurrentvalue}}
+      {}% no default, so leave it
+    \fi%
+	\let\pgfkeyscurrentkey=\pgfkeyscurrentpath% make sure that \pgfkeys@code doesn't know about 'try'. Important for .is choice
+	% FIXME: maybe there are more things like that - also adjust currentname!?
+    \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov%
+    \pgfkeyssuccesstrue%
+  }%
+  {%
+    \pgfkeysifdefined{\pgfkeyscurrentpath}%
+    {%
+      \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text%
+        \pgfkeysvalueof{\pgfkeyscurrentpath}%
+      \else%
+        \pgfkeyslet{\pgfkeyscurrentpath}\pgfkeyscurrentvalue%
+      \fi%
+      \pgfkeyssuccesstrue%
+    }%
+    {\pgfkeyssuccessfalse}%
+  }%
+}
+% ======================================================
+
+\def\pgfutilensuremath#1{%
+	\ifmmode#1\else$#1$\fi
+}
+
+\tikzoption{ybar}[]{\let\tikz@plot@handler=\pgfplothandlerybar}
+\tikzoption{xbar}[]{\let\tikz@plot@handler=\pgfplothandlerxbar}
+\tikzoption{ybar interval}[]{\let\tikz@plot@handler=\pgfplothandlerybarinterval}
+\tikzoption{xbar interval}[]{\let\tikz@plot@handler=\pgfplothandlerxbarinterval}
+\tikzoption{const plot}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}
+\tikzoption{const plot mark left}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}
+\tikzoption{const plot mark right}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkright}
+\tikzoption{jump mark right}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkright}
+\tikzoption{jump mark left}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkleft}
+
+
+
+
+% ======================================================
+
+
+\newif\ifpgfmathcomparison
+
+% Assigns \pgfmathresult to 1.0 if #1 ~= #1.
+%
+% It will also set the boolean \ifpgfmathcomparison accordingly
+% (globally).
+\def\pgfmathapproxequalto#1#2{%
+	\edef\pgfmath@marshal{%
+		\noexpand\pgfmathparse{#2}
+		\noexpand\let\noexpand\pgfmath@arg\noexpand\pgfmathresult%
+		\noexpand\pgfmathparse{#1}%
+	}%
+	\pgfmath@marshal%
+	\pgfmathapproxequalto@{\pgfmathresult}{\pgfmath@arg}}
+\def\pgfmathapproxequalto@#1#2{%
+	\begingroup%
+		\pgfmath@x#1pt%
+		\pgfmath@y#2pt%
+		\advance\pgfmath@x-\pgfmath@y%
+		\ifdim\pgfmath@x<0pt
+			\multiply\pgfmath@x by-1
+		\fi
+		\ifdim\pgfmath@x<0.0001pt\relax%
+			\def\pgfmathresult{1.0}%
+			\global\pgfmathcomparisontrue
+		\else%
+			\def\pgfmathresult{0.0}%
+			\global\pgfmathcomparisonfalse
+		\fi%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup%
+}
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfkeysfiltered.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfkeysfiltered.code.tex
new file mode 100644
index 00000000000..cd5c328c700
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfkeysfiltered.code.tex
@@ -0,0 +1,927 @@
+% Copyright 2008 by Christian Feuersaenger
+%
+% 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 contains additions to pgfkeys.code.tex (loaded
+% automatically at the end of pgfkeys.code.tex)
+%
+% Improvements:
+%
+% - option filtering 
+%   you provide
+%     - a boolean predicate
+%     - a "filter handler" which will be invoked for non-matching options,
+%     - a key=value list as usual.
+%   The filter sets only matching options and invokes the handler for
+%   unmatching ones.
+%
+% - Fast family support as in xkeyval.
+%   - A key like /my tree/my option  can be associated with /my family
+%   - You can efficiently set keys which belong to a set of "active"
+%     families.
+%  Remaining options can be collected into a macro.
+
+% WARNING:
+% this file overwrites
+% \pgfkeys@addpath
+% \pgfkeys@nevermind
+%
+% all other features are 'additive'
+
+
+% these implementations will be switched dynamically with their
+% filtered versions (in \pgfkeys@install@filter@and@invoke)
+\let\pgfkeys@orig@case@one=\pgfkeys@case@one
+\let\pgfkeys@orig@@set=\pgfkeys@@set
+\let\pgfkeys@orig@@qset=\pgfkeys@@qset
+\let\pgfkeys@orig@try=\pgfkeys@try
+\let\pgfkeys@orig@unknown=\pgfkeys@unknown
+
+\newif\ifpgfkeysfilteringisactive
+\newif\ifpgfkeysfiltercontinue
+\let\pgfkeys@key@predicate=\pgfkeys@empty
+\let\pgfkeys@filtered@handler=\pgfkeys@empty
+\newtoks\pgfkeys@tmptoks
+
+% Performs 'filtered' key settings.
+%
+% For every option for which the path prefixing has already been done, 
+% the current key filter predicate will be invoked. If the predicate
+% returns true, pgfkeys will process this key in the normal manner.
+% If not, a key filter handler will be invoked.
+%
+% The *predicate* and *handler* semantics are as follows:
+% PRECONDITION:
+% 		1. The variables
+% 			\pgfkeyscurrentkey (full path including name)
+% 			\pgfkeyscurrentkeyRAW (the current key as it has been
+% 			                       found in the key=value list
+% 			                       without path modification)
+% 			\pgfkeyscurrentvalue
+% 			are all set. If the current key is a handler variable,
+%	 			\pgfkeyscurrentname 
+%	 		and
+% 				\pgfkeyscurrentpath
+% 			are also set.
+%		2. The type of option has already been checked, that means
+%			case (1) whether '.@cmd' exists
+%			case (2) whether the key as such has its value
+%			case (3) it is a handler like '.code', '.cd' or whatever.
+%			case (0) it is unknown.
+%			The actual case number (0-3) will be provided as contents
+%			of the macro
+%				\pgfkeyscasenumber.
+%			Please note that unknown options will be processed with
+%			the usual '.unknown' handlers unless the key filter takes
+%			control over unknown options as well.
+%
+% POSTCONDITION:
+% 		the predicate sets 
+% 			\pgfkeysfiltercontinuetrue 
+% 		or
+% 			\pgfkeysfiltercontinuefalse
+% 		(the boolean \ifpgfkeysfiltercontinue).
+% Depending on this 'if', option processing will be continued or
+% skipped.
+%
+% The handler can do anything with the option, for example collect
+% unmatched ones.
+%
+% ATTENTION: \pgfkeysfiltered can't be nested (yet). Use the
+% \pgfkeyspredicateAND if you need multiple predicates at once.
+% Nesting would produce unexpected results because the current filter
+% state can't be stored/restored without TeX-groups, therefor it is
+% disabled.
+%
+% ATTENTION: you can't filter error messages.
+%
+% REMARK: In case (3), the macros \pgfkeyscurrentpath and
+% \pgfkeyscurrentname have already been computed, you do not need to
+% invoke \pgfkeyssplitpath. In any other case, neither path nor name
+% are required for the options processing - if you need them for
+% predicates/handlers, you need to compute them by hand.
+% 
+%
+% Example:
+%   \def\unmatched{}
+%   \pgfkeys{/pgf/key filters/is descendant of/.install key filter=/my group}
+%   \pgfkeys{/pgf/key filter handlers/append filtered to/.install key filter handler=\unmatched}
+%   \pgfkeysfiltered%
+%   	{/my group/option 1=value 1,/tikz/option 2=value 2}
+% ->
+%  will set '/my group/option 1' as usual, but '/tikz/option 2' will not
+%  be set. Instead, it will be appended to '\unmatched' such that 
+%  \unmatched = {/tikz/option 2=value2}
+%  after the operation.
+%
+% Arguments:
+% #1:  key-value list.
+\def\pgfkeysfiltered{%
+	% produce 
+	% '{<default path>}'
+	% each expanded exactly one time into the register:  
+	\expandafter\pgfkeysfiltered@@install\expandafter{\pgfkeysdefaultpath}%
+}
+
+% #1: old value of default path.
+% #2: key-value-list.
+\def\pgfkeysfiltered@@install#1#2{%
+	\pgfkeys@install@filter@and@invoke{%
+		\let\pgfkeysdefaultpath\pgfkeys@root%
+		\pgfkeys@parse#2,\pgfkeys@mainstop%
+		\def\pgfkeysdefaultpath{#1}%
+	}%
+}
+
+% Assuming that macro #1 contains a key=value list, this command
+% performs an \pgfkeysalso command for the content of macro #1.
+%
+% It can be used in conjunction with 
+%   - \pgfkeysfiltered and
+%   - \pgfkeysappendfilterednamestomacro:
+% the first pass fill only process options matching the filter, then,
+% a \pgfkeysalsofrom can be used at a later time to set the remaining
+% options.
+%
+% Example:
+% \pgfkeys{/my group/.cd,/utils/exec=\pgfkeysalsofrom\filtered}
+\def\pgfkeysalsofrom#1{%
+	\expandafter\pgfkeysalso\expandafter{#1}%
+}
+
+% The same as \pgfkeysalsofrom, but it invokes \pgfkeysalsofiltered.
+\def\pgfkeysalsofilteredfrom#1{%
+	\expandafter\pgfkeysalsofiltered\expandafter{#1}%
+}
+
+% #1 = options
+\long\def\pgfkeysalsofiltered#1{%
+	\pgfkeys@install@filter@and@invoke{\pgfkeysalso{#1}}%
+}%
+
+% The same like \pgfkeysfiltered, but with quick search path setting.
+%
+% #1: default path
+% #2: key-value-pairs
+\def\pgfqkeysfiltered#1{%
+	\expandafter\pgfqkeysfiltered@@install\expandafter{\pgfkeysdefaultpath}{#1}%
+}
+
+% #1: old value of default path.
+% #2: default path
+% #3: key-value-list.
+\def\pgfqkeysfiltered@@install#1#2#3{%
+	\pgfkeys@install@filter@and@invoke{%
+		\def\pgfkeysdefaultpath{#2/}\pgfkeys@parse#3,\pgfkeys@mainstop\def\pgfkeysdefaultpath{#1}%
+	}%
+}
+
+% Family management
+%
+% The family code provides the following features:
+% 1. every key can be associated with 0 or 1 'family'.
+% 2. Families are a loose association which are independend of the key
+% hierarchy.
+%   For example, /my tree/key1  can belong to family /tikz.
+%
+% 3. It is possible to "activate" or "deactivate" single families.
+%    Furthermore, it is possible to set only keys which belong to 
+%    active families (using \pgfkeysfiltered).
+% 4. Runtime complexities:
+%    If you have N options and you only want to process K active
+%    families, the runtime is O( N + K ):
+%      - activate every family O(K)
+%      - use \pgfkeyshasactivefamily as filter predicate O(N)
+%      - deactivate every family O(K)
+
+
+% Activates family #1.
+%
+% #1 maybe a macro.
+\def\pgfkeysactivatefamily#1{%
+	\pgfkeysiffamilydefined
+		{#1}%
+		{\csname pgfk@#1/familyactivetrue\endcsname}%
+		{\pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov}%
+%\message{[ACTIVATING FAMILY #1]}%
+}
+
+% Deactivates family #1.
+%
+% #1 maybe a macro.
+\def\pgfkeysdeactivatefamily#1{
+	\pgfkeysiffamilydefined
+		{#1}%
+		{\csname pgfk@#1/familyactivefalse\endcsname}%
+		{\pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov}%
+%\message{[DEACTIVATING FAMILY #1]}%
+}
+
+% Activates all families in the comma separated list #1.
+%
+% It will also generate code for deactivation of all those families
+% into the command #2.
+%
+% #1: a comma-separated list of fully qualified family names.
+% #2: a command which will be filled with a deactivate-all command.
+\def\pgfkeysactivatefamilies#1#2{%
+	\pgfkeyssavekeyfilterstateto\pgfkeys@cur@state
+	\expandafter\pgfkeysactivatefamilies@impl\expandafter{\pgfkeys@cur@state}{#1}{#2}%
+}
+% #1: commands needed to restore the old filtering state
+% #2: family name list
+% #3: macro name for de-activate command
+\def\pgfkeysactivatefamilies@impl#1#2#3{%
+	\pgfkeysinstallkeyfilter{/pgf/key filters/false}{}%
+	\let#3=\pgfkeys@empty%
+	\def\pgfkeys@filtered@handler{\pgfkeys@family@activate@handler{#3}}%
+	\pgfkeysalsofiltered{#2}%
+	#1%
+}
+
+\def\pgfkeys@family@activate@handler#1{%
+	\pgfkeysactivatefamily{\pgfkeyscurrentkey}%
+	% produce 
+	%   <old list> '\pgfkeysdeactivatefamily{' <current key> '}'
+	\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter#1\expandafter\pgfkeysdeactivatefamily\expandafter{\pgfkeyscurrentkey}}%
+	\edef#1{\the\pgfkeys@tmptoks}%
+}
+
+% If for testing whether a family exists.
+%
+% #1 = fully qualified family name
+% #2 = if-case
+% #3 = else-case
+%
+% Description:
+%
+% If the family exists, #2 will be executed. Otherwise, #3 will be
+% called.
+\long\def\pgfkeysiffamilydefined#1#2#3{\pgfkeys@ifcsname ifpgfk@#1/familyactive\endcsname#2\else#3\fi}
+
+% Sets the TeX boolean 
+%   \ifpgfkeysfiltercontinue := ( family #1 is active )
+% 
+% Argument:
+% #1 the family name. Maybe a macro.
+\def\pgfkeysisfamilyactive#1{%
+	\pgfkeysiffamilydefined{#1}{%
+		\expandafter\let\expandafter\ifpgfkeysfiltercontinue\csname ifpgfk@#1/familyactive\endcsname
+	}{%
+		\pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov%
+		\expandafter\expandafter\expandafter\let\csname ifpgfkeysfiltercontinue\endcsname\csname iffalse\endcsname
+	}%
+}%
+
+% Retrieve the family of full key #1 into macro #2.
+%
+% Will set the TeX boolean \ifpgfkeyssuccess to whether the full key
+% really has a family.
+%
+% The family for any key is stored in the sub-key #1/family.
+%
+% Parameters:
+% #1:  the full key name for which the family is requested. Maybe a
+%      macro.
+% #2:  a macro name which will be filled with the result.
+\def\pgfkeysgetfamily#1#2{%
+	\pgfkeysifdefined{#1/family}{\pgfkeysgetvalue{#1/family}{#2}\pgfkeyssuccesstrue}{\pgfkeyssuccessfalse}%
+}
+	
+
+
+% Sets \ifpgfkeysfiltercontinue to true iff the current key belongs to
+% the /errors tree.
+\long\def\pgfkeys@cur@is@descendant@of@errors{%
+	\expandafter\pgfkeys@cur@is@descendant@of@errors@impl\pgfkeyscurrentkey/errors\pgf@@eov
+}%
+\long\def\pgfkeys@cur@is@descendant@of@errors@impl#1/errors#2\pgf@@eov{%
+	\def\pgfkeyspred@TMP{#1}%
+	\ifx\pgfkeyspred@TMP\pgfkeys@empty
+%\message{[SPECIAL CHECK] '\pgfkeyscurrentkey' is descendant of '/errors': TRUE.}%
+		\pgfkeysfiltercontinuetrue
+	\else
+%\message{[SPECIAL CHECK] '\pgfkeyscurrentkey' is descendant of '/errors': FALSE.}%
+		\pgfkeysfiltercontinuefalse
+	\fi
+}%
+
+% \pgfkeysinterruptkeyfilter
+% ...
+% \endpgfkeysinterruptkeyfilter
+% temporarily interrupts key filtering and enables it in
+% \endpgfkeysinterruptkeyfilter.
+%
+% If key filtering it not active, this has no effect at all.
+%
+% REMARK:
+% \pgfkeysinterruptkeyfilter...\endpgfkeysinterruptkeyfilter does NOT
+% introduce a \TeX-group.
+\def\pgfkeysinterruptkeyfilter{%
+	\ifpgfkeysfilteringisactive
+		\let\pgfkeys@case@one=\pgfkeys@orig@case@one
+		\let\pgfkeys@try=\pgfkeys@orig@try
+		\let\pgfkeys@unknown=\pgfkeys@orig@unknown
+	\fi
+}
+
+\def\endpgfkeysinterruptkeyfilter{%
+	\ifpgfkeysfilteringisactive
+		\let\pgfkeys@case@one=\pgfkeys@case@one@filtered
+		\let\pgfkeys@try=\pgfkeys@try@filtered
+		\let\pgfkeys@unknown=\pgfkeys@unknown@filtered
+	\fi
+}
+
+% Activates families #1, calls \pgfkeysfiltered and deactivates the
+% families afterwards.
+%
+% REMARK: you need to install a family-based key filter predicate
+% manually to benefit from the activated families!
+%
+% #1: comma separated family list
+% #2: key-value pairs
+%
+% @see \pgfkeysactivatefamiliesandfilteroptions
+\def\pgfkeysactivatefamiliesandfilteroptions#1#2{%
+	\pgfkeysactivatefamilies{#1}{\pgfkeys@family@deactivation}%
+	\pgfkeysfiltered{#2}%
+	\pgfkeys@family@deactivation
+}
+
+% The "quick" variant of \pgfkeysactivatefamiliesandfilteroptions: it
+% also assigns a default path.
+%
+% #1: comma separated family list
+% #2: default path
+% #3: key-value pairs
+\def\pgfqkeysactivatefamiliesandfilteroptions#1#2#3{%
+	\pgfkeysactivatefamilies{#1}{\pgfkeys@family@deactivation}%
+	\pgfqkeysfiltered{#2}{#3}%
+	\pgfkeys@family@deactivation
+}
+
+% Public version of split path:
+\def\pgfkeyssplitpath{\pgfkeys@split@path}%
+
+
+% The same as \pgfkeysactivatefamiliesandfilteroptions but just for
+% ONE family.
+%
+% #1: family (maybe a macro)
+% #2: key-value pairs
+\def\pgfkeysactivatesinglefamilyandfilteroptions#1#2{%
+	\pgfkeysactivatefamily{#1}%
+	\pgfkeysfiltered{#2}%
+	\pgfkeysdeactivatefamily{#1}%
+}
+
+% The "quick" variant of \pgfkeysactivatesinglefamilyandfilteroptions
+%
+% #1: family (maybe a macro)
+% #2: default path
+% #3: key-value pairs
+\def\pgfqkeysactivatesinglefamilyandfilteroptions#1#2#3{%
+	\pgfkeysactivatefamily{#1}%
+	\pgfqkeysfiltered{#2}{#3}%
+	\pgfkeysdeactivatefamily{#1}%
+}
+
+% Installs the key filter '#1' with argument '#2'.
+% This is equivalent to
+%    \pgfkeys{#1/.install key filter=#2}
+%
+% The current values of the key filter handler is stored into the public
+% macros
+% \pgfkeyscurrentkeyfilter
+% and
+% \pgfkeyscurrentkeyfilterargs
+%
+% #1: a full key name; may be a macro
+% #2: optional arguments for the key. If the key expects more than one
+% argument, supply '{{first}{second}}'
+\def\pgfkeysinstallkeyfilter#1#2{%
+	\pgfkeysifdefined{#1/.@cmd}{%
+		\edef\pgfkeyscurrentkeyfilter{#1}%
+		\def\pgfkeyscurrentkeyfilterargs{#2}%
+		\pgfkeysgetvalue{#1/.@cmd}{\pgfkeys@key@predicate@}%
+		\def\pgfkeys@key@predicate{\pgfkeys@key@predicate@#2\pgfeov}%
+	}{%
+		\pgfkeysvalueof{/errors/no such key filter/.@cmd}{#1}{#2}\pgfeov%
+	}%
+}
+
+% Installs the key filter handler '#1' with argument '#2'.
+% This is equivalent to
+%    \pgfkeys{#1/.install key filter handler=#2}
+% 
+% The current values of the key filter handler is stored into the public
+% macros
+% \pgfkeyscurrentkeyfilterhandler
+% and
+% \pgfkeyscurrentkeyfilterhandlerargs
+%
+% #1: a full key name; may be a macro
+% #2: optional arguments for the handler. If the handler expects more than one
+% argument, supply '{{first}{second}}'
+\def\pgfkeysinstallkeyfilterhandler#1#2{%
+	\pgfkeysifdefined{#1/.@cmd}{%
+		\edef\pgfkeyscurrentkeyfilterhandler{#1}%
+		\def\pgfkeyscurrentkeyfilterhandlerargs{#2}%
+		\pgfkeysgetvalue{#1/.@cmd}{\pgfkeys@filtered@handler@}%
+		\def\pgfkeys@filtered@handler{\pgfkeys@filtered@handler@#2\pgfeov}%
+	}{%
+		\pgfkeysvalueof{/errors/no such key filter handler/.@cmd}{#1}{#2}\pgfeov%
+	}%
+}
+
+% Creates a macro which contains commands to re-activate the current
+% key filter and key filter handler. It can be used to temporarily
+% switch the key filter.
+\def\pgfkeyssavekeyfilterstateto#1{%
+	% produce the string
+	% \pgfkeysinstallkeyfilter{...}{...}
+	% \pgfkeysinstallkeyfilterhandler{...}{...}
+	% where each argument is expanded once
+	% FIXME: Do the same with less overhead!
+	\pgfkeys@tmptoks={\pgfkeysinstallkeyfilter}%
+	\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilter}}%
+	\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterargs}\pgfkeysinstallkeyfilterhandler}%
+	\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterhandler}}%
+	\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterhandlerargs}}%
+	\edef#1{%
+		\the\pgfkeys@tmptoks
+	}%
+}
+
+
+\pgfkeys{%
+	/errors/family unknown/.code=\pgfkeys@error{%
+		Sorry, I do not know family '#1' and can't work with any assoicated family handling. Perhaps you misspelled it?},
+	/errors/no such key filter/.code 2 args=\pgfkeys@error{Sorry, there is no such key filter '#1'.},
+	/errors/no such key filter handler/.code 2 args=\pgfkeys@error{Sorry, there is no such key filter handler '#1'.},
+	% HANDLERS:
+	%
+	% .is family should
+	%  1. '.cd' into the families' path,
+	%  2. define booleans to activate/deactive the family 
+	%     (see \pgfkeysisfamilyactive)
+	%  3. make sure that \pgfkeyshasactivefamily returns true for
+	%     the family itsself.
+	/handlers/.is family/.append code={%
+		%\newif is an \outer macro in plain tex, so this here is not portable:
+		%\expandafter\newif\csname if\pgfkeyscurrentpath/familyactive\endcsname
+		\edef\pgfkeyspred@TMP{pgfk@\pgfkeyscurrentpath/familyactive}%
+		\expandafter\pgfkeys@non@outer@newif\expandafter{\pgfkeyspred@TMP}%
+		\edef\pgfkeyspred@TMP{\pgfkeyscurrentpath/.belongs to family=\pgfkeyscurrentpath}%
+		\expandafter\pgfkeysalso\expandafter{\pgfkeyspred@TMP}%
+	},%
+	/handlers/.activate family/.code=\pgfkeysactivatefamily{\pgfkeyscurrentpath},
+	/handlers/.deactivate family/.code=\pgfkeysdeactivatefamily{\pgfkeyscurrentpath},
+	/handlers/.belongs to family/.code={%
+			\pgfkeysiffamilydefined{#1}{%
+				\pgfkeyssetvalue{\pgfkeyscurrentpath/family}{#1}%
+			}{%
+				\pgfkeysalso{/errors/family unknown=#1}%
+			}%
+	},%
+	%
+	%
+	% An addition to the '.try' and '.retry' handlers:
+	%
+	% It is the same as '.retry', but if the option is still unknown, the
+	% usual handlers for unknown keys will be invoked.
+	/handlers/.lastretry/.code={%
+		\ifpgfkeyssuccess\else
+			\pgfkeys@try
+			\ifpgfkeyssuccess\else
+				% discard the '.lastretry' suffix:
+				\edef\pgfkeyscurrentkey{\pgfkeyscurrentpath}%
+				\pgfkeys@split@path%
+				\pgfkeys@unknown
+			\fi
+		\fi
+	},
+	%
+	%
+	/handlers/.install key filter/.code={%
+		\pgfkeysinstallkeyfilter{\pgfkeyscurrentpath}{#1}%
+	},%
+	/handlers/.install key filter handler/.code={%
+		\pgfkeysinstallkeyfilterhandler{\pgfkeyscurrentpath}{#1}%
+	},%
+	%
+	%
+	% KEY FILTER HANDLERS:
+	%
+	/pgf/key filter handlers/append filtered to/.code={%
+		% Produce
+		%  <orig key> '={' <value> '}'
+		% where both, the key and the value are expanded just ONCE:
+		\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\pgfkeyscurrentkeyRAW\expandafter=\expandafter{\pgfkeyscurrentvalue}}%
+		\ifx#1\pgfkeys@empty
+		\else
+			% Produce <old list> ','  <orig key> '={' <value> '}'
+			\pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter#1\expandafter,\the\pgfkeys@tmptoks}%
+		\fi
+		\edef#1{\the\pgfkeys@tmptoks}%
+	},%
+	/pgf/key filter handlers/ignore/.code={},
+	/pgf/key filter handlers/ignore/.install key filter handler,
+	/pgf/key filter handlers/log/.code={%
+		\immediate\write16{LOG: the option '\pgfkeyscurrentkey' (was originally '\pgfkeyscurrentkeyRAW') (case \pgfkeyscasenumber) has not been processed due to pgfkeysfiltered.}%
+	},
+	%
+	% 
+	% KEY FILTER PREDICATES:
+	%
+	% Returns true iff the currently processed key belongs to an active family.
+	% A family is active if it has been activated before.
+	/pgf/key filters/active families/.code={%
+		\ifnum\pgfkeyscasenumber=0
+			% unknown options shall be processed with the
+			% unknown-handlers.
+			\pgfkeysfiltercontinuetrue
+		\else
+			\ifnum\pgfkeyscasenumber=3
+				\pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP
+			\else
+				\pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP
+			\fi
+			\ifpgfkeyssuccess
+				\pgfkeysisfamilyactive{\pgfkeyspred@TMP}%
+			\else% Ok, it does not belong to any family.
+				\pgfkeysfiltercontinuefalse
+			\fi
+		\fi
+	},%
+	%
+	%
+	%
+	% This filter works as follows:
+	% 1. if the current key belongs to a family:
+	% 	return whether its family is active,
+	% 2. if the current key does NOT belong to a family:
+	%   return the result of criterion '#1',
+	% 3. the current key is unknown:
+	% 	return the result of criterion '#2'.
+	%
+	% Arguments:
+	% #1: the predicate which will be invoked in case 2.
+	%   It will be invoked with the current case number as argument.
+	% #2: the predicate which will be invoked in case 3 with 
+	%   the current case number as argument.
+	/pgf/key filters/active families or no family/.code 2 args={%
+		\ifnum\pgfkeyscasenumber=0
+			\pgfkeysevalkeyfilterwith{#2}%
+		\else
+			\ifnum\pgfkeyscasenumber=3
+				\pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP
+			\else
+				\pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP
+			\fi
+			\ifpgfkeyssuccess
+				\pgfkeysisfamilyactive{\pgfkeyspred@TMP}%
+			\else% Ok, it does not belong to any family.
+				\pgfkeysevalkeyfilterwith{#1}%
+			\fi
+		\fi
+	},
+	/pgf/key filters/active families or no family DEBUG/.code 2 args={%
+		\ifnum\pgfkeyscasenumber=0
+			\immediate\write16{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) invoking unknown handler '#2']}%
+			\pgfkeysevalkeyfilterwith{#2}%
+		\else
+			\ifnum\pgfkeyscasenumber=3
+				\pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP
+			\else
+				\pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP
+			\fi
+			\ifpgfkeyssuccess
+				\pgfkeysisfamilyactive{\pgfkeyspred@TMP}%
+				\ifpgfkeysfiltercontinue
+					\immediate\write16{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) family is ACTIVE]}%
+				\else
+					\immediate\write16{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) family is NOT active.]}%
+				\fi
+			\else% Ok, it does not belong to any family.
+				\immediate\write16{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) invoking has-no-family-handler '#1']}%
+				\pgfkeysevalkeyfilterwith{#1}%
+			\fi
+		\fi
+	},
+	%
+	% Processes only options which are childs of #1.
+	% Example:
+	%   is descendant of/.install key filter=/foo
+	% will be true for
+	%  /foo/bar/x=y
+	%  /foo/.cd
+	%  /foo/bar/.style=...
+	% but not for
+	%  /bar/foo/...
+	/pgf/key filters/is descendant of/.code={%
+		\ifnum\pgfkeyscasenumber=0
+			% unknown options shall be processed with the
+			% unknown-handlers.
+			\pgfkeysfiltercontinuetrue
+		\else
+			% string prefix comparison:
+			\long\def\pgfkeysisdescendantof@impl##1#1##2\pgf@@eov{%
+				\def\pgfkeyspred@TMP{##1}%
+				\ifx\pgfkeyspred@TMP\pgfkeys@empty
+%\message{'\pgfkeyscurrentkey' (case \pgfkeyscasenumber) is descendant of '#1': TRUE.}%
+					\pgfkeysfiltercontinuetrue
+				\else
+%\message{'\pgfkeyscurrentkey' (case \pgfkeyscasenumber) is descendant of '#1': FALSE.}%
+					\pgfkeysfiltercontinuefalse
+				\fi
+			}%
+			\expandafter\pgfkeysisdescendantof@impl\pgfkeyscurrentkey#1\pgf@@eov
+		\fi
+	},%
+	%
+	%
+	% 
+	% Returns true if the currently processed full key equals #2.
+	/pgf/key filters/equals/.code={%
+		\ifnum\pgfkeyscasenumber=0
+			% Unknown option:
+			\pgfkeysfiltercontinuetrue
+		\else
+			\def\pgfkeyspred@TMP{#1}%
+			\ifx\pgfkeyscurrentkey\pgfkeyspred@TMP
+				\pgfkeysfiltercontinuetrue
+			\else
+				\pgfkeysfiltercontinuefalse
+			\fi
+		\fi
+	},%
+	%
+	%
+	% Argument #1 can be any other (evaluated) filter predicate, its logical return
+	% value will be inverted.
+	% Example:
+	%   not/.install key filter={is descendend of=/tikz}
+	% will install a key filter which evaluates 'is descendant of' with argument '/tikz' and returns the logical negation of the result.
+	/pgf/key filters/not/.code={%
+		\pgfkeysevalkeyfilterwith{#1}%
+		\ifpgfkeysfiltercontinue
+			\pgfkeysfiltercontinuefalse
+		\else
+			\pgfkeysfiltercontinuetrue
+		\fi
+	},%
+	/pgf/key filters/and/.code 2 args={%
+		\pgfkeysevalkeyfilterwith{#1}%
+		\ifpgfkeysfiltercontinue
+			\pgfkeysevalkeyfilterwith{#2}%
+		\fi
+	},%
+	/pgf/key filters/or/.code 2 args={%
+		\pgfkeysevalkeyfilterwith{#1}%
+		\ifpgfkeysfiltercontinue
+		\else
+			\pgfkeysevalkeyfilterwith{#2}%
+		\fi
+	},%
+	/pgf/key filters/true/.code={\pgfkeysfiltercontinuetrue},%
+	/pgf/key filters/true/.install key filter,
+	/pgf/key filters/false/.code={\pgfkeysfiltercontinuefalse},%
+	%
+	% Returns false if the current key is unknown, which avoids calling
+	% the unknown handlers.
+	/pgf/key filters/defined/.code={%
+		\ifnum\pgfkeyscasenumber=0
+			\pgfkeysfiltercontinuefalse
+		\else
+			\pgfkeysfiltercontinuetrue
+		\fi
+	},
+}%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% Private IMPLEMENTATION
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+% This command does THE SAME work as \pgfkeys@case@one,
+% but it applies filtering whenever it identified the type of an
+% option.
+\def\pgfkeys@case@one@filtered{%
+	\pgfkeys@cur@is@descendant@of@errors
+	\ifpgfkeysfiltercontinue
+		\pgfkeys@orig@case@one
+	\else
+		\pgfkeysfiltercontinuetrue
+		\pgfkeysifdefined{\pgfkeyscurrentkey/.@cmd}{%
+			% CASE ONE: a command option
+			\def\pgfkeyscasenumber{1}%
+			\pgfkeys@key@predicate%
+			\ifpgfkeysfiltercontinue
+%\message{PROCESSING KEY \pgfkeyscurrentkey!}%
+				\pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}%
+				\expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov
+			\else
+%\message{FILTEReD OUT  KEY \pgfkeyscurrentkey!}%
+				\pgfkeys@filtered@handler%
+			\fi
+		}{%
+			% CASE TWO: a normal value option
+			\pgfkeysifdefined{\pgfkeyscurrentkey}{%
+				\def\pgfkeyscasenumber{2}%
+				\pgfkeys@key@predicate%
+				\ifpgfkeysfiltercontinue
+%\message{PROCESSING KEY \pgfkeyscurrentkey!}%
+					\pgfkeys@case@two@extern
+				\else
+%\message{FILTEReD OUT  KEY \pgfkeyscurrentkey!}%
+					\pgfkeys@filtered@handler%
+				\fi
+			}{%
+				\pgfkeys@split@path
+				% CASE THREE: a handler
+				\pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}{%
+					\def\pgfkeyscasenumber{3}%
+					\pgfkeys@key@predicate%
+					\ifpgfkeysfiltercontinue
+%\message{PROCESSING KEY \pgfkeyscurrentkey!}%
+						\pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}%
+						\expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov
+					\else
+%\message{FILTERED OUT  KEY \pgfkeyscurrentkey!}%
+						\pgfkeys@filtered@handler%
+					\fi
+				}{%
+					\pgfkeys@unknown
+				}%
+			}%
+		}%
+	\fi
+}%
+
+\def\pgfkeys@unknown@filtered{%
+	% CASE ZERO: an unknown option.
+	\def\pgfkeyscasenumber{0}%
+	\pgfkeys@key@predicate%
+	\ifpgfkeysfiltercontinue
+%\message{PROCESSING  KEY \pgfkeyscurrentkey!}%
+		% start normal 'unknown' handlers:
+		\pgfkeys@orig@unknown
+	\else
+%\message{FILTEReD OUT  KEY \pgfkeyscurrentkey!}%
+		\pgfkeys@filtered@handler%
+	\fi
+}
+
+% Does the same as \pgfkeys@try, but it also invokes the key filters.
+\def\pgfkeys@try@filtered{%
+	\ifpgfkeysfiltercontinue
+		\pgfkeys@orig@try
+	\else
+		\pgfkeysfiltercontinuetrue
+		\pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}%
+		{%
+			% CASE ONE: a command option
+			\def\pgfkeyscasenumber{1}%
+			\pgfkeys@key@predicate%
+			\ifpgfkeysfiltercontinue
+				\pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}%
+				\ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% Hmm... no value
+					\pgfkeysifdefined{\pgfkeyscurrentpath/.@def}%
+					{\pgfkeysgetvalue{\pgfkeyscurrentpath/.@def}{\pgfkeyscurrentvalue}}
+					{}% no default, so leave it
+				\fi%
+				\expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov%
+			\else
+				\pgfkeys@filtered@handler%
+			\fi
+			\pgfkeyssuccesstrue%
+		}%
+		{%
+			\pgfkeysifdefined{\pgfkeyscurrentpath}%
+			{% CASE TWO: a normal value option
+				\def\pgfkeyscasenumber{2}%
+				\pgfkeys@key@predicate%
+				\ifpgfkeysfiltercontinue
+					\ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text%
+						\pgfkeysvalueof{\pgfkeyscurrentpath}%
+					\else%
+						\pgfkeyslet{\pgfkeyscurrentpath}\pgfkeyscurrentvalue%
+					\fi%
+				\else
+					\pgfkeys@filtered@handler%
+				\fi
+				\pgfkeyssuccesstrue%
+			}%
+			{\pgfkeyssuccessfalse}%
+		}%
+	\fi
+}
+
+
+% #1 the code to invoke after init and before cleanup
+\def\pgfkeys@install@filter@and@invoke#1{%
+	\ifpgfkeysfilteringisactive
+		\pgfkeys@error{Sorry, nested calls to key filtering routines are not allowed. (reason: It is not possible to properly restore the previous filtering state after returning from the nested call)}%
+	\fi
+	\pgfkeysfilteringisactivetrue
+	\let\pgfkeys@case@one=\pgfkeys@case@one@filtered
+	\let\pgfkeys@try=\pgfkeys@try@filtered
+	\let\pgfkeys@unknown=\pgfkeys@unknown@filtered
+	#1%
+	\let\pgfkeys@case@one=\pgfkeys@orig@case@one
+	\let\pgfkeys@try=\pgfkeys@orig@try
+	\let\pgfkeys@unknown=\pgfkeys@orig@unknown
+	\pgfkeysfilteringisactivefalse
+}
+
+
+%--------------------------------------------------
+% \def\pgfkeys@eval@key@filter@subroutine@case@one{%
+% 	\pgfkeysifdefined{\pgfkeyscurrentkey/.@cmd}{%
+% 		\pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}%
+% 		\let\pgfkeyspred@TMP=\pgfkeyscurrentvalue
+% 		\pgfkeys@eval@key@filter@subroutine@restorestate
+% 		\expandafter\pgfkeys@code\pgfkeyspred@TMP\pgfeov
+% 	}{%
+% 		\pgfkeysvalueof{/errors/no such key filter/.@cmd}\pgfkeyscurrentkey\pgfkeyscurrentvalue\pgfeov%
+% 	}%
+% }
+% % THIS VERSION IS TOO SLOW. See below.
+% \def\pgfkeysevalkeyfilterwith#1{%
+% 	\edef\pgfkeys@eval@key@filter@subroutine@restorestate{%
+% 		\noexpand\def\noexpand\pgfkeyscurrentkey{\pgfkeyscurrentkey}%
+% 		\noexpand\def\noexpand\pgfkeyscurrentkeyRAW{\pgfkeyscurrentkeyRAW}%
+% 		\noexpand\def\noexpand\pgfkeyscurrentname{\pgfkeyscurrentname}%
+% 		\noexpand\def\noexpand\pgfkeyscurrentvalue{\pgfkeyscurrentvalue}%
+% 		\noexpand\pgfkeys@pathtoks={\pgfkeyscurrentpath}%
+% 	}%
+% 	\pgfkeysinterruptkeyfilter
+% 	\let\pgfkeys@case@one=\pgfkeys@eval@key@filter@subroutine@case@one
+% 	\pgfkeysalso{#1}%
+% 	\endpgfkeysinterruptkeyfilter% this here also restored \pgfkeys@case@one.
+% 	\pgfkeys@eval@key@filter@subroutine@restorestate
+% }%
+%-------------------------------------------------- 
+
+
+% Evaluates a key filter '#1'. Example:
+% \pgfkeysevalkeyfilterwith{/pgf/key filters/equals=/tikz}
+%
+% \pgfkeysevalkeyfilterwith works only if key filtering is
+% active.
+%
+% The argument '#1' MUST be a FULL KEY.
+%
+% The implementation employs a subset of the \pgfkeysalso code.
+\def\pgfkeysevalkeyfilterwith#1{%
+	\pgfkeys@eval@key@filter@subroutine@unpack#1=\pgfkeysnovalue=\pgfkeys@stop
+}%
+\def\pgfkeys@eval@key@filter@subroutine@unpack#1=#2=#3\pgfkeys@stop{%
+	\pgfkeys@spdef\pgfkeyspred@TMP{#1}%
+	\edef\pgfkeyspred@TMP{\pgfkeyspred@TMP}%
+	\pgfkeys@spdef\pgfkeyspred@TMPB{#2}% TMPB=value
+	\ifx\pgfkeyspred@TMPB\pgfkeysnovalue@text% Hmm... no value
+		\pgfkeysifdefined{\pgfkeyspred@TMP/.@def}%
+		{\pgfkeysgetvalue{\pgfkeyspred@TMP/.@def}{\pgfkeyspred@TMPB}}
+		{}% no default, so leave it
+	\fi%
+	\ifx\pgfkeyspred@TMPB\pgfkeysvaluerequired%
+		\pgfkeysvalueof{/errors/value required/.@cmd}\pgfkeyspred@TMP\pgfkeyspred@TMPB\pgfeov%
+	\else%
+		\pgfkeysifdefined{\pgfkeyspred@TMP/.@cmd}{%
+			\pgfkeysgetvalue{\pgfkeyspred@TMP/.@cmd}{\pgfkeys@code}%
+			\expandafter\pgfkeys@code\pgfkeyspred@TMPB\pgfeov
+		}{%
+			\pgfkeysvalueof{/errors/no such key filter/.@cmd}\pgfkeyspred@TMP\pgfkeyspred@TMPB\pgfeov%
+		}%
+	\fi%
+}
+
+
+\def\pgfkeys@nevermind#1\relax{\let\pgfkeyscurrentkeyRAW=\pgfkeyscurrentkey}
+\def\pgfkeys@addpath#1\relax{\def\pgfkeyscurrentkeyRAW{#1}% old @addpath:	
+	\edef\pgfkeyscurrentkey{\pgfkeysdefaultpath#1}%
+}
+
+\def\pgfkeys@non@outer@newif@#1#2{%
+	\expandafter\edef\csname #2true\endcsname{\noexpand\let\noexpand#1=\noexpand\iftrue}%
+	\expandafter\edef\csname #2false\endcsname{\noexpand\let\noexpand#1=\noexpand\iffalse}%
+	\csname #2false\endcsname
+}%
+
+% For latex and context, this here has the same effect as a \newif
+% applied to 'if#1'. For plain tex, it has also the same effect, but
+% it is not an \outer macro as the plain-tex \newif.
+\def\pgfkeys@non@outer@newif#1{%
+	\expandafter\pgfkeys@non@outer@newif@\csname if#1\endcsname{#1}%
+}
+\endinput
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgflibraryplothandlers.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgflibraryplothandlers.code.tex
new file mode 100644
index 00000000000..0d120a8b722
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgflibraryplothandlers.code.tex
@@ -0,0 +1,922 @@
+% Copyright 2006 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.
+
+\ProvidesFileRCS[v\pgfversion] $Header: /cvsroot/pgfplots/pgfplots/generic/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgflibraryplothandlers.code.tex,v 1.3 2008/06/07 17:08:33 ludewich Exp $
+
+\newif\ifpgf@plot@started
+
+
+% This handler converts each plot stream command into a curveto
+% command, except for the first, which is converted to the previously
+% specified action.
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfsetlinetofirstplotpoint
+% \pgfplothandlercurveto
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlercurveto{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@initial%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgf@plot@curveto@handler@finish%
+    \global\pgf@plot@startedfalse%
+  }%
+}
+
+\def\pgf@plot@curveto@handler@initial#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@plot@first@action{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \xdef\pgf@plot@curveto@first{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+  \global\let\pgf@plot@curveto@first@support=\pgf@plot@curveto@first%
+  \global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@second%
+}
+
+\def\pgf@plot@curveto@handler@second#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@curveto@second{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@third%
+  \global\pgf@plot@startedtrue%
+}
+
+\def\pgf@plot@curveto@handler@third#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@curveto@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  % compute difference vector:
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\pgf@plot@curveto@first}
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  % compute support directions:
+  \pgf@xa=\pgf@plottension\pgf@xa%
+  \pgf@ya=\pgf@plottension\pgf@ya%
+  % first marshal:
+  \pgf@process{\pgf@plot@curveto@second}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \advance\pgf@xb by-\pgf@xa%
+  \advance\pgf@yb by-\pgf@ya%
+  \advance\pgf@xc by\pgf@xa%
+  \advance\pgf@yc by\pgf@ya%
+  \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@curveto@first@support}%
+    {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@curveto@second}}%
+  {\pgf@marshal}%
+  % Prepare next:
+  \global\let\pgf@plot@curveto@first=\pgf@plot@curveto@second%
+  \global\let\pgf@plot@curveto@second=\pgf@plot@curveto@current%
+  \xdef\pgf@plot@curveto@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+}
+
+\def\pgf@plot@curveto@handler@finish{%
+  \ifpgf@plot@started%
+    \pgfpathcurveto{\pgf@plot@curveto@first@support}{\pgf@plot@curveto@second}{\pgf@plot@curveto@second}%
+  \fi%
+}
+
+
+% This commands sets the tension for smoothing of plots.
+%
+% #1 = tension of curves. A value of 1 will yield a circle when the
+%      control points are at quarters of a circle. A smaller value
+%      will result in a tighter curve. Default is 0.5. 
+%
+% Example:
+%
+% \pgfsetplottension{0.2}
+
+\def\pgfsetplottension#1{%
+  \pgf@x=#1pt\relax%
+  \pgf@x=0.2775\pgf@x\relax%
+  \edef\pgf@plottension{\pgf@sys@tonumber\pgf@x}}
+\pgfsetplottension{0.5}
+
+
+% This handler converts the plot stream command into a curveto
+% command that is closed using a closepath.
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfplothandlerclosedcurve
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlerclosedcurve{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@initial%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgf@plot@closedcurve@handler@finish%
+  }%
+}
+
+\def\pgf@plot@closedcurve@handler@initial#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \xdef\pgf@plot@closedcurve@initial{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@second%
+  \global\pgf@plot@startedfalse%
+}
+
+\def\pgf@plot@closedcurve@handler@second#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@closedcurve@after@initial{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  {\pgfpathmoveto{}}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@third%
+}
+
+\def\pgf@plot@closedcurve@handler@third#1{%
+  \global\pgf@plot@startedtrue%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@closedcurve@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  % compute difference vector:
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\pgf@plot@closedcurve@initial}
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  % compute support directions:
+  \pgf@xa=\pgf@plottension\pgf@xa%
+  \pgf@ya=\pgf@plottension\pgf@ya%
+  % first marshal:
+  \pgf@process{\pgf@plot@closedcurve@after@initial}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \advance\pgf@xb by-\pgf@xa%
+  \advance\pgf@yb by-\pgf@ya%
+  \advance\pgf@xc by\pgf@xa%
+  \advance\pgf@yc by\pgf@ya%
+  \global\let\pgf@plot@closedcurve@first=\pgf@plot@closedcurve@after@initial%
+  \global\let\pgf@plot@closedcurve@second=\pgf@plot@closedcurve@current%
+  \xdef\pgf@plot@closedcurve@after@initial@presupport{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}%
+  \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@fourth%
+}
+
+\def\pgf@plot@closedcurve@handler@fourth#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@closedcurve@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  % compute difference vector:
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\pgf@plot@closedcurve@first}
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  % compute support directions:
+  \pgf@xa=\pgf@plottension\pgf@xa%
+  \pgf@ya=\pgf@plottension\pgf@ya%
+  % first marshal:
+  \pgf@process{\pgf@plot@closedcurve@second}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \advance\pgf@xb by-\pgf@xa%
+  \advance\pgf@yb by-\pgf@ya%
+  \advance\pgf@xc by\pgf@xa%
+  \advance\pgf@yc by\pgf@ya%
+  \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}%
+    {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@second}}%
+  {\pgf@marshal}%
+  % Prepare next:
+  \global\let\pgf@plot@closedcurve@first=\pgf@plot@closedcurve@second%
+  \global\let\pgf@plot@closedcurve@second=\pgf@plot@closedcurve@current%
+  \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+}
+
+\def\pgf@plot@closedcurve@handler@finish{%
+  \ifpgf@plot@started
+    %
+    % first, draw line from 2nd last to last:
+    %
+    \pgf@process{\pgf@plot@closedcurve@initial}%
+    % compute difference vector:
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgf@plot@closedcurve@first}%
+    \advance\pgf@xa by-\pgf@x%
+    \advance\pgf@ya by-\pgf@y%
+    % compute support directions:
+    \pgf@xa=\pgf@plottension\pgf@xa%
+    \pgf@ya=\pgf@plottension\pgf@ya%
+    % first marshal:
+    \pgf@process{\pgf@plot@closedcurve@second}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \advance\pgf@xb by-\pgf@xa%
+    \advance\pgf@yb by-\pgf@ya%
+    \advance\pgf@xc by\pgf@xa%
+    \advance\pgf@yc by\pgf@ya%
+    \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}%
+      {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@second}}%
+    {\pgf@marshal}%
+    \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+    %
+    % second, draw line from last point to start:
+    %
+    \pgf@process{\pgf@plot@closedcurve@after@initial}%
+    % compute difference vector:
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgf@plot@closedcurve@second}%
+    \advance\pgf@xa by-\pgf@x%
+    \advance\pgf@ya by-\pgf@y%
+    % compute support directions:
+    \pgf@xa=\pgf@plottension\pgf@xa%
+    \pgf@ya=\pgf@plottension\pgf@ya%
+    % first marshal:
+    \pgf@process{\pgf@plot@closedcurve@initial}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \advance\pgf@xb by-\pgf@xa%
+    \advance\pgf@yb by-\pgf@ya%
+    \advance\pgf@xc by\pgf@xa%
+    \advance\pgf@yc by\pgf@ya%
+    \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}%
+      {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@initial}}%
+    {\pgf@marshal}%
+    %
+    % third, draw line from first to second point:
+    %
+    \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+      {\noexpand\pgf@plot@closedcurve@after@initial@presupport}{\noexpand\pgf@plot@closedcurve@after@initial}}%
+    {\pgf@marshal}%
+    \pgfpathclose%
+  \fi%
+}
+
+
+
+
+
+% This handler converts each point in a stream into a line from the
+% $y$-axis to the given points coordinate, resulting in a
+% ``comb.'' 
+%
+% Example:
+%
+% \pgfplothandlerxcomb
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlerxcomb{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@xcomb@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotxzerolevelstreamend%
+	\pgfplotxzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@xcomb@handler#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \begingroup
+  \pgfplotxzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \pgfpathmoveto{\pgfqpoint{\pgf@yb}{\pgf@ya}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+}
+
+
+% This handler converts each point in a stream into a line from the
+% $x$-axis straight up to the given points coordinate, resulting in a
+% ``comb.'' 
+%
+% Example:
+%
+% \pgfplothandlerycomb
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlerycomb{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@ycomb@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotyzerolevelstreamend%
+	\pgfplotyzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@ycomb@handler#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \begingroup
+  \pgfplotyzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+}
+
+% PGF Bar or comb plots usually draw something from zero to the current plot's coordinate.
+% 
+% The 'zero' offset can be changed using an input stream.
+%
+% There are two such streams which can be configured independently.
+% The first one returns "zeros" for coordinate x, the second one
+% returns "zeros" for coordinate y.
+% 
+% \pgfplotxzerolevelstreamstart
+% \pgfplotxzerolevelstreamnext % assigns \pgf@x globally
+% \pgfplotxzerolevelstreamnext
+% \pgfplotxzerolevelstreamnext
+% \pgfplotxzerolevelstreamend
+%
+% and 
+% \pgfplotyzerolevelstreamstart
+% \pgfplotyzerolevelstreamnext % assigns \pgf@x globally
+% \pgfplotyzerolevelstreamend
+%
+\def\pgfplotxzerolevelstreamstart{\pgf@plotxzerolevelstreamstart}%
+\def\pgfplotxzerolevelstreamend{\pgf@plotxzerolevelstreamend}%
+\def\pgfplotxzerolevelstreamnext{\pgf@plotxzerolevelstreamnext}
+\def\pgfplotyzerolevelstreamstart{\pgf@plotyzerolevelstreamstart}%
+\def\pgfplotyzerolevelstreamend{\pgf@plotyzerolevelstreamend}%
+\def\pgfplotyzerolevelstreamnext{\pgf@plotyzerolevelstreamnext}
+
+% This zero level stream always returns '#1' (a dimension).
+\def\pgfplotxzerolevelstreamconstant#1{%
+	\edef\pgfplotxzerolevelstreamconstant@val{#1}%
+	\def\pgf@plotxzerolevelstreamstart{%
+		\global\let\pgf@plotxzerolevelstreamend=\relax
+		\gdef\pgf@plotxzerolevelstreamnext{\global\pgf@x=\pgfplotxzerolevelstreamconstant@val\relax}%
+	}%
+}%
+\pgfplotxzerolevelstreamconstant{0pt}%
+
+% This zero level stream always returns '#1'.
+\def\pgfplotyzerolevelstreamconstant#1{%
+	\edef\pgfplotyzerolevelstreamconstant@val{#1}%
+	\def\pgf@plotyzerolevelstreamstart{%
+		\global\let\pgf@plotyzerolevelstreamend=\relax
+		\gdef\pgf@plotyzerolevelstreamnext{\global\pgf@x=\pgfplotyzerolevelstreamconstant@val\relax}%
+	}%
+}%
+\pgfplotyzerolevelstreamconstant{0pt}%
+
+\def\pgfplotbarwidth{\pgfkeysvalueof{/pgf/bar width}}
+
+\pgfqkeys{/pgf}{%
+	bar width/.initial=10pt,
+	bar shift/.initial=0pt,
+	bar interval width/.initial=1,
+	bar interval shift/.initial=0.5,
+}
+
+% This handler places a rectangle at each point in the plot stream, a
+% rectangle which touches the x-axis at one end and the current point
+% at the other end:
+%    --(X)--
+%    |     |
+%    |     |
+%    |     |
+%    --(0)--
+% Example:
+%
+% \pgfplothandlerybar
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerybar{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@ybar@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotyzerolevelstreamend%
+	\pgfmathparse{\pgfplotbarwidth}%
+	\xdef\pgfplotbarwidth@{\pgfmathresult pt}%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar shift}}%
+	\xdef\pgfplotbarshift@{\pgfmathresult pt}%
+	\pgfplotyzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@ybar@handler#1{%
+  \pgf@process{#1}%
+  \pgf@ya=\pgf@y
+  \expandafter\pgf@xb\pgfplotbarwidth@\relax
+  \pgf@xc=\pgf@x
+  \advance\pgf@xc by-.5\pgf@xb
+  \advance\pgf@xc by\pgfplotbarshift@\relax
+  \begingroup
+  \pgfplotyzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \advance\pgf@ya by-\pgf@yb
+  \pgfpathrectangle
+	{\pgfqpoint{\pgf@xc}{\pgf@yb}}%
+	{\pgfqpoint{\pgf@xb}{\pgf@ya}}%
+}
+
+% This handler places a rectangle at each point in the plot stream, a
+% rectangle which touches the y-axis at one end and the current point
+% at the other end:
+%    ---------
+%    |       |
+%   (0)     (X)
+%    |       |
+%    ---------
+% Example:
+%
+% \pgfplothandlerxbar
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerxbar{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@xbar@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotxzerolevelstreamend%
+	\pgfmathparse{\pgfplotbarwidth}%
+	\xdef\pgfplotbarwidth@{\pgfmathresult pt}%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar shift}}%
+	\xdef\pgfplotbarshift@{\pgfmathresult pt}%
+	\pgfplotxzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@xbar@handler#1{%
+  \pgf@process{#1}%
+  \pgf@ya=\pgf@x
+  \expandafter\pgf@xb\pgfplotbarwidth@\relax
+  \pgf@xc=\pgf@y
+  \advance\pgf@xc by-.5\pgf@xb
+  \advance\pgf@xc by\pgfplotbarshift@\relax
+  \begingroup
+  \pgfplotxzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \advance\pgf@ya by-\pgf@yb
+  \pgfpathrectangle
+	{\pgfqpoint{\pgf@yb}{\pgf@xc}}%
+	{\pgfqpoint{\pgf@ya}{\pgf@xb}}%
+}
+
+% This handler is a variant of \pgfplothandlerybar which works with
+% intervals instead of points.
+% 
+% Bars are drawn between successive input coordinates and the width is
+% determined relatively to the interval length.
+%
+% It looks like this:
+%
+%    |---|      |-----| 
+%    |   |      |     |    
+%    |   |      |     |     
+%    |   |      |     |       
+% (X)------(X)-----------(X)
+%
+% where (X) denotes the x-axis offsets of input coordinates.
+%
+% In more detail, if (x_i,y_i) and (x_{i+1},y_{i+1}) denote successive
+% input coordinates, the bar will be placed above the
+% interval [x_i,x_{i+1}], centered at
+%
+%    x_i + \pgfkeysvalueof{/pgf/bar interval shift} * (x_{i+1} - x_i)
+%
+% with width
+%
+%    \pgfkeysvalueof{/pgf/bar interval width} * (x_{i+1} - x_i).
+%
+% If you have N+1 input points, you will get N bars (one for each
+% interval). The y_i value of the last bar will be ignored.
+%
+% Example:
+%
+% \pgfplothandlerybarinterval
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerybarinterval{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@ybarinterval@handler@first%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotyzerolevelstreamend%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar interval width}}%
+	\xdef\pgfplotbarintervalwidth@{\pgfmathresult}%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar interval shift}}%
+	\xdef\pgfplotbarintervalshift@{\pgfmathresult}%
+	\pgfplotyzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@ybarinterval@handler@first#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@x}%
+  \xdef\pgf@plot@barinterval@bar{\the\pgf@y}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@ybarinterval@handler%
+}
+\def\pgf@plot@ybarinterval@handler#1{%
+  \pgf@process{#1}%
+  \pgf@ya=\pgf@plot@barinterval@bar
+  \xdef\pgf@plot@barinterval@bar{\the\pgf@y}%
+  \pgf@xc=\pgf@plot@barinterval@intervalstart\relax
+  \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@x}%
+  \pgf@xb=\pgf@x
+  \advance\pgf@xb by-\pgf@xc
+  \advance\pgf@xc by\pgfplotbarintervalshift@\pgf@xb
+  \pgf@xb=\pgfplotbarintervalwidth@\pgf@xb
+  \advance\pgf@xc by-.5\pgf@xb% center
+  \begingroup
+  \pgfplotyzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \advance\pgf@ya by-\pgf@yb
+  \pgfpathrectangle
+	{\pgfqpoint{\pgf@xc}{\pgf@yb}}%
+	{\pgfqpoint{\pgf@xb}{\pgf@ya}}%
+}
+
+% Like \pgfplothandlerybarinterval but for xbar.
+\def\pgfplothandlerxbarinterval{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@xbarinterval@handler@first%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\pgfplotxzerolevelstreamend%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar interval width}}%
+	\xdef\pgfplotbarintervalwidth@{\pgfmathresult}%
+	\pgfmathparse{\pgfkeysvalueof{/pgf/bar interval shift}}%
+	\xdef\pgfplotbarintervalshift@{\pgfmathresult}%
+	\pgfplotxzerolevelstreamstart
+  }%
+}
+
+\def\pgf@plot@xbarinterval@handler@first#1{%
+  \pgf@process{#1}%
+  \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@y}%
+  \xdef\pgf@plot@barinterval@bar{\the\pgf@x}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@xbarinterval@handler%
+}
+\def\pgf@plot@xbarinterval@handler#1{%
+  \pgf@process{#1}%
+  \pgf@ya=\pgf@plot@barinterval@bar
+  \xdef\pgf@plot@barinterval@bar{\the\pgf@x}%
+  \pgf@xc=\pgf@plot@barinterval@intervalstart\relax
+  \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@y}%
+  \pgf@xb=\pgf@y
+  \advance\pgf@xb by-\pgf@xc
+  \advance\pgf@xc by\pgfplotbarintervalshift@\pgf@xb
+  \pgf@xb=\pgfplotbarintervalwidth@\pgf@xb
+  \advance\pgf@xc by-.5\pgf@xb% center
+  \begingroup
+  \pgfplotxzerolevelstreamnext
+  \endgroup
+  \pgf@yb=\pgf@x
+  \advance\pgf@ya by-\pgf@yb
+  \pgfpathrectangle
+	{\pgfqpoint{\pgf@yb}{\pgf@xc}}%
+	{\pgfqpoint{\pgf@ya}{\pgf@xb}}%
+}
+
+
+% This handler is very similar to \pgfplothandlerlineto, but it
+% produces CONSTANT connected pieces of the form
+%
+%          x
+%          |
+%   x---   |
+%   |  x----
+% x-|
+%
+% Example:
+%
+% \pgfplothandlerconstantlineto
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerconstantlineto{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@const@line@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+\def\pgf@plot@const@line@handler#1{%
+  \pgf@plot@first@action{#1}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@y}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@const@line@handler@@%
+}
+\def\pgf@plot@const@line@handler@@#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x
+  \pgf@ya=\pgf@y
+  \expandafter\pgf@yb\pgf@plot@const@line@handler@last
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@ya}%
+}
+
+% A variant of \pgfplothandlerconstantlineto which places its mark on
+% the right line ends.
+% 
+%       |---x
+% ---x  |
+%    |--x
+% x
+%
+% Example:
+%
+% \pgfplothandlerconstantlinetomarkright
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerconstantlinetomarkright{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@const@line@mark@right@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+\def\pgf@plot@const@line@mark@right@handler#1{%
+  \pgf@plot@first@action{#1}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@x}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@const@line@mark@right@handler@@%
+}
+\def\pgf@plot@const@line@mark@right@handler@@#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x
+  \pgf@ya=\pgf@y
+  \expandafter\pgf@yb\pgf@plot@const@line@handler@last
+  \pgfpathlineto{\pgfqpoint{\pgf@yb}{\pgf@ya}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@xa}%
+}
+
+% This handler is in fact a variant of \pgfplothandlerconstantlineto,
+% but it does not draw vertical lines. It produces a sequence of
+% line-to and move-to operations such that plot marks are placed at
+% each right end:
+%
+%          ---x
+%   ---x   
+%       ---x
+% --x
+%
+% Example:
+%
+% \pgfplothandlerjumpmarkright
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerjumpmarkright{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkright@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+\def\pgf@plot@jumpmarkright@handler#1{%
+  \pgf@plot@first@action{#1}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@x}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkright@handler@@%
+}
+\def\pgf@plot@jumpmarkright@handler@@#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x
+  \pgf@ya=\pgf@y
+  \expandafter\pgf@yb\pgf@plot@const@line@handler@last
+  \pgfpathmoveto{\pgfqpoint{\pgf@yb}{\pgf@ya}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@xa}%
+}
+
+% This handler is in fact a variant of \pgfplothandlerconstantlineto,
+% but it does not draw vertical lines. It produces a sequence of
+% line-to and move-to operations such that plot marks are placed at
+% each left end:
+%
+%          x---
+%   x---   
+%       x---
+% x--
+%
+% Example:
+%
+% \pgfplothandlerjumpmarkleft
+% \pgfplotxyfile{mytable}
+\def\pgfplothandlerjumpmarkleft{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkleft@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+\def\pgf@plot@jumpmarkleft@handler#1{%
+  \pgf@plot@first@action{#1}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@y}%
+  \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkleft@handler@@%
+}
+\def\pgf@plot@jumpmarkleft@handler@@#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x
+  \pgf@ya=\pgf@y
+  \expandafter\pgf@yb\pgf@plot@const@line@handler@last
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}%
+  \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \xdef\pgf@plot@const@line@handler@last{\the\pgf@ya}%
+}
+
+
+
+% This handler converts each point in a stream into a line from the
+% origin to the point's coordinate, resulting in a ``star''.
+%
+% Example:
+%
+% \pgfplothandlerpolarcomb
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlerpolarcomb{%
+  \def\pgf@plotstreamstart{%
+    \global\let\pgf@plotstreampoint=\pgf@plot@polarcomb@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+
+\def\pgf@plot@polarcomb@handler#1{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgfpathmoveto{\pgfpointorigin}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+}
+
+
+
+
+% This handler draws a given mark at each point. 
+%
+% #1 = some code to be executed at each point (with the coordinate
+%      system translated to that point).
+%      Typically, this code will be \pgfuseplotmark{whatever}.
+%
+% Example:
+%
+% \pgfplothandlermark{\pgfuseplotmark{*}}
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlermark#1{%
+  \pgf@plothandlermark{%
+    \ifnum\pgf@plot@mark@count<\pgf@plot@mark@repeat\relax%
+    \else%
+      \global\pgf@plot@mark@count=0\relax%
+      #1%
+    \fi%
+    }%
+}
+
+\newcount\pgf@plot@mark@count
+\def\pgf@plot@mark@phase{0}
+
+\def\pgf@plothandlermark#1{%
+  \def\pgf@plot@mark{#1}%
+  \def\pgf@plotstreamstart{%
+    \global\pgf@plot@mark@count=\pgf@plot@mark@repeat\relax%
+    \global\advance\pgf@plot@mark@count by-\pgf@plot@mark@phase\relax%
+    \global\let\pgf@plotstreampoint=\pgf@plot@mark@handler%
+    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
+    \global\let\pgf@plotstreamend=\relax%
+  }%
+}
+
+\def\pgf@plot@mark@handler#1{%
+  \global\advance\pgf@plot@mark@count by1\relax%
+  {\pgftransformshift{#1}\pgf@plot@mark}%
+}
+
+
+% Set the repeat count for marks. For example, if 3 is given as a
+% value, only every third point will get a mark.
+%
+% #1 = repeat count
+%
+% Example:
+%
+% \pgfsetplotmarkrepeat{2}
+
+\def\pgfsetplotmarkrepeat#1{\def\pgf@plot@mark@repeat{#1}}
+\pgfsetplotmarkrepeat{1}
+
+
+% Set the phase for marks. For example, if 3 is the repeat and 3 is 
+% the phase, already the first point will be marked. 
+%
+% #1 = the index of the first point that should be marked.
+%
+% Example:
+%
+% \pgfsetplotmarkphase{3}
+
+\def\pgfsetplotmarkphase#1{\def\pgf@plot@mark@phase{#1}}
+\pgfsetplotmarkphase{1}
+
+
+
+% This handler draws a given mark at those points whose number is
+% given in the (pgffor-like) list.
+%
+% #1 = some code to be executed at each point (with the coordinate
+%      system translated to that point).
+%      Typically, this code will be \pgfuseplotmark{whatever}.
+% #2 = list of positions like "1,2,4,...,9,10"
+%
+% Example:
+%
+% \pgfplothandlermarklisted{\pgfuseplotmark{*}}{1,2,4,...,9}
+% \pgfplotxyfile{mytable}
+
+\def\pgfplothandlermarklisted#1#2{%
+  \let\pgf@plot@mark@list=\pgfutil@empty%
+  \edef\pgf@marshal{\noexpand\foreach\noexpand\pgf@temp in{#2}}
+  \pgf@marshal{\xdef\pgf@plot@mark@list{\pgf@plot@mark@list(\pgf@temp)}}%
+  \pgf@plothandlermark{%
+    \edef\pgf@marshal{\noexpand\pgfutil@in@{(\the\pgf@plot@mark@count)}{\pgf@plot@mark@list}}%
+    \pgf@marshal%
+    \ifpgfutil@in@#1\fi}%
+}
+
+
+% Define a new plot mark for use with \pgfplotmark.
+%
+% #1 = a plot mark mnemonic
+% #2 = code for drawing the mark
+%
+% Example:
+%
+% \pgfdeclareplotmark{*}{\pgfpathcircle{\pgfpointorigin}{2pt}\pgfusepathqfill}
+
+\def\pgfdeclareplotmark#1#2{\expandafter\def\csname pgf@plot@mark@#1\endcsname{#2}}
+
+
+% Set the size of plot marks. For circles, this will be the radius,
+% for other shapes it should be about half the width/height.
+%
+% Example:
+%
+% \pgfsetplotmarksize{1pt}
+
+\def\pgfsetplotmarksize#1{\pgfmathsetlength\pgfplotmarksize{#1}}
+
+\newdimen\pgfplotmarksize
+\pgfplotmarksize=2pt
+
+
+% Insert a plot mark's code at the origin.
+%
+% #1 = plot mark mnemonic
+%
+% Example:
+%
+% \pgfuseplotmark{*}
+
+\def\pgfuseplotmark#1{\csname pgf@plot@mark@#1\endcsname}
+
+
+% A stroke-filled circle mark
+
+\pgfdeclareplotmark{*}
+{%
+  \pgfpathcircle{\pgfpointorigin}{\pgfplotmarksize}
+  \pgfusepathqfillstroke
+}
+
+
+% A plus-sign like mark
+
+\pgfdeclareplotmark{+}
+{%
+  \pgfpathmoveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}
+  \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}
+  \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}
+  \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}
+  \pgfusepathqstroke
+}
+
+
+% An x-shaped mark
+
+\pgfdeclareplotmark{x}
+{%
+  \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}
+  \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}
+  \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}
+  \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}
+  \pgfusepathqstroke
+}
+
+% See pgflibraryplotmarks for more plot marks
+
+
+
+
+
+
+\endinput
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfmathfloat.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfmathfloat.code.tex
new file mode 100644
index 00000000000..cb479f8dc73
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfmathfloat.code.tex
@@ -0,0 +1,2007 @@
+% Copyright 2008 by Christian Feuersaenger
+%
+% 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 contains methods for basic floating point arithmetics, rounding
+% to arbitrary precision and number pretty printing.
+%
+% Version 0.9.4 2008/03/18
+
+\global\newif\ifpgfmathfloatcomparison
+\newif\ifpgfmathfloatroundhasperiod
+\newif\ifpgfmathprintnumberskipzeroperiod
+
+
+% used internally in grouped macros:
+\toksdef\pgfmathfloat@tmptoks=1
+\newif\ifpgfmathfloat@fixed@digits@after@period
+\newif\ifpgfmathfloatroundmayneedrenormalize
+\toksdef\pgfmathfloat@a@Mtok=0
+
+%% WARNING: avoid conflicting register names!
+\let\pgfmathfloat@a@S=\c@pgf@counta
+\let\pgfmathfloat@a@M=\pgf@xa
+\let\pgfmathfloat@a@E=\c@pgf@countb
+\let\pgfmathfloat@b@S=\c@pgf@countc
+\let\pgfmathfloat@b@M=\pgf@xb
+\let\pgfmathfloat@b@E=\c@pgf@countd
+
+% can be changed with options.
+\def\pgfmathfloat@round@precision{2}
+
+
+% Computes a normalised floating point representation for #1 of the
+% form
+%   [FLAGS] MANTISSE EXPONENT
+% meaning
+%   [+-]X.XXXXXXX*10^C
+% where 
+%   X.XXXXXX is a mantisse with first number != 0, C is an integer and
+% FLAGS contains the sign and some other special cases.
+%
+% This method does NOT use TeX Registers to represent the numbers! The
+% computation is COMPLETELY STRING BASED.
+% This allows numbers such at 10000000 or 5.23e-10 to be represented
+% properly, although TeX-registers would produce overflow/underflow
+% errors in these cases. 
+%
+% It is to be used to compute logs, because log(X*10^Y) = log(X) + log(10)*Y
+%
+% Arguments:
+% #1:  an arbitrary number which shall be parsed. Maybe a macro.
+%     Examples:
+%     [+-]XXXXX.XXXXXX
+%     [+-]XXXXX.XXXXXXeXXXX
+%     [+-]0.0000XXXXXX
+%     [+-]0.0000XXXXXXeXXXX
+%     [+-]inf
+%     nan
+%    Maybe a macro containing such a number.
+%
+% Return value:
+% \pgfmathresult will be \def'ed to
+%  FLAGS MANTISSE 'e' EXPONENT
+% where
+% FLAGS is a number in [0-5] where
+% 		0 == '0' (the number is +- 0.0),
+% 		1 == '+', 
+% 		2 == '-',
+% 		3 == 'not a number'
+% 		4 == '+ infinity'
+% 		5 == '- infinity'
+%
+% MANTISSE is a normalised number 1 <= M < 10. It always contains a
+% period and at least one digit after the period.
+%
+% EXPONENT is an integer value.
+%
+% Example:
+% \pgfmathfloatparsenumber{1}
+% -> \pgfmathresult = 11.0e0
+% \pgfmathfloatparsenumber{141.212}
+% -> \pgfmathresult = 11.41212e2
+\def\pgfmathfloatparsenumber#1{%
+	\begingroup
+	\expandafter\pgfmathfloatparsenumber@impl#1\pgfmathfloat@EOI
+	\ifpgfmathfloatparsenumberpendingperiod
+		\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.0}%
+	\fi
+	\edef\pgfmathresult{%
+		\the\pgfmathfloat@a@S\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+% The same as \pgfmathfloatparsenumber, but does not perform sanity checking.
+\def\pgfmathfloatqparsenumber#1{%
+	\begingroup
+	\let\pgfmathfloatparsenumber@sanitize@digit=\relax
+	\expandafter\pgfmathfloatparsenumber@impl#1\pgfmathfloat@EOI
+	\ifpgfmathfloatparsenumberpendingperiod
+		\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.0}%
+	\fi
+	\edef\pgfmathresult{%
+		\the\pgfmathfloat@a@S\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+
+% decomposes a lowlevel floating point representation into flags,
+% mantisse and exponent.
+%
+% #4: integer register for the flags.
+% #5: dimen registers for the mantisse.
+% #6: integer register for the exponent.
+\def\pgfmathfloat@decompose#1#2e#3\relax#4#5#6{%
+   #4=#1\relax
+   #5=#2pt%
+   #6=#3\relax%
+}
+% overloaded, #5 needs to be a token register for the mantisse.
+\def\pgfmathfloat@decompose@tok#1#2e#3\relax#4#5#6{%
+   #4=#1\relax
+   #5={#2}%
+   #6=#3\relax%
+}
+% overloaded, returns only ONE of the three components into #4:
+\def\pgfmathfloat@decompose@F#1#2e#3\relax#4{#4=#1\relax}%
+\def\pgfmathfloat@decompose@M#1#2e#3\relax#4{#4=#2pt}%
+\def\pgfmathfloat@decompose@Mtok#1#2e#3\relax#4{#4={#2}}%
+\def\pgfmathfloat@decompose@E#1#2e#3\relax#4{#4=#3\relax}%
+
+% Takes a floating point number #1 as input and writes flags to macro
+% #2, mantisse to macro #3 and exponent to macro #4.
+\def\pgfmathfloattomacro#1#2#3#4{%
+	\begingroup
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\xdef\pgfmathfloat@TMPB{%
+		\noexpand\def\noexpand#2{\the\pgfmathfloat@a@S}%
+		\noexpand\def\noexpand#3{\the\pgfmathfloat@a@Mtok}%
+		\noexpand\def\noexpand#4{\the\pgfmathfloat@a@E}%
+	}%
+	\endgroup
+	\pgfmathfloat@TMPB
+}
+
+% Takes a floating point number #1 as input and writes flags to count
+% register #2, mantisse to dimen register #3 and exponent to count
+% register #4.
+\def\pgfmathfloattoregisters#1#2#3#4{%
+	\expandafter\pgfmathfloat@decompose#1\relax{#2}{#3}{#4}%
+}
+
+% the same, but writes the mantisse into a token register.
+\def\pgfmathfloattoregisterstok#1#2#3#4{%
+	\expandafter\pgfmathfloat@decompose@tok#1\relax{#2}{#3}{#4}%
+}
+
+% Extracts the flags of #1 into the count register #2.
+\def\pgfmathfloatgetflags#1#2{%
+	\expandafter\pgfmathfloat@decompose@F#1\relax{#2}%
+}
+% Extracts the mantisse of #1 into the dimen register #2.
+\def\pgfmathfloatgetmantisse#1#2{%
+	\expandafter\pgfmathfloat@decompose@M#1\relax{#2}%
+}
+% Extracts the mantisse of #1 into the token register #2.
+\def\pgfmathfloatgetmantissetok#1#2{%
+	\expandafter\pgfmathfloat@decompose@Mtok#1\relax{#2}%
+}
+% Extracts the exponent of #1 into the count register #2.
+\def\pgfmathfloatgetmantisse#1#2{%
+	\expandafter\pgfmathfloat@decompose@E#1\relax{#2}%
+}
+
+% Defines \pgfmathresult as the floating point number encoded by
+% the flags #1, mantisse #2 and exponent #3.
+%
+% All arguments are characters and will be expanded using '\edef'.
+\def\pgfmathfloatcreate#1#2#3{%
+	\edef\pgfmathresult{#1#2e#3}%
+}%
+
+
+% Compares #1 with #2 and sets \pgfmathresult either to 1.0 or 0.0.
+% 
+% It also sets the boolean \ifpgfmathfloatcomparison (globally.
+\def\pgfmathfloatlessthan@#1#2{%
+%\def\pgfmathfloatlessthan#1#2#3\and#4#5#6{%
+	\global\pgfmathfloatcomparisonfalse
+	\begingroup
+	\expandafter\pgfmathfloat@decompose#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@M\pgfmathfloat@a@E
+	\expandafter\pgfmathfloat@decompose#2\relax\pgfmathfloat@b@S\pgfmathfloat@b@M\pgfmathfloat@b@E
+	\ifcase\pgfmathfloat@a@S
+		% x = 0 -> (x<y <=> y >0)
+		\ifnum1=\pgfmathfloat@b@S
+			\global\pgfmathfloatcomparisontrue
+		\fi
+	\or
+		% x > 0 -> (x<y <=> ( y > 0 && |x| < |y|) )
+		\ifnum1=\pgfmathfloat@b@S
+			% y>0:
+			\pgfmathfloatlessthan@positive
+		\fi
+	\or
+		% x < 0 -> (x<y <=> (y >= 0 ||   |x| > |y|) )
+		\ifnum2=\pgfmathfloat@b@S
+			% 'y<0':
+			\pgfmathfloatgreaterthan@positive
+		\else
+			\global\pgfmathfloatcomparisontrue
+		\fi
+	\else
+		\pgfmath@error{Sorry, 'pgfmathfloatlessthan@{#1}{#2}' not yet supported.}%
+	\fi
+	\endgroup
+	\ifpgfmathfloatcomparison
+		\def\pgfmathresult{1.0}%
+	\else
+		\def\pgfmathresult{0.0}%
+	\fi
+}
+\let\pgfmathfloatlessthan=\pgfmathfloatlessthan@
+
+% compares \pgfmathfloat@a@[SME] < \pgfmathfloat@b@[SME]
+\def\pgfmathfloatlessthan@positive{%
+	\ifnum\pgfmathfloat@a@E<\pgfmathfloat@b@E
+		\global\pgfmathfloatcomparisontrue
+	\else
+		\ifnum\pgfmathfloat@a@E=\pgfmathfloat@b@E
+			\ifdim\pgfmathfloat@a@M<\pgfmathfloat@b@M
+				\global\pgfmathfloatcomparisontrue
+			\fi
+		\fi
+	\fi
+}
+
+% compares \pgfmathfloat@a@[SME] > \pgfmathfloat@b@[SME]
+\def\pgfmathfloatgreaterthan@positive{%
+	\ifnum\pgfmathfloat@a@E>\pgfmathfloat@b@E
+		\global\pgfmathfloatcomparisontrue
+	\else
+		\ifnum\pgfmathfloat@a@E=\pgfmathfloat@b@E
+			\ifdim\pgfmathfloat@a@M>\pgfmathfloat@b@M
+				\global\pgfmathfloatcomparisontrue
+			\fi
+		\fi
+	\fi
+}
+
+
+\def\pgfmathfloatmax@#1#2{%
+	\pgfmathfloatlessthan{#1}{#2}%
+	\ifpgfmathfloatcomparison
+		\edef\pgfmathresult{#2}%
+	\else
+		\edef\pgfmathresult{#1}%
+	\fi
+}
+\let\pgfmathfloatmax=\pgfmathfloatmax@
+
+\def\pgfmathfloatmin@#1#2{%
+	\pgfmathfloatlessthan{#1}{#2}%
+	\ifpgfmathfloatcomparison
+		\edef\pgfmathresult{#1}%
+	\else
+		\edef\pgfmathresult{#2}%
+	\fi
+}
+\let\pgfmathfloatmin=\pgfmathfloatmin@
+
+% Renormalizes #1 to extended precision mantisse, meaning
+% 100 <= m < 1000
+% instead of 1 <= m < 10.
+% 
+% The 'extended precision' means we have higher accuracy when we apply pgfmath operations to mantisses.
+%
+% The input argument is expected to be a normalized floating point number; the output argument is a non-normalized floating point number (well, normalized to extended precision).
+%
+% The operation is supposed to be very fast.
+\def\pgfmathfloattoextentedprecision#1{%
+	\begingroup
+	\pgfmathfloattoextentedprecision@a{#1}%
+	\pgfmathfloatcreate{\pgfmathfloat@a@S}{\pgfmathresult}{\pgfmathfloat@a@E}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}%
+
+% Does the same work as \pgfmathfloattoextentedprecision, but this one here fills the 
+% registers \pgfmathfloat@a@S and \pgfmathfloat@a@E with the flags and (renormalized) exponent.
+% It destroys the content of \pgfmathfloat@a@Mtok.
+\def\pgfmathfloattoextentedprecision@a#1{%
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\ifnum\pgfmathfloat@a@S<3
+		\advance\pgfmathfloat@a@E by-2\relax% compensate for shift above
+		\expandafter\pgfmathfloattoextentedprecision@@\the\pgfmathfloat@a@Mtok 00\pgfmathfloat@EOI
+	\else
+		\edef\pgfmathresult{#1}%
+	\fi
+}%
+\def\pgfmathfloattoextentedprecision@@#1.#2#3#4\pgfmathfloat@EOI{%
+	\edef\pgfmathresult{#1#2#3.#4}%
+}%
+
+
+% Similar to \pgfmathfloattoextentedprecision@a, this one here fills the '@b' registers.
+\def\pgfmathfloattoextentedprecision@b#1{%
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@b@E
+	\ifnum\pgfmathfloat@b@S<3
+		\advance\pgfmathfloat@b@E by-2\relax
+		\expandafter\pgfmathfloattoextentedprecision@@\the\pgfmathfloat@a@Mtok 00\pgfmathfloat@EOI
+	\else
+		\edef\pgfmathresult{#1}%
+	\fi
+}%
+
+% Addition of two floating point numbers using 8 significant digits.
+\def\pgfmathfloatadd@#1#2{%
+	\begingroup
+	%
+	% renormalize argument to 100 <= m < 1000 for extended accuracy:
+	\pgfmathfloattoextentedprecision@a{#1}%
+	\let\pgfmathfloat@arga=\pgfmathresult
+	%
+	\pgfmathfloattoextentedprecision@b{#2}%
+	\let\pgfmathfloat@argb=\pgfmathresult
+	%
+	\pgfmathfloatcomparisontrue% re-use this boolean here to handle special cases.
+	\ifcase\pgfmathfloat@a@S
+		\edef\pgfmathresult{#2}%
+		\pgfmathfloatcomparisonfalse
+	\or
+	\or
+		\edef\pgfmathfloat@arga{-\pgfmathfloat@arga}%
+	\else
+		\pgfmathfloatcomparisonfalse
+		\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{0.0}{0}%
+	\fi
+	\ifcase\pgfmathfloat@b@S
+		\edef\pgfmathresult{#1}%
+		\pgfmathfloatcomparisonfalse
+	\or
+	\or
+		\edef\pgfmathfloat@argb{-\pgfmathfloat@argb}%
+	\else
+		\pgfmathfloatcomparisonfalse
+		\pgfmathfloatcreate{\the\pgfmathfloat@b@S}{0.0}{0}%
+	\fi
+	\ifpgfmathfloatcomparison
+		% Shift lesser mantisse to fit the larger one:
+		\ifnum\pgfmathfloat@a@E<\pgfmathfloat@b@E
+			\pgfmathfloatadd@shift{\pgfmathfloat@arga}{\pgfmathfloat@a@E}{\pgfmathfloat@b@E}%
+		\else
+			\pgfmathfloatadd@shift{\pgfmathfloat@argb}{\pgfmathfloat@b@E}{\pgfmathfloat@a@E}%
+		\fi
+		% add them!
+		\pgfmathadd@{\pgfmathfloat@arga}{\pgfmathfloat@argb}%
+		% renormalize sum. This is the only part were an expensive routine comes into play:
+		\edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}%
+		\expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}%
+
+
+% #1=mantisse which needs to be shifted (with smaller exponent)
+% #2=smaller exponent
+% #3=larger exponent
+% 
+% ATTENTION: this helper method DESTROYS contents of \pgfmathfloat@a@S.
+\def\pgfmathfloatadd@shift#1#2#3{%
+	\pgf@xa=#1 pt
+	\pgfmathfloat@a@S=#3
+	\advance\pgfmathfloat@a@S by-#2
+	\ifcase\pgfmathfloat@a@S
+	\or
+		\divide\pgf@xa by10\relax
+	\or
+		\divide\pgf@xa by100\relax
+	\or
+		\divide\pgf@xa by1000\relax
+	\or
+		\divide\pgf@xa by10000\relax
+	\or
+		\divide\pgf@xa by10000\relax
+		\divide\pgf@xa by10\relax
+	\or
+		\divide\pgf@xa by10000\relax
+		\divide\pgf@xa by100\relax
+	\or
+		\divide\pgf@xa by10000\relax
+		\divide\pgf@xa by1000\relax
+	\or
+		\divide\pgf@xa by10000\relax
+		\divide\pgf@xa by10000\relax
+	\else
+		\pgf@xa=0pt	
+	\fi
+	#2=#3
+	\edef#1{\pgf@sys@tonumber\pgf@xa}%
+}
+
+\let\pgfmathfloatadd=\pgfmathfloatadd@
+
+
+% Subtracts two floating point numbers.
+\def\pgfmathfloatsubtract@#1#2{%
+	\begingroup
+	\expandafter\pgfmathfloat@decompose@tok#2\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@b@E
+	\ifcase\pgfmathfloat@b@S
+		\edef\pgfmathresult{#1}%
+	\or
+		\pgfmathfloatcreate{2}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@b@E}%
+		\let\pgfmathfloatsub@arg=\pgfmathresult
+		\pgfmathfloatadd@{#1}{\pgfmathfloatsub@arg}%
+	\or
+		\pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@b@E}%
+		\let\pgfmathfloatsub@arg=\pgfmathresult
+		\pgfmathfloatadd@{#1}{\pgfmathfloatsub@arg}%
+	\else
+		\pgfmathfloatcreate{\the\pgfmathfloat@b@S}{0.0}{0}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}%
+
+\let\pgfmathfloatsubtract=\pgfmathfloatsubtract@
+
+% Scales a floating point number #1 with a fixed point number #2 using pgfmathmultiply.
+% 
+% Use this method if #2 is small number.
+\def\pgfmathfloatmultiplyfixed@#1#2{%
+	\begingroup
+	%
+	% renormalize argument to 100 <= m < 1000 for extended accuracy:
+	\pgfmathfloattoextentedprecision@a{#1}%
+	\let\pgfmathfloat@arga=\pgfmathresult
+	%
+	\pgfmathfloatcomparisontrue% re-use this boolean here to handle special cases.
+	\ifcase\pgfmathfloat@a@S
+		\edef\pgfmathresult{#1}%
+		\pgfmathfloatcomparisonfalse
+	\or
+	\or
+		\edef\pgfmathfloat@arga{-\pgfmathfloat@arga}%
+	\else
+		\pgfmathfloatcomparisonfalse
+		\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{0.0}{0}%
+	\fi
+	\ifpgfmathfloatcomparison
+		\pgfmathmultiply@{\pgfmathfloat@arga}{#2}%
+		% renormalize product. This is the only part were an expensive routine comes into play:
+		\edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}%
+		\expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}%
+
+\let\pgfmathfloatmultiplyfixed=\pgfmathfloatmultiplyfixed@
+
+% Converts a composed floating point representation to fixed point.
+%
+% Example:
+% \pgfmathfloattofixed{142e1}
+% -> \pgfmathresult = 42.0
+\def\pgfmathfloattofixed@#1{%
+	\begingroup
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\ifcase\pgfmathfloat@a@S
+		\def\pgfmathresult{0.0}%
+	\or
+		\expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax
+	\or
+		\expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax
+		\edef\pgfmathresult{-\pgfmathresult}%
+	\or\def\pgfmathresult{nan}%
+	\or\def\pgfmathresult{inf}%
+	\or\def\pgfmathresult{-inf}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+\let\pgfmathfloattofixed=\pgfmathfloattofixed@
+
+% Divides or multiplies the input number by 10^#4 using an arithmetic
+% left/right shift.
+%
+% Input:
+% #1 a normalised floating point number.
+% #2 a positive or negative integer number denoting the shift.
+%
+% Example:
+% \pgfmathfloatshift{11e3}{4}%
+% -> pgfmathresult = 11e7
+\def\pgfmathfloatshift@#1#2{%
+	\begingroup
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\expandafter\advance\expandafter\pgfmathfloat@a@E#2\relax
+	\edef\pgfmathresult{\the\pgfmathfloat@a@S\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+\let\pgfmathfloatshift=\pgfmathfloatshift@
+
+% Computes a good guess for log(X.XXXX) where the input number should
+% be between 0 < x < 10.
+%
+% If it is not in this range, the returned value will be bad.
+%
+% For use in the newton implementation of log(x). Please note that we
+% first compute a normalized floating point representation of x, and
+% the mantisse is always between 0 and 10.
+\def\pgfmathlog@smaller@ten@newton@startval#1.#2\to#3{%
+	\ifcase#1
+	\pgfmath@error{pgfmathlog@newton: INTERNAL ERROR: should not happen! 
+		[\#1=0 should have been caught before!]}%
+	\or#3=0.530628pt
+	\or#3=0.993pt
+	\or#3=1.308pt
+	\or#3=1.5pt
+	\or#3=1.71pt
+	\or#3=1.872pt
+	\or#3=2.01pt
+	\or#3=2.145pt
+	\or#3=2.24pt
+	\fi
+}
+
+% FIXME : eliminate \pgfmathlog@invoke@expanded ?
+
+% Expands #2 using \edef and invokes #1 with the resulting string.
+%
+% Example:
+%   \pgfmath@y=7.9pt
+%   \pgfmathlog@invoke@expanded\pgfmathexp@{{\pgf@sys@tonumber{\pgfmath@y}}}%
+% will invoke
+%   \pgfmathexp@{7.9}
+\def\pgfmathlog@invoke@expanded#1#2{%
+	\edef\pgfmath@resulttemp{#2}%
+	\expandafter#1\pgfmath@resulttemp
+}
+
+% This implementation of log(X) is done with a newton method applied to x-exp(y) = 0.
+% The implementation \pgfmathexp is used for exp(y).
+%
+% see \pgfmathlog@
+\def\pgfmathlog@newton#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\pgfmathlog@newton@float{\pgfmathresult}%
+}
+
+% the same as \pgfmathlog@newton, but this one takes a floating point number as input.
+\def\pgfmathlog@newton@float#1{%
+	\begingroup%
+		% compute #1 = M*10^E with normalised mantisse M = [+-]*[1-9].XXXXX
+		\expandafter\pgfmathfloat@decompose#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@M\pgfmathfloat@a@E
+		\let\pgfmathlog@loopcount=\pgfmathfloat@b@S% this counter is not used here... use it as loop counter.
+		%
+		\ifnum\pgfmathfloat@a@S=1
+		% Now, compute log(#1) = log(M) + E*log(10)
+			\expandafter\pgfmathlog@smaller@ten@newton@startval\the\pgfmathfloat@a@M.\to\pgfmathfloat@b@M
+			\pgfmathlog@loopcount=0
+			\loop
+			\ifnum\pgfmathlog@loopcount<3
+				\pgfmathlog@invoke@expanded\pgfmathexp@{{\pgf@sys@tonumber{\pgfmathfloat@b@M}}}%
+				\let\pgfmathlog@tmp=\pgfmathresult
+				\pgfmathlog@invoke@expanded\pgfmathdivide@{{\pgf@sys@tonumber{\pgfmathfloat@a@M}}{\pgfmathlog@tmp}}%
+				\expandafter\pgfmath@ya\pgfmathresult pt
+				\advance\pgfmathfloat@b@M by\pgfmath@ya
+				\advance\pgfmathfloat@b@M by-1pt
+				\advance\pgfmathlog@loopcount by1
+			\repeat
+			\pgfmathfloat@a@M=2.302585pt% = log(10)
+			\multiply\expandafter\pgfmathfloat@a@M\pgfmathfloat@a@E
+			\advance\pgfmathfloat@b@M by\pgfmathfloat@a@M
+			\edef\pgfmathresult{\pgf@sys@tonumber{\pgfmathfloat@b@M}}%
+		\else
+			\let\pgfmathresult=\pgfutil@empty%
+		\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup%
+}
+
+% Computes log(x) into \pgfmathresult.
+%
+% REMARK
+% This method does NOT use TeX Registers to represent the numbers! The
+% computation is COMPLETELY STRING BASED.
+% This allows numbers such at 10000000 or 5.23e-10 to be represented
+% properly, although TeX-registers would produce overflow/underflow
+% errors in these cases. 
+%
+% The natural logarithm is computed using log(X*10^Y) = log(X) + log(10)*Y
+\let\pgfmathlog@=\pgfmathlog@newton
+
+\let\pgfmathlog@float=\pgfmathlog@newton@float
+
+% Public interface method. This is expected to use \pgfmathparse but
+% it DOESN'T do that. \pgfmathparse naturally can't handle numbers
+% which exceed TeX's numerical capabilities. However, exponentials are
+% typically either too large or too small for TeX.
+%
+% @see \pgfmathnormalisedfloatingpoint for how we parse arguments.
+% @see \pgfmathlog@
+\let\pgfmathlog=\pgfmathlog@newton
+
+% Rounds a fixed point number #1 to \pgfmathfloat@round@precision digits precision and returns
+% the result into \pgfmathresult.
+%
+% Any trailing zeros after the period are discarded.
+% See \pgfmathroundtozerofill if you want trailing zeros and fixed
+% width.
+%
+% This method is PURELY text based and can work with arbirtrary
+% precision (well, limited to TeX's stack size and integer size).
+%
+% Examples:
+% \pgfmathroundto{1}
+% -> \pgfmathresult = '1'
+%
+% \pgfmathroundto{19999.9996}
+% -> \pgfmathresult = '20000'
+%
+% Arguments:
+% #1 may be either a number or a macro expanding to a number.
+%
+% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set.
+\def\pgfmathroundto#1{%
+	\pgfmathfloatroundhasperiodtrue
+	\begingroup
+	\pgfmathfloat@fixed@digits@after@periodfalse
+	\pgfmathroundto@impl{#1}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+
+% Overloaded method. 
+%
+% This variant always uses a FIXED number behind the period and fills
+% in zeros if necessary.
+% Examples:
+% \pgfmathroundtozerofill{1}
+% -> \pgfmathresult = '1.00'
+%
+% \pgfmathroundtozerofill{19999.9996}
+% -> \pgfmathresult = '20000.00'
+%
+% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set.
+\def\pgfmathroundtozerofill#1{%
+	\pgfmathfloatroundhasperiodtrue
+	\begingroup
+	\pgfmathfloat@fixed@digits@after@periodtrue
+	\pgfmathroundto@impl{#1}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+\def\pgfmathprintnumber@fixed@styleDEFAULT#1#2#3e#4\relax{%
+	\begingroup
+	\pgfkeysgetvalue{/pgf/number format/set decimal separator}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP
+	\pgfkeysgetvalue{/pgf/number format/set thousands separator}\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP
+	\c@pgf@counta=#4\relax
+	\def\pgfmathresult{}%
+	\ifpgfmathfloatroundhasperiod
+		\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1\pgfmathfloat@EOI
+	\else
+		\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1.#2\pgfmathfloat@EOI{%
+	\ifpgfmathprintnumberskipzeroperiod
+		\def\pgfmathfloat@TMPB{#1}%
+		\ifx\pgfmathfloatparsenumber@tok@ZERO\pgfmathfloat@TMPB
+		\else
+			\def\pgfmathfloat@TMPC{-0}%
+			\ifx\pgfmathfloat@TMPC\pgfmathfloat@TMPB
+				\def\pgfmathresult{-}%
+			\else
+				\def\pgfmathfloat@TMPC{+0}%
+				\ifx\pgfmathfloat@TMPC\pgfmathfloat@TMPB
+					\def\pgfmathresult{+}%
+				\else
+					\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
+				\fi
+			\fi
+		\fi
+	\else
+		\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
+	\fi
+	\begingroup
+	\toks0=\expandafter{\pgfmathresult}%
+	\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP #2}%
+	\xdef\pgfmathfloat@TMPB{\the\toks0\the\toks1}%
+	\endgroup
+	\let\pgfmathresult=\pgfmathfloat@TMPB
+}%
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod{%
+	\ifx\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP\pgfutil@empty
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
+	\else
+		\ifnum\c@pgf@counta<0\relax
+			\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+				\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
+		\else
+			\advance\c@pgf@counta by1% counta:= total number of digits, N.
+			\c@pgf@countb=\c@pgf@counta
+			\divide\c@pgf@countb by3%  countb := N DIV 3
+			\c@pgf@countc=\c@pgf@countb
+			\multiply\c@pgf@countc by3
+			\advance\c@pgf@counta by-\c@pgf@countc% now counta := N MOD 3
+			\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+				\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign
+			}%
+		\fi
+	\fi
+	\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
+}
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign#1{%
+	\def\pgfmathfloat@TMPB{#1}%
+	\ifx\pgfmathfloat@TMPB\pgfmathfloatparsenumber@tok@MINUS
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% FIXME: '-' is enough!?
+		\let\pgfmathfloat@TMPB=\pgfutil@empty
+	\else
+	\ifx\pgfmathfloat@TMPB\pgfmathfloatparsenumber@tok@PLUS
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% FIXME: '+' is enough?
+		\let\pgfmathfloat@TMPB=\pgfutil@empty
+	\fi\fi
+	\ifnum\c@pgf@counta>0
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits\pgfmathfloat@TMPB
+		}%
+	\else
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird\pgfmathfloat@TMPB
+		}%
+	\fi
+	\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
+}
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits#1#2{%
+	\ifcase\c@pgf@counta
+	\or
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#2%
+		}%
+	\or
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2}%
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird%
+		}%
+	\fi
+	\ifnum\c@pgf@countb>0\relax
+		\begingroup
+		\toks0=\expandafter{\pgfmathresult}%
+		\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
+		\xdef\pgfmathfloat@TMPB{\the\toks0\the\toks1}%
+		\endgroup
+		\let\pgfmathresult=\pgfmathfloat@TMPB
+	\fi
+	\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
+}
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#1#2#3{%
+	\ifnum\c@pgf@countb>0\relax
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2#3}%
+		\advance\c@pgf@countb by-1
+		\ifnum\c@pgf@countb>0\relax
+			\begingroup
+			\toks0=\expandafter{\pgfmathresult}%
+			\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
+			\xdef\pgfmathfloat@TMPB{\the\toks0\the\toks1}%
+			\endgroup
+			\let\pgfmathresult=\pgfmathfloat@TMPB
+		\fi
+		\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
+			\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird%
+		}%
+	\else
+		% in thise case, #1#2#3 are expected to be
+		% \pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
+		\def\pgfmathfloat@TMPB{\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI}%
+		\def\pgfmathfloat@TMPC{#1#2#3}%
+		\ifx\pgfmathfloat@TMPC\pgfmathfloat@TMPB
+		\else
+			\pgfmath@error{INTERNAL ERROR in fixed style - The input sequence did not terminate as expected; which indicates a wrong exponent argument provided to \string\pgfmathprintnumber@fixed@style}%
+		\fi
+		\let\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT=\relax
+	\fi
+	\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
+}
+\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI{%
+	\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
+}%
+
+% #1 maybe a macro
+\def\pgfmathprintnumber@fixed@stylePERIOD#1#2#3e#4\relax{%
+	\def\pgfmathresult{#1}%
+}
+
+% #1 maybe a macro
+\def\pgfmathprintnumber@fixed@styleCOMMA#1#2#3e#4\relax{%
+	\ifpgfmathfloatroundhasperiod
+		\expandafter\pgfmathprintnumber@fixed@styleCOMMA@impl#1\pgfmathfloat@EOI
+	\else
+		\def\pgfmathresult{#1}%
+	\fi
+}
+\def\pgfmathprintnumber@fixed@styleCOMMA@impl#1.#2\pgfmathfloat@EOI{\def\pgfmathresult{#1{,}#2}}
+
+% The default style to display fixed point numbers.
+%
+% It does not apply numerics, but it is responsable to typeset the
+% rounded number.
+% It can access the \ifpgfmathfloatroundhasperiod boolean.
+%
+% Arguments:
+% #1#2#3e#4\relax
+
+% Input: 
+% #1  the fixed point number to be displayed (maybe a macro).
+% #2#3e#4:  the (possibly unformatted) floating point representation which belongs to #1.
+%     It is used to determine sign and exponent.
+\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT
+
+
+% Rounds a normalized floating point number to \pgfmathfloat@round@precision 
+% digits precision and writes the result to \pgfmathresult.
+%
+% This method uses \pgfmathroundto for the mantisse.
+%
+% @see pgfmathfloatroundzerofill
+%
+% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set to
+% whether the final mantisse #5 has a period or not.
+\def\pgfmathfloatround#1{%
+	\pgfmathfloatroundhasperiodtrue
+	\begingroup
+	\pgfmathfloat@fixed@digits@after@periodfalse
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\pgfmathfloatround@impl
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+% Overload.
+%
+% This method uses a fixed width for the mantisse and fills in zeros
+% if necessary.
+%
+% This method uses \pgfmathroundtozerofill for the mantisse.
+%
+% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set to
+% whether the final mantisse #5 has a period or not.
+\def\pgfmathfloatroundzerofill#1{%
+	\pgfmathfloatroundhasperiodtrue
+	\begingroup
+	\pgfmathfloat@fixed@digits@after@periodtrue
+	\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+	\pgfmathfloatround@impl
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+\newif\ifpgfmathfloatround@allow@empty@mantisse
+\def\pgfmathfloatround@mantisse@ONE{1.0}%
+
+% #1: sign
+% #2: mantisse
+% #3: exponent
+% #4: CODE to display if the mantisse is drawn.
+% #5: CODE to display if the mantisse is NOT draw.
+% #6: CODE to display the exponent.
+\def\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax#4#5#6{%
+	\expandafter\ifcase#1\relax
+		\pgfmathprintnumber@fixed@style{#2}#1#2e0\relax%
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #4#6}%
+	\or\pgfmathprintnumber@fixed@style{#2}#1#2e0\relax%
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #4#6}%
+	\or\pgfmathprintnumber@fixed@style{#2}#1#2e0\relax%
+		\expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter-\pgfmathresult #4#6}%
+	\or\def\pgfmathresult{NaN}%
+	\or\def\pgfmathresult{\infty}%
+	\or\def\pgfmathresult{-\infty}%
+	\fi
+}
+
+\def\pgfmathfloatrounddisplaystyle@std#1#2e#3\relax{%
+	\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{\cdot}{}{10^{#3}}%
+}
+\def\pgfmathfloatrounddisplaystyle@subscript#1#2e#3\relax{%
+	\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}{_{#3}}%
+}
+\def\pgfmathfloatrounddisplaystyle@e#1#2e#3\relax{%
+	\ifnum#3<0\relax
+		{\count0=#3\relax
+		\multiply\count0 by-1
+		\xdef\pgfmathfloat@TMPB{e{-}\the\count0}%
+		}%
+		\let\pgfmathresult=\pgfmathfloat@TMPB
+	\else
+		\def\pgfmathresult{e{+}#3}%
+	\fi
+	\def\pgfmathfloat@TMPB{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}%
+	\expandafter\pgfmathfloat@TMPB\expandafter{\pgfmathresult}%
+}
+\def\pgfmathfloatrounddisplaystyle@E#1#2e#3\relax{%
+	\ifnum#3<0\relax
+		{\count0=#3\relax
+		\multiply\count0 by-1
+		\xdef\pgfmathfloat@TMPB{E{-}\the\count0}%
+		}%
+		\let\pgfmathresult=\pgfmathfloat@TMPB
+	\else
+		\def\pgfmathresult{E{+}#3}%
+	\fi
+	\def\pgfmathfloat@TMPB{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}%
+	\expandafter\pgfmathfloat@TMPB\expandafter{\pgfmathresult}%
+}
+
+% A macro which takes three arguments, sign, mantisse and exponent and
+% expands to the final TeX-representation for that floating point
+% number.
+%
+% PRECONDITION:
+%   the floating point number has already been rounded properly and
+%   the mantisse has been rounded correcty.
+%
+% #1: SIGN
+% #2: MANTISSE
+% #3: EXPONENT
+\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std
+\newif\ifpgfmathfloat@usezerofill@sci
+\newif\ifpgfmathfloat@usezerofill@fixed
+\newif\ifpgfmathprintnumber@assumemathmode
+
+\pgfkeys{%
+	/pgf/number format/.is family,
+	/pgf/number format,
+	fixed/.code=			\pgfmath@set@number@printer{pgfmathprintnumber@FIXED},
+	%fixed zerofill/.code=	\pgfmath@set@number@printer{pgfmathprintnumber@FIXED@ZEROFILL},
+	%sci zerofill/.code=		\pgfmath@set@number@printer{pgfmathprintnumber@SCI@ZEROFILL},
+	sci/.code=				\pgfmath@set@number@printer{pgfmathprintnumber@SCI},
+	std/.code=				\pgfmath@set@number@printer{pgfmathprintnumber@STD},
+	int detect/.code=		\pgfmath@set@number@printer{pgfmathprintnumber@INT@DETECT},
+	int trunc/.code=		\pgfmath@set@number@printer{pgfmathprintnumber@INT@TRUNC},
+	assume math mode/.is if=pgfmathprintnumber@assumemathmode,
+	assume math mode/.default=true,
+	fixed zerofill/.is if=	pgfmathfloat@usezerofill@fixed,
+	fixed zerofill/.default=true,
+	sci zerofill/.is if=	pgfmathfloat@usezerofill@sci,
+	sci zerofill/.default=true,
+	zerofill/.style=		{/pgf/number format/fixed zerofill=#1,/pgf/number format/sci zerofill=#1},
+	zerofill/.default=		true,
+	precision/.store in=	\pgfmathfloat@round@precision,
+	fixed default/.code=		{\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT},
+	set decimal separator/.initial=,
+	dec sep/.style={/pgf/number format/set decimal separator=#1},
+	set thousands separator/.initial=,
+	1000 sep/.style={/pgf/number format/set thousands separator=#1},
+	use period/.style=		{/pgf/number format/set decimal separator={.},/pgf/number format/set thousands separator={{{,}}}},
+	use comma/.style=		{/pgf/number format/set decimal separator={{{,}}},/pgf/number format/set thousands separator={.}},
+	skip 0./.is if=pgfmathprintnumberskipzeroperiod,
+	skip 0./.default=true,
+	skip 0.= false,
+	use period,
+	sci 10^e/.code=			{\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std},
+	sci 10e/.code=			{\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std},
+	sci e/.code=			{\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@e},
+	sci E/.code=			{\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@E},
+	sci subscript/.code=	{\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@subscript},
+%	sci may skip mantisse/.is if=pgfmathfloatround@allow@empty@mantisse,
+%	sci may skip mantisse/.default=true,
+}
+
+
+
+\def\pgfmathprintnumber@STD#1{%
+	% parse the input:
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfmathprintnumber@STD@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@STD@issci#1#2e#3\relax{%
+	\expandafter\ifnum#1<3
+		\expandafter\ifnum#3>4
+			\pgfmathprintnumber@SCI@issci#1#2e#3\relax%
+		\else
+			\begingroup
+			\c@pgf@counta=\pgfmathfloat@round@precision\relax
+			\divide\c@pgf@counta by-2\relax
+			\ifnum#3<\c@pgf@counta
+				\pgfmathprintnumber@SCI@issci#1#2e#3\relax%
+			\else
+				\pgfmathprintnumber@FIXED@issci#1#2e#3\relax%
+			\fi
+			\pgfmath@smuggleone\pgfmathresult
+			\endgroup
+		\fi
+	\else% nan or inf:
+		\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
+	\fi
+}
+
+
+\def\pgfmathprintnumber@INT@TRUNC#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfmathprintnumber@INT@TRUNC@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@INT@TRUNC@impl#1.#2\relax#3#4e#5\relax{%
+	\pgfmathfloatroundhasperiodfalse
+	\pgfmathprintnumber@fixed@style{#1}#3#4e#5\relax%
+}
+\def\pgfmathprintnumber@INT@TRUNC@issci#1#2e#3\relax{%
+	\ifnum#1<3\relax
+		\pgfmathfloattofixed{#1#2e#3}%
+		\expandafter\pgfmathprintnumber@INT@TRUNC@impl\pgfmathresult\relax#1#2e#3\relax
+	\else
+		\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
+	\fi
+}
+
+
+\def\pgfmathprintnumber@INT@DETECT#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfmathprintnumber@INT@DETECT@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@INT@DETECT@issci#1#2e#3\relax{%
+	\begingroup
+	\ifnum#1<3\relax
+		\pgfmathfloattofixed{#1#2e#3}%
+		\def\pgfmathfloat@round@precision{6}%
+		\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
+		\ifpgfmathfloatroundhasperiod
+			\pgfmathprintnumber@SCI@issci#1#2e#3\relax
+		\else
+			\expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax
+		\fi
+	\else
+		\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+\def\pgfmathprintnumber@FIXED#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@FIXED@issci#1#2e#3\relax{%
+	\begingroup
+	\ifnum#1<3
+		\pgfmathfloattofixed{#1#2e#3}%
+		\ifpgfmathfloat@usezerofill@fixed
+			\expandafter\pgfmathroundtozerofill\expandafter{\pgfmathresult}%
+		\else
+			\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
+		\fi
+		\ifpgfmathfloatroundmayneedrenormalize
+			\pgfmathfloat@a@E=#3\relax
+			\advance\pgfmathfloat@a@E by1
+			\edef\pgfmathfloat@TMPB{\noexpand\pgfmathprintnumber@fixed@style{\pgfmathresult}#1#2e\the\pgfmathfloat@a@E}%
+			\pgfmathfloat@TMPB\relax%
+		\else
+			\expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax%
+		\fi
+	\else% nan or inf:
+		\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+
+\def\pgfmathprintnumber@SCI#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfmathprintnumber@SCI@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@SCI@issci#1#2e#3\relax{%
+	\ifpgfmathfloat@usezerofill@sci
+		\pgfmathfloatroundzerofill{#1#2e#3}%
+	\else
+		\pgfmathfloatround{#1#2e#3}%
+	\fi
+	\expandafter\pgfmathfloatrounddisplaystyle\pgfmathresult\relax
+}
+
+% Prints argument #1 using the current pretty printer environment (all
+% variables in /pgf/number format).
+%
+% You may specify optional arguments with \pgfmathprintnumber[...].
+\def\pgfmathprintnumber{%
+	\pgfutil@ifnextchar[%
+		{\pgfmathprintnumber@OPT}%
+		{\pgfmathprintnumber@noopt}%
+}
+
+\def\pgfmathprintnumber@noopt#1{%
+	\pgfmathprintnumber@{#1}%
+	\ifpgfmathprintnumber@assumemathmode
+	\else
+		\pgfutilensuremath{\pgfmathresult}%
+	\fi
+}%
+\def\pgfmathprintnumber@OPT[#1]#2{%
+	\begingroup
+	\pgfqkeys{/pgf/number format}{#1}%
+	\pgfmathprintnumber@{#2}%
+	\ifpgfmathprintnumber@assumemathmode
+	\else
+		\pgfutilensuremath{\pgfmathresult}%
+	\fi
+	\endgroup
+}%
+
+% As \pgfmathprintnumber, but it produces its output into the second
+% argument.
+\def\pgfmathprintnumberto{%
+	\pgfutil@ifnextchar[%
+		{\pgfmathprintnumberto@OPT}%
+		{\pgfmathprintnumberto@noopt}%
+}
+
+\def\pgfmathprintnumberto@noopt#1#2{%
+	\begingroup
+	\pgfmathprintnumber@{#1}%
+	\ifpgfmathprintnumber@assumemathmode
+		\global\let\pgfmathfloat@TMPB=\pgfmathresult
+	\else
+		\toks0=\expandafter{\pgfmathresult}%
+		\xdef\pgfmathfloat@TMPB{\noexpand\pgfutilensuremath{\the\toks0}}%
+	\fi
+	\endgroup
+	\let#2=\pgfmathfloat@TMPB
+}%
+\def\pgfmathprintnumberto@OPT[#1]#2#3{%
+	\begingroup
+	\pgfqkeys{/pgf/number format}{#1}%
+	\pgfmathprintnumber@{#2}%
+	\ifpgfmathprintnumber@assumemathmode
+		\global\let\pgfmathfloat@TMPB=\pgfmathresult
+	\else
+		\toks0=\expandafter{\pgfmathresult}%
+		\xdef\pgfmathfloat@TMPB{\noexpand\pgfutilensuremath{\the\toks0}}%
+	\fi
+	\endgroup
+	\let#3=\pgfmathfloat@TMPB
+}%
+	
+
+% Changes the current number pretty printer to #1.
+%
+% #1 is the macro base name for the pretty print routine, without the
+% leading '\'.
+\def\pgfmath@set@number@printer#1{%
+	\expandafter\let\expandafter\pgfmathprintnumber@\csname #1\endcsname
+	\expandafter\let\expandafter\pgfmathprintnumber@issci\csname #1@issci\endcsname
+}
+
+\pgfmath@set@number@printer{pgfmathprintnumber@STD}
+%\pgfmath@set@number@printer{pgfmathprintnumber@FIXED}
+%\pgfmath@set@number@printer{pgfmathprintnumber@FIXED@ZEROFILL}
+%\pgfmath@set@number@printer{pgfmathprintnumber@SCI@ZEROFILL}
+%\pgfmath@set@number@printer{pgfmathprintnumber@SCI}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 
+% IMPL
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% equals only itsself when compared with \ifx:
+\def\pgfmathfloat@EOI{\pgfmathfloat@EOI}%
+
+% Re-use counters internally.
+%
+% They are always grouped and only used inside of the rounding
+% routines.
+\let\c@pgfmathroundto@prec=\pgfmathfloat@b@S% ATTENTION: DOUBLE-USED REGISTERS!
+\let\c@pgfmathroundto@offsetbehindperiod=\pgfmathfloat@b@E
+\newcount\c@pgfmathroundto@lastzeros
+
+\newif\ifpgfmathround@impl@PREPERIOD@is@negative@zero
+
+% PRECONDITION:
+%  	\ifpgfmathfloatroundhasperiod=\iftrue  holds outside of the
+%  	current TeX group.
+%
+% POSTCONDITION:
+%   \ifpgfmathfloatroundhasperiod will be set correctly AFTER the
+%   current TeX group.
+%   \ifpgfmathfloatroundmayneedrenormalize will be set globally
+\def\pgfmathroundto@impl#1{%
+	\global\pgfmathfloatroundmayneedrenormalizefalse
+	\pgfmathfloat@tmptoks={}%
+	\let\pgfmathround@next=\pgfutil@empty
+	\let\pgfmathround@cur=\pgfutil@empty
+	\let\pgfmathresult=\pgfutil@empty
+	\edef\pgfmathround@input{#1}%
+	\expandafter\c@pgfmathroundto@prec\pgfmathfloat@round@precision\relax
+	\c@pgfmathroundto@lastzeros=0
+	\c@pgfmathroundto@offsetbehindperiod=-1 % means: no period found so far
+	\pgfmathround@impl@PREPERIOD@is@negative@zerotrue
+	\expandafter\pgfmathroundto@impl@ITERATE@NODOT@firstcall\pgfmathround@input\pgfmathfloat@EOI
+}
+
+% \pgfmathroundto implementation in WORDS:
+%
+% coarse idea: 
+%    1. collect all digits/sign BEFORE the first period in REVERSE order
+%    2. then, collect UP TO \prec digits after the period in REVERSE order
+% Steps 1. and 2. lead to the digit [sign] sequence
+%    "x_{-p} x_{-p+1} ... x_{-2} x_{-1} '.' x_0 ... x_r"
+% where 'r' is the total number of digits. The integer 'p' denotes the
+% ACTUALLY collected number of digits behind the period.
+%
+% Let 'k' be the desired precision.
+%
+% Please note that pgfmathroundto rounds the mantisse, that means |abs(x)|.
+%
+% There are exactly TWO cases:
+% 1. The case with p<=k and x_{-p-1} = end of input.
+% 2. The case with p=k and x_{-p-1} is a further, next character.
+%
+% Then, for case 1.):
+% 	discard any unused zeros at the tail of our number (possibly
+% 	including the period)
+%
+% and in case 2.)
+%   if NEXT DIGIT < 5:
+%       do exactly the same as in case 1.) above and discard any
+%       following digits.
+%   else
+%   	let q := -p
+%   	while(x_q = 9 and q<=r )
+%   		if q>=0
+%   			set x_q = '0'
+%   		else
+%   			discard digit x_q='9'
+%   		fi
+%   		++q
+%   		if q=0
+%   			discard the period 
+%   		fi
+%   	end while
+%   	if q = r+1
+%   		insert a '1'
+%   	else
+%   		set x_q = x_q + 1
+%   	fi
+%   fi
+%
+% All these loops have been implemented in spaghetti-code below.
+% Sorry, I fear its hard to understand. In principle, everything is
+% realised using more or less finite state machines (with some number
+% counting logic).
+%
+% Some comments:
+%   - The token register \pgfmathfloat@tmptoks is used to accumulate the REVERSED input number.
+%	- \pgfmathfloat@EOI always denotes 'END OF INPUT'.
+%	- in the second stage, we need to reverse \pgfmathfloat@tmptoks.
+%	  This is -again- done with \pgfmathfloat@tmptoks.
+
+\def\pgfmathroundto@impl@discard@period#1.#2\pgfmathfloat@EOI{%
+	\pgfmathfloatroundhasperiodfalse
+	\aftergroup\pgfmathfloatroundhasperiodfalse
+	\def\pgfmathresult{#1}%
+}
+
+\def\pgfmathroundto@impl@gobble@rest@and@start#1\pgfmathfloat@EOI{%
+	\pgfmathroundto@impl@start
+}
+\def\pgfmathroundto@impl@gobble@and@start\pgfmathfloat@EOI{%
+	\pgfmathroundto@impl@start
+}
+\def\pgfmathroundto@impl@gobble\pgfmathfloat@EOI{}%
+\def\pgfmathroundto@impl@gobble@rest#1\pgfmathfloat@EOI{}%
+
+% This method will be invoked as soon as the first step, the reverse
+% collection of up to PREC digits after the period, has finished.
+\def\pgfmathroundto@impl@start{%
+	\ifx\pgfmathround@next\pgfutil@empty
+		\ifnum\c@pgfmathroundto@offsetbehindperiod<0
+			% no period found.
+			\ifpgfmathfloat@fixed@digits@after@period
+				\ifnum\c@pgfmathroundto@prec=0\relax
+					\pgfmathfloatroundhasperiodfalse
+					\aftergroup\pgfmathfloatroundhasperiodfalse
+					\edef\pgfmathresult{\pgfmathround@input}%
+				\else
+					\pgfmathfloat@tmptoks=\expandafter{\pgfmathround@input.}%
+					\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
+					\pgfmathroundto@impl@append@zeros
+					\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
+				\fi
+			\else
+				\pgfmathfloatroundhasperiodfalse
+				\aftergroup\pgfmathfloatroundhasperiodfalse
+				\edef\pgfmathresult{\pgfmathround@input}%
+			\fi
+		\else
+			%\ifnum\c@pgfmathroundto@offsetbehindperiod>\c@pgfmathroundto@prec
+			%	\pgfmath@error{Internal logic error in pgfmathroundto at [I] - should not have happened!?}%
+			%\fi
+			\pgfmathroundto@impl@finish@with@truncation
+		\fi
+	\else
+		%\ifnum\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
+		%\else
+		%	\pgfmath@error{Internal logic error in pgfmathroundto at [II] - should not have happened!? I have offsetbehindperiod=\the\c@pgfmathroundto@offsetbehindperiod and prec = \the\c@pgfmathroundto@prec}%
+		%\fi
+		\expandafter\ifnum\pgfmathround@next<5\relax
+			\pgfmathroundto@impl@finish@with@truncation
+		\else
+			\multiply\c@pgfmathroundto@offsetbehindperiod by-1
+			\expandafter\pgfmathroundto@impl@ADD@ONE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+		\fi
+	\fi
+}
+			
+% takes the current input and decides whether trailing zeros shall be
+% discarded or more zeros need to be filled in.
+\def\pgfmathroundto@impl@finish@with@truncation{%
+	\ifpgfmathfloat@fixed@digits@after@period
+		\expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+		\ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod
+			\ifpgfmathround@impl@PREPERIOD@is@negative@zero
+				% write '0.0000' instead of '-0.0000':
+				\expandafter\pgfmathroundto@impl@discard@minus\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+			\fi
+		\fi
+		\ifnum\c@pgfmathroundto@prec=0\relax
+			\expandafter\pgfmathroundto@impl@discard@period\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+		\else
+			\advance\c@pgfmathroundto@prec by-\c@pgfmathroundto@offsetbehindperiod
+			\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
+			\pgfmathroundto@impl@append@zeros
+			\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
+		\fi
+	\else
+		\pgfmathroundto@impl@discard@suffix@zeros
+	\fi
+}
+
+\def\pgfmathroundto@impl@discard@minus-#1\pgfmathfloat@EOI{\pgfmathfloat@tmptoks={#1}}%
+
+% appends \c@pgfmathroundto@offsetbehindperiod zeros at the end of \pgfmathfloat@tmptoks.
+\def\pgfmathroundto@impl@append@zeros{%
+	\ifnum\c@pgfmathroundto@offsetbehindperiod>0
+		\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
+		\advance\c@pgfmathroundto@offsetbehindperiod by-1
+		\pgfmathroundto@impl@append@zeros
+	\fi
+}
+
+\def\pgfmathroundto@impl@ADD@ONE{%
+	\pgfmathfloat@tmptoks={}% no longer needed because its old value will be read from input
+	\pgfmathroundto@impl@ADD@ONE@ITERATE
+}
+\def\pgfmathroundto@impl@ADD@ONE@ITERATE{%
+	\pgfutil@ifnextchar\pgfmathfloat@EOI{%
+		\global\pgfmathfloatroundmayneedrenormalizetrue
+		\edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}%
+		\pgfmathroundto@impl@gobble
+	}{%
+		\pgfutil@ifnextchar.{%
+			\ifnum\c@pgfmathroundto@prec=0
+				% silently discard period in special case precision=0
+				\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}%
+			\else
+				\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT}%
+			\fi
+			\pgfmathround@nextcmd
+		}{%
+			\pgfutil@ifnextchar+{%
+				\global\pgfmathfloatroundmayneedrenormalizetrue
+				\edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}%
+				\pgfmathroundto@impl@gobble@rest
+			}{%
+				\pgfutil@ifnextchar-{%
+					\global\pgfmathfloatroundmayneedrenormalizetrue
+					\edef\pgfmathresult{-1\the\pgfmathfloat@tmptoks}%
+					\pgfmathroundto@impl@gobble@rest
+				}{%
+					\pgfmathroundto@impl@ADD@ONE@NEXT
+				}%
+			}%
+		}%
+	}%
+}
+
+\def\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot.{%
+	\pgfmathfloatroundhasperiodfalse
+	\aftergroup\pgfmathfloatroundhasperiodfalse
+	\pgfmathroundto@impl@ADD@ONE@ITERATE
+}
+
+\def\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT#1{%
+	\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
+	\pgfmathroundto@impl@ADD@ONE@ITERATE
+}
+\def\pgfmathroundto@impl@ADD@ONE@NEXT#1{%
+	\ifnum#1=9
+		\ifnum\c@pgfmathroundto@offsetbehindperiod<0
+			\ifpgfmathfloat@fixed@digits@after@period
+				\pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}%
+			\else
+				% silently DROP digit
+			\fi
+		\else
+			\pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}%
+		\fi
+		\advance\c@pgfmathroundto@offsetbehindperiod by1
+		\ifnum\c@pgfmathroundto@offsetbehindperiod=0
+			\ifpgfmathfloat@fixed@digits@after@period
+				\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}%
+			\else
+				\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}%
+			\fi
+		\else
+			\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}%
+		\fi
+	\else
+		% re-use this counter:
+		\c@pgfmathroundto@lastzeros=#1
+		\advance\c@pgfmathroundto@lastzeros by1
+		\edef\pgfmathresult{\the\c@pgfmathroundto@lastzeros\the\pgfmathfloat@tmptoks}%
+		\pgfmathfloat@tmptoks=\expandafter{\pgfmathresult}%
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE@ITERATE}%
+	\fi
+	\pgfmathround@nextcmd
+}
+
+
+\def\pgfmathroundto@impl@discard@suffix@zeros{%
+	\ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod
+		\ifpgfmathround@impl@PREPERIOD@is@negative@zero
+			\pgfmathfloatroundhasperiodfalse
+			\aftergroup\pgfmathfloatroundhasperiodfalse
+			\def\pgfmathresult{0}% write '0' instead of '-0'
+		\else
+			\expandafter\pgfmathroundto@impl@discard@period\pgfmathround@input\pgfmathfloat@EOI
+		\fi
+	\else
+		\ifnum\c@pgfmathroundto@lastzeros=0
+			\expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+		\else
+			\expandafter\pgfmathroundto@impl@discard@suffix@zeros@ITERATE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
+		\fi
+	\fi
+}
+
+% PRECONDITION: 
+%    \c@pgfmathroundto@lastzeros > 0
+\def\pgfmathroundto@impl@discard@suffix@zeros@ITERATE#1{%
+	\advance\c@pgfmathroundto@lastzeros by-1
+	\ifnum\c@pgfmathroundto@lastzeros=0
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE}%
+	\else
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@discard@suffix@zeros@ITERATE}%
+	\fi
+	\pgfmathround@nextcmd
+}
+
+% Usage:
+% \pgfmathroundto@impl@REVERSE#1\pgfmathfloat@EOI
+% -> writes #1 reversed into \pgfmathfloat@tmptoks
+\def\pgfmathroundto@impl@REVERSE{%
+	\pgfmathfloat@tmptoks={}%
+	\pgfmathroundto@impl@REVERSE@ITERATE
+}
+
+\def\pgfmathroundto@impl@REVERSE@ITERATE{%
+	\pgfutil@ifnextchar\pgfmathfloat@EOI{%
+		\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
+		\pgfmathroundto@impl@gobble
+	}{%
+		\pgfmathroundto@impl@REVERSE@NEXT
+	}%
+}
+
+\def\pgfmathroundto@impl@REVERSE@NEXT#1{%
+	\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
+	\pgfmathroundto@impl@REVERSE@ITERATE
+}
+
+\def\pgfmathroundto@impl@BEGIN@DOT.{%
+	\pgfmathfloat@tmptoks=\expandafter{\expandafter.\the\pgfmathfloat@tmptoks}%
+	\c@pgfmathroundto@offsetbehindperiod=0
+	\pgfmathroundto@impl@ITERATE@DOT
+}
+\def\pgfmathroundto@impl@ITERATE@DOT{%
+	\pgfutil@ifnextchar\pgfmathfloat@EOI{%
+		% finished.
+		\pgfmathroundto@impl@gobble@and@start
+	}{%
+		\pgfmathroundto@impl@NEXT@DOT
+	}%
+}
+\def\pgfmathroundto@impl@NEXT@DOT#1{%
+	\ifnum\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
+		\def\pgfmathround@next{#1}%
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@gobble@rest@and@start}%
+	\else
+		\advance\c@pgfmathroundto@offsetbehindperiod by1
+		\ifnum#1=0
+			\advance\c@pgfmathroundto@lastzeros by1
+		\else
+			\c@pgfmathroundto@lastzeros=0
+		\fi
+		\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@DOT}%
+	\fi
+	\pgfmathround@nextcmd
+}%
+
+% in contrast to pgfmathroundto@impl@ITERATE@NODOT, this method here
+% checks also for signs
+\def\pgfmathroundto@impl@ITERATE@NODOT@firstcall#1{%
+	\def\pgfmathround@cur{#1}%
+	\ifx\pgfmathround@cur\pgfmathfloat@EOI
+		\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}%
+	\else
+		\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD
+			\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
+			\def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}%
+		\else
+			\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@MINUS
+			\else
+				\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
+			\fi
+			\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
+			\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}%
+		\fi
+	\fi
+	\pgfmathround@nextcmd
+}
+
+\def\pgfmathroundto@impl@ITERATE@NODOT#1{%
+	\def\pgfmathround@cur{#1}%
+	\ifx\pgfmathround@cur\pgfmathfloat@EOI
+		\def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}%
+	\else
+		\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD
+			\def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}%
+		\else
+			\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@ZERO
+			\else
+				\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
+			\fi
+			\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
+			\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}%
+		\fi
+	\fi
+	\pgfmathround@nextcmd
+}
+
+%--------------------------------------------
+% END of pgfmathroundto implementation.
+%--------------------------------------------
+
+
+% flags, mantisse and exponent has already been stored into
+% \pgfmathfloat@a@* [using ...@Mtok]
+%
+% PRECONDITION:
+%   \ifpgfmathfloatroundhasperiod = \iftrue outside of the current
+%   group
+%
+% POSTCONDITION:
+%   \ifpgfmathfloatroundhasperiod will be set after the current TeX
+%   group.
+\def\pgfmathfloatround@impl{%
+	\expandafter\pgfmathroundto@impl\expandafter{\the\pgfmathfloat@a@Mtok}%
+	\ifpgfmathfloatroundmayneedrenormalize
+		\ifpgfmathfloatroundhasperiod
+			\expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult\pgfmathfloat@EOI%
+		\else
+			\expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult.\pgfmathfloat@EOI%
+		\fi
+		\advance\pgfmathfloat@a@E by1
+	\fi
+	\edef\pgfmathresult{\the\pgfmathfloat@a@S\pgfmathresult e\the\pgfmathfloat@a@E}%
+}
+
+\def\pgfmathfloatround@impl@renormalize#1#2.#3\pgfmathfloat@EOI{%
+	\pgfmathroundto@impl{#1.#2#3}%
+}
+
+
+
+
+
+% ATTENTION: this thing REQUIRES a period in the mantisse!
+% collects everything into \pgfmathresult
+\def\pgfmathfloattofixed@impl#1.#2\relax{%
+	\ifnum\pgfmathfloat@a@E<0
+		\pgfmathfloat@a@Mtok={0.}%
+		\loop
+		\ifnum\pgfmathfloat@a@E<-1
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}%
+			\advance\pgfmathfloat@a@E by1
+		\repeat
+		\def\pgfmathfloat@TMPB{#2}%
+		\def\pgfmathfloat@TMPC{0}%
+		\ifx\pgfmathfloat@TMPB\pgfmathfloat@TMPC
+			\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1}%
+		\else
+			\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1#2}%
+		\fi
+	\else
+		\ifnum\pgfmathfloat@a@E=0%
+			\edef\pgfmathresult{#1.#2}%
+		\else
+			\pgfmathfloat@a@Mtok={#1}%
+			\pgfmathfloattofixed@impl@collectmantisse#2\count\pgfmathfloat@a@E
+			\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok}%
+		\fi
+	\fi
+}
+
+\def\pgfmathfloattofixed@impl@collectmantisse#1#2\count#3{%
+	\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok #1}%
+	\advance\pgfmathfloat@a@E by-1%
+	\def\pgfmathfloat@TMPB{#2}%
+	\ifx\pgfmathfloat@TMPB\pgfutil@empty
+		\loop
+		\ifnum\pgfmathfloat@a@E>0%
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}%
+			\advance\pgfmathfloat@a@E by-1%
+		\repeat
+		\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .0}%
+	\else
+		\ifnum\pgfmathfloat@a@E=0
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .#2}%
+		\else
+			\pgfmathfloattofixed@impl@collectmantisse#2\count#3%
+		\fi
+	\fi
+}
+
+
+% ============================================
+%
+%
+% \pgfmathfloatparsenumber implementation
+%
+%
+% ============================================
+
+
+% accepted parser tokens:
+\def\pgfmathfloatparsenumber@tok@ONE{1}
+\def\pgfmathfloatparsenumber@tok@TWO{2}
+\def\pgfmathfloatparsenumber@tok@THREE{3}
+\def\pgfmathfloatparsenumber@tok@FOUR{4}
+\def\pgfmathfloatparsenumber@tok@FIVE{5}
+\def\pgfmathfloatparsenumber@tok@SIX{6}
+\def\pgfmathfloatparsenumber@tok@SEVEN{7}
+\def\pgfmathfloatparsenumber@tok@EIGHT{8}
+\def\pgfmathfloatparsenumber@tok@NINE{9}
+\def\pgfmathfloatparsenumber@tok@ZERO{0}
+\def\pgfmathfloatparsenumber@tok@e{e}
+\def\pgfmathfloatparsenumber@tok@E{E}
+\def\pgfmathfloatparsenumber@tok@PLUS{+}
+\def\pgfmathfloatparsenumber@tok@MINUS{-}
+\def\pgfmathfloatparsenumber@tok@n{n}
+\def\pgfmathfloatparsenumber@tok@N{N}
+\def\pgfmathfloatparsenumber@tok@i{i}
+\def\pgfmathfloatparsenumber@tok@I{I}
+\def\pgfmathfloatparsenumber@tok@PERIOD{.}
+
+\newif\ifpgfmathfloatparsenumberpendingperiod
+
+% Starts a finite-start-machine parser to read a number.
+%
+% It assigns \pgfmathfloat@a@S, \pgfmathfloat@a@Mtok, \pgfmathfloat@a@E.
+\def\pgfmathfloatparsenumber@impl#1{%
+	\pgfmathfloatparsenumberpendingperiodfalse
+	\pgfmathfloat@tmptoks={}% this register is used to collect PENDING ZEROS
+	\pgfmathfloat@a@E=0
+	% start parsing: check for sign:
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@PLUS
+		\pgfmathfloat@a@S=1\relax%
+		\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@init}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@MINUS
+			\pgfmathfloat@a@S=2\relax%
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@init}%
+		\else
+			\pgfmathfloat@a@S=1\relax%
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@init#1}%
+		\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@sanitize@digit{%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ONE
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@TWO
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@THREE
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@FOUR
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@FIVE
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@SIX
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@SEVEN
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@EIGHT
+	\else
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@NINE
+	\else
+		\def\pgfmathfloatparsenumber@NEXT{\expandafter\pgfmathfloatparsenumber@impl@error\pgfmathfloatparsenumber@curtok}%
+	\fi\fi\fi\fi\fi\fi\fi\fi\fi
+}
+
+% FROM: checksign.
+%
+\def\pgfmathfloatparsenumber@impl@init#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@n
+		\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readnan}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@i
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readinf}%
+		\else
+			\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+				\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@leadingzero}%
+			\else
+				\def\pgfmathfloatparsenumber@NEXT{%
+					\pgfmathfloat@a@Mtok={#1}%
+					\pgfmathfloatparsenumberpendingperiodtrue
+					\pgfmathfloatparsenumber@impl@positiveexp}%
+				\pgfmathfloatparsenumber@sanitize@digit
+			\fi
+		\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@impl@error#1\pgfmathfloat@EOI{%
+	\begingroup
+	\pgfmathfloat@a@Mtok={#1}%
+	\pgfmath@error{Could not read input number, sorry. The unreadable part was near '\the\pgfmathfloat@a@Mtok'.}%
+	\endgroup
+}%
+
+\def\pgfmathfloatparsenumber@impl@finish#1\pgfmathfloat@EOI{}
+
+\def\pgfmathfloatparsenumber@impl@readnan an{%
+	\pgfmathfloat@a@S=3\relax%
+	\pgfmathfloat@a@Mtok={nan}%
+	\pgfmathfloat@a@E=0%
+	\pgfmathfloatparsenumber@impl@finish
+}
+\def\pgfmathfloatparsenumber@impl@readinf nf{%
+	\ifnum\pgfmathfloat@a@S=1
+		\pgfmathfloat@a@S=4\relax%
+		\pgfmathfloat@a@Mtok={inf}%
+	\else
+		\pgfmathfloat@a@S=5\relax%
+		\pgfmathfloat@a@Mtok={-inf}%
+	\fi
+	\pgfmathfloat@a@E=0%
+	\pgfmathfloatparsenumber@impl@finish
+}
+\def\pgfmathfloatparsenumber@impl@leadingzero#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloatparsenumber@impl@leadingzero}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@PERIOD
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@E=-1
+				\pgfmathfloatparsenumber@impl@leadingzero@foundperiod}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloat@a@Mtok={#1}%
+			\pgfmathfloatparsenumberpendingperiodtrue
+			\pgfmathfloatparsenumber@impl@positiveexp}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+		\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@impl@leadingzero@foundperiod#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\advance\pgfmathfloat@a@E by-1
+			\pgfmathfloatparsenumber@impl@leadingzero@foundperiod}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{%
+				\pgfmathfloat@a@S=0\relax%
+				\pgfmathfloat@a@Mtok={0.0}%
+				\pgfmathfloat@a@E=0%
+				}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloat@a@Mtok={#1}%
+			\pgfmathfloatparsenumberpendingperiodtrue
+			\pgfmathfloatparsenumber@impl@finish@number@after@period}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+
+\def\pgfmathfloatparsenumber@impl@positiveexp#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\advance\pgfmathfloat@a@E by1
+			\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
+			\pgfmathfloatparsenumber@impl@pendingzeros@positiveexp}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@PERIOD
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@finish@number@after@period}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\advance\pgfmathfloat@a@E by1
+			\ifpgfmathfloatparsenumberpendingperiod
+				\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
+				\pgfmathfloatparsenumberpendingperiodfalse
+			\fi
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
+			\pgfmathfloatparsenumber@impl@positiveexp}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+		\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@impl@readexponent#1\pgfmathfloat@EOI{%
+	\advance\pgfmathfloat@a@E by#1\relax
+}
+
+\def\pgfmathfloatparsenumber@impl@pendingzeros@positiveexp#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
+			\advance\pgfmathfloat@a@E by1
+			\pgfmathfloatparsenumber@impl@pendingzeros@positiveexp}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@PERIOD
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@finish@number@after@period}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\advance\pgfmathfloat@a@E by1
+			\ifpgfmathfloatparsenumberpendingperiod
+				\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
+				\pgfmathfloatparsenumberpendingperiodfalse
+			\fi
+			\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
+			\pgfmathfloat@tmptoks={}%
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
+			\pgfmathfloatparsenumber@impl@positiveexp}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+		\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@impl@finish@number@after@period#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
+			\pgfmathfloatparsenumber@impl@pendingzeros}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\ifpgfmathfloatparsenumberpendingperiod
+				\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
+				\pgfmathfloatparsenumberpendingperiodfalse
+			\fi
+			\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
+			\pgfmathfloat@tmptoks={}%
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
+			\pgfmathfloatparsenumber@impl@finish@number@after@period}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+\def\pgfmathfloatparsenumber@impl@pendingzeros#1{%
+	\def\pgfmathfloatparsenumber@curtok{#1}%
+	\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@ZERO
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
+			\pgfmathfloatparsenumber@impl@pendingzeros}%
+	\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@e
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloatparsenumber@tok@E
+			\def\pgfmathfloatparsenumber@NEXT{\pgfmathfloatparsenumber@impl@readexponent}%
+		\else
+		\ifx\pgfmathfloatparsenumber@curtok\pgfmathfloat@EOI
+			\def\pgfmathfloatparsenumber@NEXT{}%
+		\else
+		\def\pgfmathfloatparsenumber@NEXT{%
+			\ifpgfmathfloatparsenumberpendingperiod
+				\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
+				\pgfmathfloatparsenumberpendingperiodfalse
+			\fi
+			\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
+			\pgfmathfloat@tmptoks={}%
+			\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
+			\pgfmathfloatparsenumber@impl@finish@number@after@period}%
+		\pgfmathfloatparsenumber@sanitize@digit
+		\fi\fi\fi
+	\fi
+	\pgfmathfloatparsenumber@NEXT
+}
+
+
+
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.code.tex
new file mode 100644
index 00000000000..ed8e8e611ec
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.code.tex
@@ -0,0 +1,5918 @@
+%--------------------------------------------
+%
+% Package pgfplots
+%
+% Provides a user-friendly interface to create function plots (normal
+% plots, semi-logplots and double-logplots).
+% 
+% It is based on Till Tantau's PGF package.
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+
+\input pgfplotsliststructure.code.tex
+\input pgfplotsarray.code.tex
+\input pgfplotstable.code.tex
+\input pgfplotsoldpgfsupp_loader.code.tex
+\input pgfplots.stackedplots.code.tex
+
+\usetikzlibrary{decorations,decorations.pathmorphing,decorations.pathreplacing}
+
+% FIXME: reduce number of variables!
+\newtoks\pgfplots@toka
+
+\newcount\pgfplots@ticknum
+\newif\ifpgfplots@xislinear
+\newif\ifpgfplots@yislinear
+\newcount\pgfplots@numplots
+\newdimen\pgfplots@xcoordminTEX
+\newdimen\pgfplots@xcoordmaxTEX
+\newdimen\pgfplots@ycoordminTEX
+\newdimen\pgfplots@ycoordmaxTEX
+\newdimen\pgfplots@tmpa
+\newdimen\pgfplots@tmpb
+\newif\ifpgfplots@warn@for@filter@discards
+\newif\ifpgfplots@isuniformtick
+\newif\ifpgfplots@addplot@table@from@macro
+\newif\ifpgfplots@clip@limits
+\newif\ifpgfplots@enlargelimits
+\newif\ifpgfplots@enlargelimits@rel@thresh
+\newif\ifpgfplots@enlargelimits@auto
+\newif\ifpgfplots@tickshow
+\newif\ifpgfplots@xminorticks
+\newif\ifpgfplots@xmajorticks
+\newif\ifpgfplots@yminorticks
+\newif\ifpgfplots@ymajorticks
+\newif\ifpgfplots@xminorgrids
+\newif\ifpgfplots@xmajorgrids
+\newif\ifpgfplots@yminorgrids
+\newif\ifpgfplots@ymajorgrids
+\newif\ifpgfplots@scaled@ticks
+\newif\ifpgfplots@identify@log@minor@tick@pos
+\newif\ifpgfplots@disablelogfilter
+\newif\ifpgfplots@disabledatascaling
+\newif\ifpgfplots@hide
+\newif\ifpgfplots@is@old@list@format
+\newif\ifpgfplots@errorbars@enabled
+\newif\ifpgfplots@scale@only@axis
+\newif\ifpgfplots@xticklabel@interval
+\newif\ifpgfplots@yticklabel@interval
+\newif\ifpgfplots@stacked@x
+\newif\ifpgfplots@stackedmode
+\newif\ifpgfplots@stacked@reverse
+\newif\ifpgfplots@stacked@plus
+\let\pgfplots@TMP=\pgfutil@empty
+\let\pgfplots@TMPB=\pgfutil@empty
+\let\pgfplots@TMPC=\pgfutil@empty
+\let\pgfnodepartimagebox=\pgfnodeparttextbox
+
+\newif\ifpgfplots@collect@firstplot@astick
+
+\def\pgfplots@errorbars@xdirection{0}% pre-init, see below
+\def\pgfplots@errorbars@ydirection{0}%
+
+\def\pgfplots@error#1{\PackageError{pgfplots}{#1}{}}%
+\def\pgfplots@warning#1{\pgfplots@message{#1}}%
+\def\pgfplots@message#1{%
+	\immediate\write16{#1}%
+}%
+
+\def\pgfplots@leftover{}
+\def\pgfplots@rightover{}
+\def\axisdefaultwidth{240pt}
+\def\axisdefaultheight{207pt}
+
+
+% Assigns list contents #2 to a list macro #1.
+%
+% The list contents may be provided in one of two formats:
+% a) in the (deprecated) list format 'first\\second\\thirst\\'
+% or
+% b) in the PGF foreach list format 'first,second,third'.
+\def\pgfplots@assign@list#1#2{%
+	\def\pgfplots@TMP{#2}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+		\pgfplotslistnewempty#1%
+	\else
+		\pgfplots@check@backwards@compatible@list@format #2\\\pgfplots@EOI
+		\ifpgfplots@is@old@list@format
+			\pgfplotslistnew#1{#2}%
+		\else
+			\pgfplots@foreach@to@list{#2}\to#1
+		\fi
+	\fi
+}%
+
+\def\pgfplots@EOI{\pgfplots@EOI}%
+
+% Sets the boolean \ifpgfplots@is@old@list@format  to true if and only
+% if the input is a list in the format '{first\\second\\}'.
+%
+% This format is deprecated, but is still provided for backwards
+% compatibility.
+%
+% Usage:
+% \pgfplots@check@backwards@compatible@list@format <argument>'\\'\pgfplots@EOI
+% you NEED to append '\\\pgfplots@EOI' at the end.
+\def\pgfplots@check@backwards@compatible@list@format#1\\#2\pgfplots@EOI{%
+	\def\pgfplots@TMP{#2}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+		\pgfplots@is@old@list@formatfalse
+	\else
+		\pgfplots@is@old@list@formattrue
+	\fi
+}%
+
+
+
+% Creates a named plot cycle list.
+%
+% #1:  the name of the final list. Can be used in 'cycle list name'
+% #2:  the list entries. You can use either a comma-separated list or
+%      a '\\'-terminated list. The latter case also requires '\\'
+%      AFTER the last entry.
+\def\pgfcreateplotcyclelist#1#2{\pgfplots@assign@list#1{#2}}
+
+\pgfcreateplotcyclelist{\blackwhiteplotspeclist}{%
+	mark options={fill=gray},mark=*\\%
+	mark options={fill=gray},mark=square*\\%
+	mark options={fill=gray},mark=otimes*\\%
+	mark=star\\%
+	mark options={fill=gray},mark=diamond*\\%
+	densely dashed,mark options={solid,fill=gray},mark=*\\%
+	densely dashed,mark options={solid,fill=gray},mark=square*\\%
+	densely dashed,mark options={solid,fill=gray},mark=otimes*\\%
+	densely dashed,mark options={solid},mark=star\\%
+	densely dashed,mark options={solid,fill=gray},mark=diamond*\\%
+}
+\pgfcreateplotcyclelist{\coloredplotspeclist}{%
+	blue,mark options={fill=blue!80!black},mark=*\\%
+	red,mark options={fill=red!80!black},mark=square*\\%
+	brown!60!black,mark options={fill=brown!80!black},mark=otimes*\\%
+	black,mark=star\\%
+	blue,mark options={fill=blue!80!black},mark=diamond*\\%
+	red,densely dashed,mark options={solid,fill=red!80!black},mark=*\\%
+	brown!60!black,densely dashed,mark options={solid,fill=brown!80!black},mark=square*\\%
+	black,densely dashed,mark options={solid,fill=gray},mark=otimes*\\%
+	blue,densely dashed,mark=star,mark options=solid\\%
+	red,densely dashed,mark options={solid,fill=red!80!black},mark=diamond*\\%
+}
+
+\def\pgfplotsset{\pgfqkeys{/pgfplots}}
+
+\def\pgfplotsdeprecatedstylecheck#1{%
+	\pgfkeysifdefined{#1/.@cmd}{%
+		\begingroup
+		\edef\pgfkeyscurrentkey{#1}%
+		\pgfkeyssplitpath
+		\pgfplots@warning{Warning: Loading deprecated style option 
+			\pgfkeyscurrentpath/\pgfkeyscurrentname.  
+			Please replace '\string\tikzstyle{\pgfkeyscurrentname}' 
+			with '\string\pgfplotsset{\pgfkeyscurrentname/.style={}}'
+			(or '\string\pgfplotsset{\pgfkeyscurrentname/.append style={}}').}%
+		\endgroup
+		\pgfkeysvalueof{#1/.@cmd}\pgfeov
+	}{}%
+}%
+
+\pgfkeys{%
+	/pgfplots/search path for tikz/.unknown/.code={%
+		\let\searchname=\pgfkeyscurrentname%
+		\pgfkeysalso{%
+			/tikz/\searchname/.try=#1,
+			/pgfplots/\searchname/.lastretry=#1
+		}%
+	},%
+	/pgfplots/.is family,
+	/pgfplots/scale/.is family,
+	/pgfplots/legend/.is family,
+	/pgfplots/tick/.is family,
+	/pgfplots/axis/.is family,
+	/pgfplots/descriptions/.is family,
+	/pgfplots/style commands/.is family,
+	/pgfplots/naming commands/.is family,
+	/pgfplots/error bars/.is family,
+	/pgfplots/every axis/.style={},
+	/pgfplots/every axis/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis}},
+	/pgfplots/every axis/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every semilogx axis/.style={},
+	/pgfplots/every semilogx axis/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every semilogx axis}},
+	/pgfplots/every semilogx axis/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every semilogy axis/.style={},
+	/pgfplots/every semilogy axis/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every semilogy axis}},
+	/pgfplots/every semilogy axis/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every loglog axis/.style={},
+	/pgfplots/every loglog axis/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every loglog axis}},
+	/pgfplots/every loglog axis/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every linear axis/.style={},
+	/pgfplots/every linear axis/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every linear axis}},
+	/pgfplots/every linear axis/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis plot/.style={},
+	/pgfplots/every axis plot/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis plot}},
+	/pgfplots/every axis plot/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis plot post/.style={},
+	/pgfplots/every axis plot post/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis plot}},
+	/pgfplots/every axis label/.style={},
+	/pgfplots/every axis label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis label}},
+	/pgfplots/every axis label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis x label/.style={at={(0.5,0)},below,yshift=-15pt},
+	/pgfplots/every axis x label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis x label}},
+	/pgfplots/every axis x label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis y label/.style={at={(0,0.5)},xshift=-35pt,rotate=90},
+	/pgfplots/every axis y label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis y label}},
+	/pgfplots/every axis y label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis title/.style={at={(0.5,1)},above,yshift=6pt},
+	/pgfplots/every axis title/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis title}},
+	/pgfplots/every axis title/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every tick/.style={very thin,gray},
+	/pgfplots/every tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every tick}},
+	/pgfplots/every tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor tick/.style={},
+	/pgfplots/every minor tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor tick}},
+	/pgfplots/every minor tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major tick/.style={},
+	/pgfplots/every major tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major tick}},
+	/pgfplots/every major tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every x tick/.style={},
+	/pgfplots/every x tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every x tick}},
+	/pgfplots/every x tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor x tick/.style={},
+	/pgfplots/every minor x tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor x tick}},
+	/pgfplots/every minor x tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major x tick/.style={},
+	/pgfplots/every major x tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major x tick}},
+	/pgfplots/every major x tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every y tick/.style={},
+	/pgfplots/every y tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every y tick}},
+	/pgfplots/every y tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor y tick/.style={},
+	/pgfplots/every minor y tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor y tick}},
+	/pgfplots/every minor y tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major y tick/.style={},
+	/pgfplots/every major y tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major y tick}},
+	/pgfplots/every major y tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis grid/.style={help lines},
+	/pgfplots/every axis grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis grid}},
+	/pgfplots/every axis grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor grid/.style={},
+	/pgfplots/every minor grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor grid}},
+	/pgfplots/every minor grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major grid/.style={},
+	/pgfplots/every major grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major grid}},
+	/pgfplots/every major grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis x grid/.style={},
+	/pgfplots/every axis x grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis x grid}},
+	/pgfplots/every axis x grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor x grid/.style={},
+	/pgfplots/every minor x grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor x grid}},
+	/pgfplots/every minor x grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major x grid/.style={},
+	/pgfplots/every major x grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major x grid}},
+	/pgfplots/every major x grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis y grid/.style={},
+	/pgfplots/every axis y grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis y grid}},
+	/pgfplots/every axis y grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every minor y grid/.style={},
+	/pgfplots/every minor y grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every minor y grid}},
+	/pgfplots/every minor y grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every major y grid/.style={},
+	/pgfplots/every major y grid/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every major y grid}},
+	/pgfplots/every major y grid/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every tick label/.style={},
+	/pgfplots/every tick label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every tick label}},
+	/pgfplots/every tick label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every x tick label/.style={},
+	/pgfplots/every x tick label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every x tick label}},
+	/pgfplots/every x tick label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every extra x tick/.style={},
+	/pgfplots/every extra x tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every extra x tick}},
+	/pgfplots/every extra x tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/extra x tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/extra x tick style/.code={%
+		\pgfkeysalso{/pgfplots/every extra x tick/.append style={#1}}%
+	},
+	/pgfplots/every x tick scale label/.style={at={(1,0)},yshift=-2em,left,inner sep=0pt},
+	/pgfplots/every x tick scale label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every x tick scale label}},
+	/pgfplots/every x tick scale label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every y tick label/.style={},
+	/pgfplots/every y tick label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every y tick label}},
+	/pgfplots/every y tick label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every extra y tick/.style={},
+	/pgfplots/every extra y tick/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every extra y tick}},
+	/pgfplots/every extra y tick/.belongs to family=/pgfplots/style commands,
+	/pgfplots/extra y tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/extra y tick style/.code={%
+		\pgfkeysalso{/pgfplots/every extra y tick/.append style={#1}}%
+	},
+	/pgfplots/every y tick scale label/.style={at={(0,1)},above right,inner sep=0pt,yshift=0.3em},
+	/pgfplots/every y tick scale label/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every y tick scale label}},
+	/pgfplots/every y tick scale label/.belongs to family=/pgfplots/style commands,
+	/pgfplots/every axis legend/.style={%
+		cells={anchor=center},
+		inner xsep=3pt,inner ysep=2pt,nodes={inner sep=2pt,text depth=0.15em},
+		anchor=north east,%
+		shape=rectangle,%
+		fill=white,%
+		draw=black,
+		at={(0.98,0.98)},
+	},
+	/pgfplots/every axis legend/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every axis legend}},
+	/pgfplots/every axis legend/.belongs to family=/pgfplots/style commands,
+% tick options:
+	/pgfplots/xticklabel/.store in=	\pgfplots@xticklabel,
+	/pgfplots/xticklabel/.belongs to family=/pgfplots/tick,
+	/pgfplots/xticklabel=,
+	/pgfplots/xticklabels/.belongs to family=/pgfplots/tick,
+	/pgfplots/xticklabels/.code={%
+		\pgfplots@foreach@to@list{#1}\to\pgfplots@xticklabels
+		\let\pgfplots@xticklabel=\pgfplots@user@ticklabel@list@x
+	},
+	/pgfplots/yticklabels/.belongs to family=/pgfplots/tick,
+	/pgfplots/yticklabels/.code={%
+		\pgfplots@foreach@to@list{#1}\to\pgfplots@yticklabels
+		\let\pgfplots@yticklabel=\pgfplots@user@ticklabel@list@y
+	},
+	/pgfplots/yticklabel/.store in=	\pgfplots@yticklabel,
+	/pgfplots/yticklabel/.belongs to family=/pgfplots/tick,
+	/pgfplots/yticklabel=,
+	/pgfplots/x tick label as interval/.is if=pgfplots@xticklabel@interval,
+	/pgfplots/x tick label as interval/.default=true,
+	/pgfplots/x tick label as interval/.belongs to family=/pgfplots/tick,
+	/pgfplots/y tick label as interval/.is if=pgfplots@yticklabel@interval,
+	/pgfplots/y tick label as interval/.default=true,
+	/pgfplots/y tick label as interval/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra x tick label/.store in=	\pgfplots@extra@xticklabel,
+	/pgfplots/extra x tick label/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra x tick label=,
+	/pgfplots/extra x tick labels/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra x tick labels/.code={%
+		\pgfplots@foreach@to@list{#1}\to\pgfplots@extra@xticklabels
+		\let\pgfplots@extra@xticklabel=\pgfplots@user@extra@ticklabel@list@x
+	},
+	/pgfplots/extra y tick labels/.code={%
+		\pgfplots@foreach@to@list{#1}\to\pgfplots@extra@yticklabels
+		\let\pgfplots@extra@yticklabel=\pgfplots@user@extra@ticklabel@list@y
+	},
+	/pgfplots/xtick/.store in=			\pgfplots@xtick,
+	/pgfplots/xtick/.belongs to family=/pgfplots/tick,
+	/pgfplots/xtick=,
+	/pgfplots/extra x ticks/.store in=\pgfplots@extra@xtick,
+	/pgfplots/extra x ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra x ticks=,
+	/pgfplots/xtickten/.store in=		\pgfplots@xtickten,
+	/pgfplots/xtickten/.belongs to family=/pgfplots/tick,
+	/pgfplots/xtickten=,
+	/pgfplots/extra y tick label/.store in=	\pgfplots@extra@yticklabel,
+	/pgfplots/extra y tick label/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra y tick label=,
+	/pgfplots/ytick/.store in=			\pgfplots@ytick,
+	/pgfplots/ytick/.belongs to family=/pgfplots/tick,
+	/pgfplots/ytick=,
+	/pgfplots/extra y ticks/.store in=\pgfplots@extra@ytick,
+	/pgfplots/extra y ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/extra y ticks=,
+	/pgfplots/ytickten/.store in=		\pgfplots@ytickten,
+	/pgfplots/ytickten/.belongs to family=/pgfplots/tick,
+	/pgfplots/ytickten=,
+	/pgfplots/tick scale label code/.code={$\cdot 10^{#1}$},
+	/pgfplots/tick scale label code/.belongs to family=/pgfplots/tick,
+	/pgfplots/scaled ticks/.is if=pgfplots@scaled@ticks,
+	/pgfplots/scaled ticks/.default=false,
+	/pgfplots/scaled ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/scaled ticks=true,
+	/pgfplots/scale ticks above exponent/.store in=	\pgfplots@scale@ticks@above@exponent,
+	/pgfplots/scale ticks above exponent/.belongs to family=/pgfplots/tick,
+	/pgfplots/scale ticks above exponent=3,
+	/pgfplots/scale ticks below exponent/.store in=	\pgfplots@scale@ticks@below@exponent,
+	/pgfplots/scale ticks below exponent/.belongs to family=/pgfplots/tick,
+	/pgfplots/scale ticks below exponent=-1,
+	/pgfplots/subtickwidth/.store in=	\pgfplots@subtickwidth,
+	/pgfplots/subtickwidth/.belongs to family=/pgfplots/tick,
+	/pgfplots/subtickwidth=0.1cm,
+	/pgfplots/tickwidth/.store in=		\pgfplots@tickwidth,
+	/pgfplots/tickwidth/.belongs to family=/pgfplots/tick,
+	/pgfplots/tickwidth=0.15cm,
+	/pgfplots/minor x tick num/.initial=0,
+	/pgfplots/minor x tick num/.belongs to family=/pgfplots/tick,
+	/pgfplots/minor y tick num/.initial=0,
+	/pgfplots/minor y tick num/.belongs to family=/pgfplots/tick,
+	/pgfplots/minor tick num/.style={/pgfplots/minor x tick num=#1,/pgfplots/minor y tick num=#1},
+	/pgfplots/minor tick num/.belongs to family=/pgfplots/tick,
+	/pgfplots/minor tick length/.estore in=\pgfplots@subtickwidth,
+	/pgfplots/minor tick length/.belongs to family=/pgfplots/tick,
+	/pgfplots/major tick length/.estore in=\pgfplots@tickwidth,
+	/pgfplots/major tick length/.belongs to family=/pgfplots/tick,
+	/pgfplots/max space between ticks/.estore in=\axisdefaulttickwidth,
+	/pgfplots/max space between ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/max space between ticks=35,% the maximum space between adjacent ticks (in pt, but don't specify the unit 'pt')
+	/pgfplots/try min ticks/.estore in=			\axisdefaulttryminticks,
+	/pgfplots/try min ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/try min ticks=4,
+	/pgfplots/try min ticks log/.estore in=			\pgfplots@default@try@minticks@log,
+	/pgfplots/try min ticks log/.belongs to family=/pgfplots/tick,
+	/pgfplots/try min ticks log=3,
+	/pgfplots/log plot exponent style/.style={/pgf/number format/fixed,/pgf/number format/precision=2},
+	/pgfplots/log plot exponent style/.belongs to family=/pgfplots/tick,
+	/pgfplots/log identify minor tick positions/.is if=pgfplots@identify@log@minor@tick@pos,
+	/pgfplots/log identify minor tick positions/.belongs to family=/pgfplots/tick,
+	/pgfplots/log identify minor tick positions=true,
+	/pgfplots/log number format code/.code={{%
+		\pgfmathlogtologten@{#1}%
+		\ifpgfplots@identify@log@minor@tick@pos
+			\expandafter\pgfplots@is@log@tick@a@minor@tick@pos\pgfmathresult\relax%
+		\else
+			\pgfplots@log@tick@isminor@tick@posfalse
+		\fi
+		\ifpgfplots@log@tick@isminor@tick@pos
+			\pgfmathprintnumber[sci]{\pgfmathresult}%
+		\else
+			\pgfkeysalso{/pgfplots/log plot exponent style,/pgfplots/log base 10 number format code=\pgfmathresult}%
+		\fi
+	}},
+	/pgfplots/log number format code/.belongs to family=/pgfplots/tick,
+	/pgfplots/log base 10 number format code/.code={$10^{\pgfmathprintnumber{#1}}$},
+	/pgfplots/log base 10 number format code/.belongs to family=/pgfplots/tick,
+% sets \pgfplots@tickposnum to
+% left=0
+% right=1
+% both=2
+	/pgfplots/tickpos/.is choice,
+	/pgfplots/tickpos/.belongs to family=/pgfplots/tick,
+	/pgfplots/tickpos/left/.code	={\def\pgfplots@xtickposnum{1}\def\pgfplots@ytickposnum{1}},
+	/pgfplots/tickpos/left/.belongs to family=/pgfplots/tick,
+	/pgfplots/tickpos/right/.code	={\def\pgfplots@xtickposnum{3}\def\pgfplots@ytickposnum{3}},
+	/pgfplots/tickpos/right/.belongs to family=/pgfplots/tick,
+	/pgfplots/tickpos/both/.code	={\def\pgfplots@xtickposnum{0}\def\pgfplots@ytickposnum{0}},
+	/pgfplots/tickpos/both/.belongs to family=/pgfplots/tick,
+	/pgfplots/tickpos=both,
+% sets \pgfplots@{x,y}tickalignnum to
+% inside=0
+% outside=1
+% center=2
+	/pgfplots/tick align/.is choice,
+	/pgfplots/tick align/.belongs to family=/pgfplots/tick,
+	/pgfplots/tick align/inside/.code	={\def\pgfplots@xtickalignnum{0}\def\pgfplots@ytickalignnum{0}},
+	/pgfplots/tick align/inside/.belongs to family=/pgfplots/tick,
+	/pgfplots/tick align/outside/.code	={\def\pgfplots@xtickalignnum{1}\def\pgfplots@ytickalignnum{1}},
+	/pgfplots/tick align/outside/.belongs to family=/pgfplots/tick,
+	/pgfplots/tick align/center/.code	={\def\pgfplots@xtickalignnum{2}\def\pgfplots@ytickalignnum{2}},
+	/pgfplots/tick align/center/.belongs to family=/pgfplots/tick,
+	/pgfplots/tick align=inside,
+% 'axis' options:
+	/pgfplots/anchor/.belongs to family=/pgfplots,
+	/pgfplots/anchor/.store in=			\pgfplots@anchorname,
+	/pgfplots/anchor=south west,
+% tick options:
+	/pgfplots/ticks/.is choice,
+	/pgfplots/ticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/ticks/none/.belongs to family=/pgfplots/tick,
+	/pgfplots/ticks/none/.code={%
+		\pgfplots@xminorticksfalse
+		\pgfplots@yminorticksfalse
+		\pgfplots@xmajorticksfalse
+		\pgfplots@ymajorticksfalse
+	},
+	/pgfplots/ticks/major/.belongs to family=/pgfplots/tick,
+	/pgfplots/ticks/major/.code={%
+		\pgfplots@xminorticksfalse
+		\pgfplots@yminorticksfalse
+		\pgfplots@xmajortickstrue
+		\pgfplots@ymajortickstrue
+	},
+	/pgfplots/ticks/minor/.belongs to family=/pgfplots/tick,
+	/pgfplots/ticks/minor/.code={%
+		\pgfplots@xminortickstrue
+		\pgfplots@yminortickstrue
+		\pgfplots@xmajorticksfalse
+		\pgfplots@ymajorticksfalse
+	},
+	/pgfplots/ticks/both/.belongs to family=/pgfplots/tick,
+	/pgfplots/ticks/both/.code={%
+		\pgfplots@xminortickstrue
+		\pgfplots@yminortickstrue
+		\pgfplots@xmajortickstrue
+		\pgfplots@ymajortickstrue
+	},
+	/pgfplots/ticks=both,
+	/pgfplots/grid/.is choice,
+	/pgfplots/grid/.belongs to family=/pgfplots/tick,
+	/pgfplots/grid/none/.belongs to family=/pgfplots/tick,
+	/pgfplots/grid/none/.code={%
+		\pgfplots@xminorgridsfalse
+		\pgfplots@yminorgridsfalse
+		\pgfplots@xmajorgridsfalse
+		\pgfplots@ymajorgridsfalse
+	},
+	/pgfplots/grid/major/.belongs to family=/pgfplots/tick,
+	/pgfplots/grid/major/.code={%
+		\pgfplots@xminorgridsfalse
+		\pgfplots@yminorgridsfalse
+		\pgfplots@xmajorgridstrue
+		\pgfplots@ymajorgridstrue
+	},
+	/pgfplots/grid/minor/.belongs to family=/pgfplots/tick,
+	/pgfplots/grid/minor/.code={%
+		\pgfplots@xminorgridstrue
+		\pgfplots@yminorgridstrue
+		\pgfplots@xmajorgridsfalse
+		\pgfplots@ymajorgridsfalse
+	},
+	/pgfplots/grid/both/.belongs to family=/pgfplots/tick,
+	/pgfplots/grid/both/.code={%
+		\pgfplots@xminorgridstrue
+		\pgfplots@yminorgridstrue
+		\pgfplots@xmajorgridstrue
+		\pgfplots@ymajorgridstrue
+	},
+	/pgfplots/grid=none,
+	/pgfplots/grid/.default=major,
+	/pgfplots/xminorticks/.is if=pgfplots@xminorticks,
+	/pgfplots/xminorticks/.default=true,
+	/pgfplots/xminorticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/xmajorticks/.is if=pgfplots@xmajorticks,
+	/pgfplots/xmajorticks/.default=true,
+	/pgfplots/xmajorticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/yminorticks/.is if=pgfplots@yminorticks,
+	/pgfplots/yminorticks/.default=true,
+	/pgfplots/yminorticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/ymajorticks/.is if=pgfplots@ymajorticks,
+	/pgfplots/ymajorticks/.default=true,
+	/pgfplots/ymajorticks/.belongs to family=/pgfplots/tick,
+	/pgfplots/xminorgrids/.is if=pgfplots@xminorgrids,
+	/pgfplots/xminorgrids/.default=true,
+	/pgfplots/xminorgrids/.belongs to family=/pgfplots/tick,
+	/pgfplots/xmajorgrids/.is if=pgfplots@xmajorgrids,
+	/pgfplots/xmajorgrids/.default=true,
+	/pgfplots/xmajorgrids/.belongs to family=/pgfplots/tick,
+	/pgfplots/yminorgrids/.is if=pgfplots@yminorgrids,
+	/pgfplots/yminorgrids/.default=true,
+	/pgfplots/yminorgrids/.belongs to family=/pgfplots/tick,
+	/pgfplots/ymajorgrids/.is if=pgfplots@ymajorgrids,
+	/pgfplots/ymajorgrids/.default=true,
+	/pgfplots/ymajorgrids/.belongs to family=/pgfplots/tick,
+% legend options:
+	/pgfplots/legend columns/.store in=\pgfplots@legend@columns,
+	/pgfplots/legend columns/.belongs to family=/pgfplots/legend,
+	/pgfplots/legend columns=1,
+	/pgfplots/legend plot pos/.is choice,
+	/pgfplots/legend plot pos/.belongs to family=/pgfplots/legend,
+	/pgfplots/legend plot pos/left/.code=	{\def\pgfplots@legend@plot@pos{0}},
+	/pgfplots/legend plot pos/left/.belongs to family=/pgfplots/legend,
+	/pgfplots/legend plot pos/right/.code=	{\def\pgfplots@legend@plot@pos{1}},
+	/pgfplots/legend plot pos/right/.belongs to family=/pgfplots/legend,
+	/pgfplots/legend plot pos/none/.code=	{\def\pgfplots@legend@plot@pos{2}},
+	/pgfplots/legend plot pos/none/.belongs to family=/pgfplots/legend,
+	/pgfplots/legend plot pos=left,
+	/pgfplots/legend image code/.code={%
+		\draw[#1,mark repeat=2,mark phase=2] 
+			plot coordinates {
+				(0cm,0cm) 
+				(0.3cm,0cm)
+				(0.6cm,0cm)%
+			};%
+	},
+	/pgfplots/legend image code/.belongs to family=/pgfplots/legend,
+% axis description options:
+	/pgfplots/title/.store in=		\pgfplots@title,
+	/pgfplots/title/.belongs to family=/pgfplots/descriptions,
+	/pgfplots/title=,
+	/pgfplots/xlabel/.store in=	\pgfplots@xlabel,
+	/pgfplots/xlabel/.belongs to family=/pgfplots/descriptions,
+	/pgfplots/xlabel=,
+	/pgfplots/ylabel/.store in=	\pgfplots@ylabel,
+	/pgfplots/ylabel/.belongs to family=/pgfplots/descriptions,
+	/pgfplots/ylabel=,
+	/pgfplots/before end axis/.code=,
+	/pgfplots/after end axis/.code=,
+	/pgfplots/extra description/.code=,
+	/pgfplots/extra description/.belongs to family=/pgfplots/descriptions,
+% axis options:
+	/pgfplots/at/.code={\tikz@scan@one@point\pgfplots@set@at#1},
+	/pgfplots/at/.belongs to family=/pgfplots,
+	/pgfplots/clip limits/.is if=pgfplots@clip@limits,
+	/pgfplots/clip limits/.default=true,
+	/pgfplots/clip limits=true,
+	/pgfplots/clip limits/.belongs to family=/pgfplots,
+	/pgfplots/xmin/.belongs to family=/pgfplots,
+	/pgfplots/xmin/.initial=,
+	/pgfplots/xmax/.belongs to family=/pgfplots,
+	/pgfplots/xmax/.initial=,
+	/pgfplots/ymin/.belongs to family=/pgfplots,
+	/pgfplots/ymin/.initial=,
+	/pgfplots/ymax/.belongs to family=/pgfplots,
+	/pgfplots/ymax/.initial=,
+	/pgfplots/stack plots/.is choice,
+	/pgfplots/stack plots/.belongs to family=/pgfplots,
+	/pgfplots/stack plots/x/.code={\pgfplots@stacked@xtrue\pgfplots@stackedmodetrue},
+	/pgfplots/stack plots/x/.belongs to family=/pgfplots,
+	/pgfplots/stack plots/y/.code={\pgfplots@stacked@xfalse\pgfplots@stackedmodetrue},
+	/pgfplots/stack plots/y/.belongs to family=/pgfplots,
+	/pgfplots/stack plots/false/.code={\pgfplots@stackedmodefalse},
+	/pgfplots/stack plots/false/.belongs to family=/pgfplots,
+	/pgfplots/stack plots=false,
+	/pgfplots/reverse stacked plots/.is if=pgfplots@stacked@reverse,
+	/pgfplots/reverse stacked plots/.belongs to family=/pgfplots,
+	/pgfplots/reverse stacked plots/.default=true,
+	/pgfplots/reverse stacked plots=true,
+	/pgfplots/stack dir/.is choice,
+	/pgfplots/stack dir/.belongs to family=/pgfplots,
+	/pgfplots/stack dir/plus/.code={\pgfplots@stacked@plustrue},
+	/pgfplots/stack dir/plus/.belongs to family=/pgfplots,
+	/pgfplots/stack dir/minus/.code={\pgfplots@stacked@plusfalse},
+	/pgfplots/stack dir/minus/.belongs to family=/pgfplots,
+	/pgfplots/stack dir=plus,
+	/pgfplots/filter discard warning/.is if=pgfplots@warn@for@filter@discards,
+	/pgfplots/filter discard warning=true,
+	/pgfplots/x filter/.code={},
+	/pgfplots/x filter/.belongs to family=/pgfplots,
+	/pgfplots/y filter/.code={},
+	/pgfplots/y filter/.belongs to family=/pgfplots,
+	/pgfplots/skip coords between index/.style 2 args={%
+		/pgfplots/x filter/.append code={%
+			\ifnum\coordindex<#1\relax
+			\else
+				\ifnum\coordindex<#2\relax
+					\let\pgfmathresult=\pgfutil@empty
+				\fi
+			\fi}
+	},
+	/pgfplots/xfilter/.initial=,% DEPRECATED
+	/pgfplots/xfilter/.belongs to family=/pgfplots,
+	/pgfplots/yfilter/.initial=,% DEPRECATED
+	/pgfplots/yfilter/.belongs to family=/pgfplots,
+	/pgfplots/width/.store in=		\pgfplots@width,
+	/pgfplots/width/.belongs to family=/pgfplots,
+	/pgfplots/width=,
+	/pgfplots/height/.store in=	\pgfplots@height,
+	/pgfplots/height/.belongs to family=/pgfplots,
+	/pgfplots/height=,
+	/pgfplots/execute at begin plot/.store in=\pgfplots@execute@at@begin@plot,
+	/pgfplots/execute at begin plot/.belongs to family=/pgfplots,
+	/pgfplots/execute at begin plot=,
+	/pgfplots/execute at end plot/.store in=		\pgfplots@execute@at@end@plot,
+	/pgfplots/execute at end plot/.belongs to family=/pgfplots,
+	/pgfplots/execute at end plot=,
+	/pgfplots/enlargelimits/.store in=		\pgfplots@enlargelimits,
+	/pgfplots/enlargelimits/.belongs to family=/pgfplots,
+	/pgfplots/enlargelimits=auto,
+	/pgfplots/enlargelimits/.default=true,
+	/pgfplots/x/.store in=		\pgfplots@x,
+	/pgfplots/x/.belongs to family=/pgfplots,
+	/pgfplots/x=,% is implicitly set by 'width' and/or '\axisdefaultwidth'
+	/pgfplots/y/.store in=		\pgfplots@y,
+	/pgfplots/y/.belongs to family=/pgfplots,
+	/pgfplots/y=,% is implicitly set by 'width' and/or '\axisdefaultwidth'
+	/pgfplots/cycle list/.code={\pgfplots@assign@list\autoplotspeclist{#1}},
+	/pgfplots/cycle list/.belongs to family=/pgfplots,
+	/pgfplots/cycle list name/.code={\let\autoplotspeclist=#1\relax},
+	/pgfplots/cycle list name/.belongs to family=/pgfplots,
+	/pgfplots/cycle list name=\coloredplotspeclist,
+	/pgfplots/legend style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/legend style/.code={%
+		\pgfkeysalso{/pgfplots/every axis legend/.append style={#1}}%
+	},
+	/pgfplots/label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/label style/.code={%
+		\pgfkeysalso{/pgfplots/every axis label/.append style={#1}}%
+	},%
+	/pgfplots/x label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/x label style/.code={%
+		\pgfkeysalso{/pgfplots/every axis x label/.append style={#1}}%
+	},
+	/pgfplots/y label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/y label style/.code={%
+		\pgfkeysalso{/pgfplots/every axis y label/.append style={#1}}%
+	},
+	/pgfplots/title style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/title style/.code={%
+		\pgfkeysalso{/pgfplots/every axis title/.append style={#1}}%
+	},
+	/pgfplots/tick label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/tick label style/.code={%
+		\pgfkeysalso{/pgfplots/every tick label/.append style={#1}}%
+	},
+	/pgfplots/x tick label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/x tick label style/.code={%
+		\pgfkeysalso{/pgfplots/every x tick label/.append style={#1}}%
+	},
+	/pgfplots/y tick label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/y tick label style/.code={%
+		\pgfkeysalso{/pgfplots/every y tick label/.append style={#1}}%
+	},
+	/pgfplots/x tick scale label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/x tick scale label style/.code={%
+		\pgfkeysalso{/pgfplots/every x scale tick label/.append style={#1}}%
+	},
+	/pgfplots/y tick scale label style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/y tick scale label style/.code={%
+		\pgfkeysalso{/pgfplots/every y scale tick label/.append style={#1}}%
+	},
+	/pgfplots/tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/tick style/.code={%
+		\pgfkeysalso{/pgfplots/every tick/.append style={#1}}%
+	},
+	/pgfplots/minor tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor tick style/.code={%
+		\pgfkeysalso{/pgfplots/every minor tick/.append style={#1}}%
+	},
+	/pgfplots/major tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major tick style/.code={%
+		\pgfkeysalso{/pgfplots/every major tick/.append style={#1}}%
+	},
+	/pgfplots/x tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/x tick style/.code={%
+		\pgfkeysalso{/pgfplots/every x tick/.append style={#1}}%
+	},
+	/pgfplots/minor x tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor x tick style/.code={%
+		\pgfkeysalso{/pgfplots/every minor x tick/.append style={#1}}%
+	},
+	/pgfplots/major x tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major x tick style/.code={%
+		\pgfkeysalso{/pgfplots/every major x tick/.append style={#1}}%
+	},
+	/pgfplots/y tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/y tick style/.code={%
+		\pgfkeysalso{/pgfplots/every y tick/.append style={#1}}%
+	},
+	/pgfplots/minor y tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor y tick style/.code={%
+		\pgfkeysalso{/pgfplots/every minor y tick/.append style={#1}}%
+	},
+	/pgfplots/major y tick style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major y tick style/.code={%
+		\pgfkeysalso{/pgfplots/every major y tick/.append style={#1}}%
+	},
+	/pgfplots/grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/grid style/.code={%
+		\pgfkeysalso{/pgfplots/every axis grid/.append style={#1}}%
+	},
+	/pgfplots/minor grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor grid style/.code={%
+		\pgfkeysalso{/pgfplots/every minor grid/.append style={#1}}%
+	},
+	/pgfplots/major grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major grid style/.code={%
+		\pgfkeysalso{/pgfplots/every major grid/.append style={#1}}%
+	},
+	/pgfplots/x grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/x grid style/.code={%
+		\pgfkeysalso{/pgfplots/every axis x grid/.append style={#1}}%
+	},
+	/pgfplots/minor x grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor x grid style/.code={%
+		\pgfkeysalso{/pgfplots/every minor x grid/.append style={#1}}%
+	},
+	/pgfplots/major x grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major x grid style/.code={%
+		\pgfkeysalso{/pgfplots/every major x grid/.append style={#1}}%
+	},
+	/pgfplots/y grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/y grid style/.code={%
+		\pgfkeysalso{/pgfplots/every axis y grid/.append style={#1}}%
+	},
+	/pgfplots/minor y grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/minor y grid style/.code={%
+		\pgfkeysalso{/pgfplots/every minor y grid/.append style={#1}}%
+	},
+	/pgfplots/major y grid style/.belongs to family=/pgfplots/style commands,
+	/pgfplots/major y grid style/.code={%
+		\pgfkeysalso{/pgfplots/every major y grid/.append style={#1}}%
+	},
+	/pgfplots/disablelogfilter/.is if=pgfplots@disablelogfilter,
+	/pgfplots/disablelogfilter/.default=true,
+	/pgfplots/disablelogfilter/.belongs to family=/pgfplots,
+	/pgfplots/disablelogfilter=false,
+	/pgfplots/disabledatascaling/.is if=pgfplots@disabledatascaling,
+	/pgfplots/disabledatascaling/.default=true,
+	/pgfplots/disabledatascaling/.belongs to family=/pgfplots,
+	/pgfplots/disabledatascaling=false,
+	/pgfplots/hide axis/.is if=pgfplots@hide,
+	/pgfplots/hide axis/.default=true,
+	/pgfplots/hide axis/.belongs to family=/pgfplots,
+	/pgfplots/hide axis=false,
+% sets \pgfplots@xaxislinesnum to
+% box=0
+% bottom=1
+% middle=2
+% top=3
+	/pgfplots/axis x line/.is choice,
+	/pgfplots/axis x line/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line/box/.code	={\def\pgfplots@xaxislinesnum{0}\def\pgfplots@xtickposnum{0}},
+	/pgfplots/axis x line/box/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line/bottom/.code	={\def\pgfplots@xaxislinesnum{1}\def\pgfplots@xtickposnum{1}},
+	/pgfplots/axis x line/bottom/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line/middle/.code	={\def\pgfplots@xaxislinesnum{2}\def\pgfplots@xtickposnum{2}},
+	/pgfplots/axis x line/middle/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line/top/.code	={\def\pgfplots@xaxislinesnum{3}\def\pgfplots@xtickposnum{3}},
+	/pgfplots/axis x line/top/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line/none/.code	={\def\pgfplots@xaxislinesnum{4}\def\pgfplots@xtickposnum{4}},
+	/pgfplots/axis x line/none/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x line=box,
+% sets \pgfplots@yaxislinesnum to
+% box=0
+% left=1
+% center=2
+% right=3
+	/pgfplots/axis y line/.is choice,
+	/pgfplots/axis y line/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line/box/.code	={\def\pgfplots@yaxislinesnum{0}\def\pgfplots@ytickposnum{0}},
+	/pgfplots/axis y line/box/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line/left/.code	={\def\pgfplots@yaxislinesnum{1}\def\pgfplots@ytickposnum{1}},
+	/pgfplots/axis y line/left/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line/center/.code	={\def\pgfplots@yaxislinesnum{2}\def\pgfplots@ytickposnum{2}},
+	/pgfplots/axis y line/center/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line/right/.code	={\def\pgfplots@yaxislinesnum{3}\def\pgfplots@ytickposnum{3}},
+	/pgfplots/axis y line/right/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line/none/.code	={\def\pgfplots@yaxislinesnum{4}\def\pgfplots@ytickposnum{4}},
+	/pgfplots/axis y line/none/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y line=box,
+% set \pgfplots@xaxisdiscontnum
+% none = 0
+% crunch = 1
+% open = 2
+	/pgfplots/axis x discontinuity/.is choice,
+	/pgfplots/axis x discontinuity/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x discontinuity/none/.code	={\def\pgfplots@xaxisdiscontnum{0}},
+	/pgfplots/axis x discontinuity/none/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x discontinuity/crunch/.code	={\def\pgfplots@xaxisdiscontnum{1}},
+	/pgfplots/axis x discontinuity/crunch/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x discontinuity/parallel/.code	={\def\pgfplots@xaxisdiscontnum{2}},
+	/pgfplots/axis x discontinuity/parallel/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis x discontinuity=none,
+% set \pgfplots@yaxisdiscontnum
+% none = 0
+% crunch = 1
+% open = 2
+	/pgfplots/axis y discontinuity/.is choice,
+	/pgfplots/axis y discontinuity/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y discontinuity/none/.code	={\def\pgfplots@yaxisdiscontnum{0}},
+	/pgfplots/axis y discontinuity/none/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y discontinuity/crunch/.code	={\def\pgfplots@yaxisdiscontnum{1}},
+	/pgfplots/axis y discontinuity/crunch/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y discontinuity/parallel/.code	={\def\pgfplots@yaxisdiscontnum{2}},
+	/pgfplots/axis y discontinuity/parallel/.belongs to family=/pgfplots, %/axis,
+	/pgfplots/axis y discontinuity=none,
+	/pgfplots/scale only axis/.is if=pgfplots@scale@only@axis,
+	/pgfplots/scale only axis/.default=true,
+	/pgfplots/scale only axis/.belongs to family=/pgfplots,
+	/pgfplots/scale only axis=false,
+% sets \pgfplots@xislinear to
+% normal=true
+% log=false
+	/pgfplots/xmode/.is choice,
+	/pgfplots/xmode/.belongs to family=/pgfplots/scale,
+	/pgfplots/xmode/normal/.code={\pgfplots@xislineartrue},
+	/pgfplots/xmode/normal/.belongs to family=/pgfplots/scale,
+	/pgfplots/xmode/linear/.code={\pgfplots@xislineartrue},
+	/pgfplots/xmode/linear/.belongs to family=/pgfplots/scale,
+	/pgfplots/xmode/log/.code={\pgfplots@xislinearfalse},
+	/pgfplots/xmode/log/.belongs to family=/pgfplots/scale,
+	/pgfplots/xmode=linear,
+	/pgfplots/ymode/.is choice,
+	/pgfplots/ymode/.belongs to family=/pgfplots/scale,
+	/pgfplots/ymode/normal/.code={\pgfplots@yislineartrue},
+	/pgfplots/ymode/normal/.belongs to family=/pgfplots/scale,
+	/pgfplots/ymode/linear/.code={\pgfplots@yislineartrue},
+	/pgfplots/ymode/linear/.belongs to family=/pgfplots/scale,
+	/pgfplots/ymode/log/.code={\pgfplots@yislinearfalse},
+	/pgfplots/ymode/log/.belongs to family=/pgfplots/scale,
+	/pgfplots/ymode=linear,
+	/pgfplots/error bars/x fixed/.code=				\def\pgfplots@errorbars@xfixed{#1}\def\pgfplots@errorbars@xmode{0},
+	/pgfplots/error bars/x fixed relative/.code=		\def\pgfplots@errorbars@xrel{#1}\def\pgfplots@errorbars@xmode{1},
+	/pgfplots/error bars/x explicit/.code=			\def\pgfplots@errorbars@xmode{2},
+	/pgfplots/error bars/x explicit relative/.code=	\def\pgfplots@errorbars@xmode{3},
+	/pgfplots/error bars/x fixed relative=0,
+	/pgfplots/error bars/x fixed=0,
+	/pgfplots/error bars/y fixed/.code=				\def\pgfplots@errorbars@yfixed{#1}\def\pgfplots@errorbars@ymode{0},
+	/pgfplots/error bars/y fixed relative/.code=		\def\pgfplots@errorbars@yrel{#1}\def\pgfplots@errorbars@ymode{1},
+	/pgfplots/error bars/y explicit/.code=			\def\pgfplots@errorbars@ymode{2},
+	/pgfplots/error bars/y explicit relative/.code=	\def\pgfplots@errorbars@ymode{3},
+	/pgfplots/error bars/y fixed relative=0,
+	/pgfplots/error bars/y fixed=0,
+	/pgfplots/error bars/x dir/.is choice,
+	/pgfplots/error bars/x dir/none/.code={%
+		\def\pgfplots@errorbars@xdirection{0}%
+		\ifnum\pgfplots@errorbars@ydirection=0
+			\pgfplots@errorbars@enabledfalse
+		\fi
+	},
+	/pgfplots/error bars/x dir/plus/.code=				\def\pgfplots@errorbars@xdirection{1}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/x dir/minus/.code=				\def\pgfplots@errorbars@xdirection{2}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/x dir/both/.code=				\def\pgfplots@errorbars@xdirection{3}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/x dir=none,
+	/pgfplots/error bars/y dir/.is choice,
+	/pgfplots/error bars/y dir/none/.code={%
+		\def\pgfplots@errorbars@ydirection{0}%
+		\ifnum\pgfplots@errorbars@xdirection=0
+			\pgfplots@errorbars@enabledfalse
+		\fi
+	},
+	/pgfplots/error bars/y dir/plus/.code=				\def\pgfplots@errorbars@ydirection{1}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/y dir/minus/.code=				\def\pgfplots@errorbars@ydirection{2}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/y dir/both/.code=				\def\pgfplots@errorbars@ydirection{3}\pgfplots@errorbars@enabledtrue,
+	/pgfplots/error bars/y dir=none,
+	/pgfplots/error bars/error mark/.initial={-},
+	/pgfplots/error bars/error mark options/.initial={rotate=90},
+	/pgfplots/error bars/error bar style/.code={%
+		\pgfkeysalso{/pgfplots/every error bar/.append style={#1}}%
+	},
+	/pgfplots/every error bar/.style={thin},
+	/pgfplots/every error bar/.append code={\pgfplotsdeprecatedstylecheck{/tikz/every error bar}},
+	/pgfplots/error bars/draw error bar/.code 2 args={%
+%\message{/pgfplots/error bars/draw error bar:  working with '#1' -- '#2'.}%
+		\pgfkeysgetvalue{/pgfplots/error bars/error mark}{\pgfplotserrorbarsmark}%
+		\pgfkeysgetvalue{/pgfplots/error bars/error mark options}{\pgfplotserrorbarsmarkopts}%
+		\draw #1 -- #2 node[pos=1,sloped,allow upside down] {%
+			\expandafter\tikz\expandafter[\pgfplotserrorbarsmarkopts]{%
+				\expandafter\pgfuseplotmark\expandafter{\pgfplotserrorbarsmark}%
+				\pgfusepath{stroke}}%
+		};
+	},
+	/pgfplots/bar cycle list/.style={/pgfplots/cycle list={%
+		{blue,fill=blue!30!white,mark=none},%
+		{red,fill=red!30!white,mark=none},%
+		{brown!60!black,fill=brown!30!white,mark=none},%
+		{black,fill=gray,mark=none},%
+		}
+	},
+	/pgfplots/area cycle list/.style={bar cycle list},
+	/pgfplots/ybar/.style={
+		bar cycle list,
+		tick align=outside,
+		/pgfplots/legend image code/.code={\draw[##1,bar width=3pt,yshift=-0.2em,bar shift=0pt] plot coordinates {(0cm,0.8em) (2*\pgfplotbarwidth,0.6em)};},
+		/pgf/bar shift={%
+				% total width = n*w + (n-1)*skip
+				% -> subtract half for centering
+				-0.5*(\numplots*\pgfplotbarwidth + (\numplots-1)*#1)  + 
+				% the '0.5*w' is for centering
+				(.5+\plotnum)*\pgfplotbarwidth + \plotnum*#1},%
+		/tikz/ybar,
+	},
+	/pgfplots/ybar/.default=2pt,
+	/pgfplots/ybar/.belongs to family=/pgfplots,
+	/pgfplots/xbar/.style={
+		bar cycle list,
+		tick align=outside,
+		/pgfplots/legend image code/.code={\draw[##1,bar width=3pt,yshift=-0.2em,bar shift=0pt] plot coordinates {(0cm,0.8em) (2*\pgfplotbarwidth,0.6em)};},
+		/pgf/bar shift={%
+				% total width = n*w + (n-1)*skip
+				% -> subtract half for centering
+				-0.5*(\numplots*\pgfplotbarwidth + (\numplots-1)*#1)  + 
+				% the '0.5*w' is for centering
+				(.5+\plotnum)*\pgfplotbarwidth + \plotnum*#1},%
+		/tikz/xbar,
+	},
+	/pgfplots/xbar/.default=2pt,
+	/pgfplots/xbar/.belongs to family=/pgfplots,
+	/pgfplots/ybar interval/.style={%
+		bar cycle list,
+		x tick label as interval,
+		xmajorgrids,
+	%	xtick=data,
+		/pgfplots/legend image code/.code={\draw[##1,yshift=-0.2em,bar interval width=0.7,bar interval shift=0.5] plot coordinates {(0cm,0.8em) (5pt,0.6em) (10pt,0.6em)};},
+		bar interval width={#1/\numplots},
+		bar interval shift={(\plotnum+0.5)/\numplots},
+		/tikz/ybar interval,
+	},
+	/pgfplots/ybar interval/.default=1,
+	/pgfplots/ybar interval/.belongs to family=/pgfplots,
+	/pgfplots/xbar interval/.style={%
+		bar cycle list,
+		y tick label as interval,
+	%	ytick=data,
+		ymajorgrids,
+		/pgfplots/legend image code/.code={\draw[##1,yshift=-0.2em,bar interval width=0.7,bar interval shift=0.5] plot coordinates {(0cm,0.8em) (5pt,0.6em) (10pt,0.6em)};},
+		bar interval width={#1/\numplots},
+		bar interval shift={(\plotnum+0.5)/\numplots},
+		/tikz/xbar interval,
+	},
+	/pgfplots/xbar interval/.default=1,
+	/pgfplots/xbar interval/.belongs to family=/pgfplots,
+	/pgfplots/xbar stacked/.style={
+		bar cycle list,
+		stack plots=x,
+		stack dir=#1,
+		/tikz/xbar,
+	},
+	/pgfplots/xbar stacked/.default=plus,
+	/pgfplots/xbar stacked/.belongs to family=/pgfplots,
+	/pgfplots/ybar stacked/.style={
+		bar cycle list,
+		stack plots=y,
+		stack dir=#1,
+		/tikz/ybar,
+	},
+	/pgfplots/ybar stacked/.default=plus,
+	/pgfplots/ybar stacked/.belongs to family=/pgfplots,
+	/pgfplots/xbar interval stacked/.style={
+		bar cycle list,
+		stack plots=x,
+		stack dir=#1,
+		/tikz/xbar interval,
+	},
+	/pgfplots/xbar interval stacked/.default=plus,
+	/pgfplots/xbar interval stacked/.belongs to family=/pgfplots,
+	/pgfplots/ybar interval stacked/.style={
+		bar cycle list,
+		stack plots=y,
+		stack dir=#1,
+		/tikz/ybar interval,
+	},
+	/pgfplots/ybar interval stacked/.default=plus,
+	/pgfplots/ybar interval stacked/.belongs to family=/pgfplots,
+	/pgfplots/yticklabel interval boundaries/.style={%
+		y tick label as interval,
+		yticklabel={$\pgfmathprintnumber{\tick}$ -- $\pgfmathprintnumber{\nexttick}$}
+	},
+	/pgfplots/xticklabel interval boundaries/.style={%
+		x tick label as interval,
+		xticklabel={$\pgfmathprintnumber{\tick}$ -- $\pgfmathprintnumber{\nexttick}$}
+	},
+}
+
+\newif\ifpgfplots@log@tick@isminor@tick@pos
+% Checks whether the tick position given as #1.#2=log10(T) belongs to
+% T=i*10^j with an integer i>1.
+%
+% If T=i*10^j,  \ifpgfplots@log@tick@isminor@tick@pos will be set to true and
+% \pgfmathresult will contain T.
+%
+% Otherwise, \ifpgfplots@log@tick@isminor@tick@pos will be set to false and
+% pgfmathresult to #1.#2
+%
+% Arguments:
+% #1.#2  the value log10(T)
+%
+% Implementation:  
+% if T = i*10^j,  log10(T) = log10(i) + j.
+% That means if log10(T) in \Z,  we have T = 10^j. If not, we need to
+% check wether i is an integer. Please note that log10(i) < 1.
+%
+% Further note: log(T) < 0 <=>  j<0.
+% In case j<0, we have 
+%   #1.#2 = j + log(i) 
+%         = - ( -j - log(i) ) 
+%         = - ( -j - 1  + (1-log(i)) )
+%         = #1 '.' #2 [ up to the '0.'
+% that means #1 = j-1  and #2 = 1-log(i).
+\def\pgfplots@is@log@tick@a@minor@tick@pos#1.#2\relax{%
+	\pgfmathapproxequalto@{#1.#2}{#1.0}%
+	\ifpgfmathcomparison
+		% in MOST cases, this here will be true:
+		\pgfplots@log@tick@isminor@tick@posfalse
+		\def\pgfmathresult{#1.#2}%
+	\else
+		% I guess this won't happen too often. In fact, it's a very
+		% special case.
+		\begingroup
+		\c@pgf@counta=#1\relax
+		\ifnum\c@pgf@counta<0
+			\advance\c@pgf@counta by-1
+			\pgfmathsubtract@{1}{0.#2}%
+			\expandafter\pgfplots@is@log@tick@a@minor@tick@pos@IDENTIFY@LOGi\pgfmathresult\relax
+			\ifpgfplots@log@tick@isminor@tick@pos
+				\aftergroup\pgfplots@log@tick@isminor@tick@postrue
+				\edef\pgfmathresult{\pgfmathresult e\the\c@pgf@counta}%
+			\else
+			\aftergroup\pgfplots@log@tick@isminor@tick@posfalse
+				\def\pgfmathresult{#1.#2}%
+			\fi
+		\else
+			\pgfplots@is@log@tick@a@minor@tick@pos@IDENTIFY@LOGi0.#2\relax
+			\ifpgfplots@log@tick@isminor@tick@pos
+				\aftergroup\pgfplots@log@tick@isminor@tick@postrue
+				\edef\pgfmathresult{\pgfmathresult e\the\c@pgf@counta}%
+			\else
+				\aftergroup\pgfplots@log@tick@isminor@tick@posfalse
+				\def\pgfmathresult{#1.#2}%
+			\fi
+		\fi
+		\pgfmath@smuggleone\pgfmathresult
+		\endgroup
+	\fi
+}
+
+% expects a positive number.
+\def\pgfplots@is@log@tick@a@minor@tick@pos@IDENTIFY@LOGi0.#1\relax{%
+	\pgfplots@log@tick@isminor@tick@postrue
+	\pgfmathapproxequalto@{0.#1}{0.3010299956639}%
+	\ifpgfmathcomparison
+		\def\pgfmathresult{2}%
+	\else
+		\pgfmathapproxequalto@{0.#1}{0.4771212547196}%
+		\ifpgfmathcomparison
+			\def\pgfmathresult{3}%
+		\else
+			\pgfmathapproxequalto@{0.#1}{0.6020599913279}%
+			\ifpgfmathcomparison
+				\def\pgfmathresult{4}%
+			\else
+				\pgfmathapproxequalto@{0.#1}{0.698970004}%
+				\ifpgfmathcomparison
+					\def\pgfmathresult{5}%
+				\else
+					\pgfmathapproxequalto@{0.#1}{0.7781512503}%
+					\ifpgfmathcomparison
+						\def\pgfmathresult{6}%
+					\else
+						\pgfmathapproxequalto@{0.#1}{0.8450980400}%
+						\ifpgfmathcomparison
+							\def\pgfmathresult{7}%
+						\else
+							\pgfmathapproxequalto@{0.#1}{0.9030899869}%
+							\ifpgfmathcomparison
+								\def\pgfmathresult{8}%
+							\else
+								\pgfmathapproxequalto@{0.#1}{0.954242509439}%
+								\ifpgfmathcomparison
+									\def\pgfmathresult{9}%
+								\else
+									\pgfplots@log@tick@isminor@tick@posfalse
+								\fi
+							\fi
+						\fi
+					\fi
+				\fi
+			\fi
+		\fi
+	\fi
+}
+
+
+\def\pgfplots@set@at#1{\def\pgfplots@at{#1}}%
+
+
+
+% converts a comma-separated list (PGF foreach)  to my internal list
+% structure.
+\long\def\pgfplots@foreach@to@list#1\to#2{%
+	\pgfplotslistnewempty\pgfplots@TMP
+	\begingroup
+	\foreach \i in {#1} {%
+		\globaldefs=1
+		\expandafter\pgfplotslistpushback\i\to\pgfplots@TMP
+		\globaldefs=0
+	}%
+	\endgroup
+	\pgfplotslistcopy\pgfplots@TMP\to#2\relax
+}
+
+% Several tick options:
+\long\def\axispreset#1{%
+	\pgfplotsset{every axis/.append style={#1}}%
+}
+\long\def\legendpreset#1{%
+	\pgfplots@error{Sorry, legendpreset is now deprecated, along with the legend options text width and font. Legends are now TikZ-matrizes which provide better alignment and can be placed horizontally. See the manual for details.}%
+}
+
+% Checks whether we need to create a separate 'tick scale label',
+% a node with ' * 10^3' on the side of the axis:
+%
+% PRECONDITION:
+%    Axis limits for #1 are given. I need their values before any data
+%    scale transformation has been applied.
+%    If  
+%    	\pgfplots@#1min@unscaled@as@float 
+%    and
+%    	\pgfplots@#1max@unscaled@as@float 
+%    exist; I will use these macros.
+%    Otherwise, I will use \pgfplots@#1min and \pgfplots@#1max;
+%    assuming that no data scale transformation is active.
+%    FIXME : does that need further attention?
+\def\pgfplots@init@scaled@tick@for#1{%
+	\begingroup
+	% the \pgfplots@xmin@unscaled@as@float  is set just before the data
+	% scale transformation is initialised.
+	%
+	% The variables are empty if there is no datascale transformation.
+	\expandafter\let\expandafter\pgfplots@cur@min@unscaled\csname pgfplots@#1min@unscaled@as@float\endcsname
+	\expandafter\let\expandafter\pgfplots@cur@max@unscaled\csname pgfplots@#1max@unscaled@as@float\endcsname
+	%
+	\ifx\pgfplots@cur@min@unscaled\pgfutil@empty
+		\xdef\pgfplots@TMP{\csname pgfplots@#1min\endcsname}%
+		\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@TMP}%
+		\let\pgfplots@cur@min@unscaled=\pgfmathresult
+		\xdef\pgfplots@TMP{\csname pgfplots@#1max\endcsname}%
+		\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@TMP}%
+		\let\pgfplots@cur@max@unscaled=\pgfmathresult
+	\fi
+	%
+	\expandafter\pgfmathfloat@decompose@E\pgfplots@cur@min@unscaled\relax\pgfmathfloat@a@E
+	\expandafter\pgfmathfloat@decompose@E\pgfplots@cur@max@unscaled\relax\pgfmathfloat@b@E
+	\ifnum\pgfmathfloat@b@E<\pgfmathfloat@a@E
+		\pgfmathfloat@b@E=\pgfmathfloat@a@E
+	\fi
+	\xdef\pgfplots@TMP{\pgfplots@scale@ticks@above@exponent}%
+	\expandafter\ifnum\pgfplots@TMP<\pgfmathfloat@b@E
+		% ok, scale it:
+		\multiply\pgfmathfloat@b@E by-1
+		\xdef\pgfplots@TMP{\the\pgfmathfloat@b@E}%
+	\else
+		\xdef\pgfplots@TMP{\pgfplots@scale@ticks@below@exponent}%
+		\expandafter\ifnum\pgfplots@TMP>\pgfmathfloat@b@E
+			% ok, scale it:
+			\multiply\pgfmathfloat@b@E by-1
+			\xdef\pgfplots@TMP{\the\pgfmathfloat@b@E}%
+		\else
+			% no scaling necessary:
+			\xdef\pgfplots@TMP{0}%
+		\fi
+	\fi
+	\endgroup
+	\expandafter\let\csname pgfplots@tick@scale@#1\endcsname=\pgfplots@TMP%
+}
+
+% x-axis tick labels for #1th tick
+% #1: options
+% #2: the axis (x or y)
+% #3: the value
+% #4,#5: coordinates for tikz
+% #6: ticknumber
+\def\pgfplots@show@ticklabel[#1]#2#3(#4,#5)#6{{%
+	\csname ifpgfplots@#2ticklabel@interval\endcsname
+		\pgfmathparse{#4}%
+		\edef\pgfplots@show@ticklabel@coord@x@new{\pgfmathresult pt}%
+		\pgfmathparse{#5}%
+		\edef\pgfplots@show@ticklabel@coord@y@new{\pgfmathresult pt}%
+		%
+		\pgfplots@show@ticklabel@{#2}{#3}%
+		\let\nexttick=\tick
+		\ifx\pgfplots@show@ticklabel@LASTTICK\pgfutil@empty
+			% its the first call. Simply remember arguments and wait
+			% for interval boundary before proceeding.
+		\else
+			% acquire options of first interval boundary:
+			\pgfplots@show@ticklabel@LASTTICK
+			% compute new node position:
+			\pgfmathparse{0.5*(\csname pgfplots@show@ticklabel@coord@#2\endcsname + \csname pgfplots@show@ticklabel@coord@#2@new\endcsname)}%
+			\expandafter\edef\csname pgfplots@show@ticklabel@coord@#2\endcsname{\pgfmathresult pt}%
+			\let\ticknum=\pgfplots@show@ticklabel@num\relax%
+			\let\tick=\pgfplots@show@ticklabel@tick%
+			\pgfplots@toka=\expandafter{\pgfplots@show@ticklabel@opts}%
+			\xdef\pgfplots@TMP{at (\pgfplots@show@ticklabel@coord@x,\pgfplots@show@ticklabel@coord@y) [\the\pgfplots@toka]}%
+			\expandafter\node\pgfplots@TMP
+				{\csname pgfplots@#2ticklabel\endcsname};%
+		\fi
+		\xdef\pgfplots@show@ticklabel@LASTTICK{%
+			\noexpand\def\noexpand\pgfplots@show@ticklabel@opts{#1}%
+			\noexpand\def\noexpand\pgfplots@show@ticklabel@tick{\nexttick}%
+			\noexpand\def\noexpand\pgfplots@show@ticklabel@coord@x{\pgfplots@show@ticklabel@coord@x@new}%
+			\noexpand\def\noexpand\pgfplots@show@ticklabel@coord@y{\pgfplots@show@ticklabel@coord@y@new}%
+			\noexpand\def\noexpand\pgfplots@show@ticklabel@num{\the#6}%
+		}%
+	\else
+		\let\ticknum=#6\relax%
+		\pgfplots@show@ticklabel@{#2}{#3}%
+		\node at (#4,#5) [#1] {\csname pgfplots@#2ticklabel\endcsname};%
+	\fi
+}}
+
+% Defines \tick by applying any necessary math to the (possibly
+% transformed) tick value #2.
+%
+% #1: axis (x or y)
+% #2: tick value.
+\def\pgfplots@show@ticklabel@#1#2{%
+	\csname ifpgfplots@apply@datatrafo@#1\endcsname
+		\csname pgfplots@inverse@datascaletrafo@#1\endcsname{#2}%
+		% FIXME: do that for any linear axis, also if no datascale is
+		% applied!
+		\ifpgfplots@scaled@ticks
+			\expandafter\pgfmathfloatshift@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
+		\fi
+		% .. and this here provides \tick as fixed point repr:
+		\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+		\let\tick=\pgfmathresult
+	\else
+		\edef\tick{#2}%
+	\fi
+}%
+
+\def\pgfplots@user@ticklabel@list@x{%
+	\pgfplotslistselect\ticknum\of\pgfplots@xticklabels\to\tick
+	\tick
+}
+\def\pgfplots@user@ticklabel@list@y{%
+	\pgfplotslistselect\ticknum\of\pgfplots@yticklabels\to\tick
+	\tick
+}
+\def\pgfplots@user@extra@ticklabel@list@x{%
+	\pgfplotslistselect\ticknum\of\pgfplots@extra@xticklabels\to\tick
+	\tick
+}
+\def\pgfplots@user@extra@ticklabel@list@y{%
+	\pgfplotslistselect\ticknum\of\pgfplots@extra@yticklabels\to\tick
+	\tick
+}
+
+\def\axisdefaultticklabel{%
+	$\pgfmathprintnumber{\tick}$%
+}
+
+\def\axisdefaultticklabellog{%
+	\pgfkeysgetvalue{/pgfplots/log number format code/.@cmd}\pgfplots@log@label@style
+	\expandafter\pgfplots@log@label@style\tick\pgfeov
+}
+	
+
+\def\pgfplots@show@label#1{%
+	\node 
+		[/pgfplots/every axis label,%
+		/pgfplots/every axis #1 label]
+	{\csname pgfplots@#1label\endcsname};
+}
+
+\def\pgfplots@show@title{%
+	\node%
+		[/pgfplots/every axis title]
+		{\pgfplots@title};
+}
+
+% Check if a label does not cross the x-axis
+\def\pgfplots@ytick@check@tickshow{%
+	\pgfplots@tickshowtrue
+	\ifnum\pgfplots@yaxislinesnum=2\relax
+		\ifcase\pgfplots@xaxislinesnum\relax
+			\ifdim\pgfplots@tmpa=\pgfplots@ycoordminTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+			\ifdim\pgfplots@tmpa=\pgfplots@ycoordmaxTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@ycoordminTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@ZERO@y\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@ycoordmaxTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\fi
+	\fi
+}
+
+\def\pgfplots@drawyaxis@placecomputedtick#1[#2]{%
+	\ifcase\pgfplots@ytickalignnum\relax
+		\def\pgfplots@ytick@offset{0pt}
+	\or
+		\def\pgfplots@ytick@offset{#1}
+	\or
+		\def\pgfplots@ytick@offset{.5*#1}
+	\fi
+	%\pgfplots@ytick@check@tickshow
+	%\ifpgfplots@tickshow
+		\draw[#2]
+		\ifcase\pgfplots@ytickposnum
+			(\pgfplots@xcoordminTEX-\pgfplots@ytick@offset, \pgfplots@tmpa) -- ++( #1, 0pt)
+
+			(\pgfplots@xcoordmaxTEX+\pgfplots@ytick@offset, \pgfplots@tmpa)	-- ++(-#1, 0pt)
+		\or
+			(\pgfplots@xcoordminTEX-\pgfplots@ytick@offset, \pgfplots@tmpa) -- ++( #1, 0pt)
+		\or
+			(\pgfplots@ZERO@x      -\pgfplots@ytick@offset, \pgfplots@tmpa) -- ++( #1, 0pt)
+		\or
+			(\pgfplots@xcoordmaxTEX+\pgfplots@ytick@offset, \pgfplots@tmpa)	-- ++(-#1, 0pt)
+		\fi
+		;
+	%\fi
+}%
+\def\pgfplots@drawyaxis@placecomputedgridline[#1]{%
+	\draw[#1]
+		(\pgfplots@xcoordminTEX\pgfplots@leftover,	\pgfplots@tmpa)
+	--	(\pgfplots@xcoordmaxTEX\pgfplots@rightover,	\pgfplots@tmpa)
+	;
+}%
+
+% Y-Achsen und Achsenbeschriftung LOG:
+% 1: Ticks
+\newif\ifpgfplots@needsminorloop
+\def\pgfplots@drawyaxis#1{%
+	\ifpgfplots@yislinear
+		\ifpgfplots@scaled@ticks
+			\pgfplots@init@scaled@tick@for y%
+		\fi
+	\fi
+	\begingroup
+	\global\pgfplots@ticknum=0
+	\edef\pgfplots@TMP{#1}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\ifpgfplots@yminorticks
+			\pgfplots@needsminorlooptrue
+		\fi
+		\ifpgfplots@yminorgrids
+			\pgfplots@needsminorlooptrue
+		\fi
+		\ifpgfplots@needsminorloop
+			\ifpgfplots@yislinear
+				\begingroup
+				\c@pgf@counta=\pgfplots@minor@ytick@num\relax
+				\advance\c@pgf@counta by1\relax
+				\pgfplots@tmpb=\pgfplots@tick@distance@y pt
+				\divide\pgfplots@tmpb by\c@pgf@counta
+				\edef\pgfmathresult{\pgf@sys@tonumber{\pgfplots@tmpb}}%
+				\pgfmath@smuggleone\pgfmathresult
+				\endgroup
+				\let\pgfplots@minor@tick@dist=\pgfmathresult
+			\else
+				\def\pgfplots@minor@ytick@num{9}%
+			\fi
+		\fi
+		\xdef\pgfplots@show@ticklabel@LASTTICK{}%
+		\foreach \y in {#1} {	
+			\pgfextracty{\pgfplots@tmpa}{\pgfpointxy{0}{\y}}%
+			\pgfplots@ytick@check@tickshow
+			%
+			\ifpgfplots@tickshow
+				\ifdim\pgfplots@tmpa<\pgfplots@ycoordminTEX
+				\else
+					\ifdim\pgfplots@tmpa>\pgfplots@ycoordmaxTEX
+					\else
+						\ifcase\pgfplots@ytickalignnum\relax
+							\def\pgfplots@ytick@offset{0pt}%
+						\or
+							\def\pgfplots@ytick@offset{\pgfplots@tickwidth}%
+						\or
+							\def\pgfplots@ytick@offset{.5*\pgfplots@tickwidth}%
+						\fi
+						\ifcase\pgfplots@ytickposnum
+							\def\pgfplots@ytick@origin{\pgfplots@xcoordminTEX}%
+						\or
+							\def\pgfplots@ytick@origin{\pgfplots@xcoordminTEX}%
+						\or
+							\def\pgfplots@ytick@origin{\pgfplots@ZERO@x}%
+						\or
+							\def\pgfplots@ytick@origin{\pgfplots@xcoordmaxTEX}%
+						\fi
+						% Axis tick labels:`
+						\ifnum\pgfplots@ytickposnum=3\relax
+							\pgfplots@show@ticklabel
+								[right,/pgfplots/every tick label,/pgfplots/every y tick label]%
+								{y}{\y}%
+								(\pgfplots@ytick@origin+\pgfplots@ytick@offset,\pgfplots@tmpa)%
+								{\pgfplots@ticknum}%
+						\else
+							\pgfplots@show@ticklabel
+								[left,/pgfplots/every tick label,/pgfplots/every y tick label]%
+								{y}{\y}%
+								(\pgfplots@ytick@origin-\pgfplots@ytick@offset,\pgfplots@tmpa)%
+								{\pgfplots@ticknum}%
+						\fi
+					\fi
+				\fi
+			\fi
+			\global\advance\pgfplots@ticknum by1
+			\scope
+			%\clip 			(\pgfplots@xcoordminTEX\pgfplots@leftover,	\pgfplots@ycoordminTEX\pgfplots@leftover) 
+			%	rectangle	(\pgfplots@xcoordmaxTEX\pgfplots@rightover,	\pgfplots@ycoordmaxTEX\pgfplots@rightover);
+			\pgfinterruptboundingbox%
+			\clip 			(\pgfplots@xcoordminTEX-5cm,	\pgfplots@ycoordminTEX) 
+				rectangle	(\pgfplots@xcoordmaxTEX+5cm,	\pgfplots@ycoordmaxTEX);
+			\endpgfinterruptboundingbox%
+			% Y-ticks left and/or right
+			% in log:
+			%  log( i*10^k ) = log\i + k\log10 -> draw ticks for i=1..9
+			\ifpgfplots@needsminorloop
+				\foreach \i in {1,...,\pgfplots@minor@ytick@num} {
+					% this code here is scoped inside of \foreach.
+					\ifpgfplots@yislinear
+						\pgfextracty{\pgfplots@tmpb}{\pgfpointxy{0}{\i*\pgfplots@minor@tick@dist}}%
+					\else
+						\pgfextracty{\pgfplots@tmpb}{\pgfpointxy{0}{\logi\i}}%
+					\fi
+					\advance\pgfplots@tmpa by\pgfplots@tmpb
+					\ifdim\pgfplots@tmpa<\pgfplots@ycoordminTEX
+					\else
+						\ifdim\pgfplots@tmpa>\pgfplots@ycoordmaxTEX
+						\else
+							\ifpgfplots@yminorgrids
+								\pgfplots@drawyaxis@placecomputedgridline[/pgfplots/every axis grid,/pgfplots/every minor grid,/pgfplots/every axis y grid,/pgfplots/every minor y grid]%
+							\fi
+							\ifpgfplots@yminorticks
+								\pgfplots@drawyaxis@placecomputedtick\pgfplots@subtickwidth[/pgfplots/every tick,/pgfplots/every minor tick,/pgfplots/every tick,/pgfplots/every minor y tick]%
+							\fi
+						\fi
+					\fi
+				}%
+			\fi
+			\ifdim\pgfplots@tmpa<\pgfplots@ycoordminTEX
+			\else
+				\ifdim\pgfplots@tmpa>\pgfplots@ycoordmaxTEX
+				\else
+					\ifpgfplots@ymajorgrids
+						\pgfplots@drawyaxis@placecomputedgridline[/pgfplots/every axis grid,/pgfplots/every major grid, /pgfplots/every axis y grid,/pgfplots/every major y grid]%
+					\fi
+					\ifpgfplots@tickshow
+						\ifpgfplots@ymajorticks
+							\pgfplots@drawyaxis@placecomputedtick\pgfplots@tickwidth[/pgfplots/every tick,/pgfplots/every major tick,/pgfplots/every y tick,/pgfplots/every major y tick]%
+						\fi
+					\fi
+				\fi
+			\fi
+			\endscope
+		}%
+	\fi
+	\pgfplots@draw@tick@scale@label@for y%
+	\endgroup
+}
+
+\def\pgfplots@draw@tick@scale@label@for#1{%
+	\csname ifpgfplots@#1islinear\endcsname
+		\ifpgfplots@scaled@ticks
+			\begingroup
+				\xdef\pgfplots@TMP{\csname pgfplots@tick@scale@#1\endcsname}%
+				\expandafter\c@pgf@counta\pgfplots@TMP\relax
+				\multiply\c@pgf@counta by-1
+				\ifnum\c@pgf@counta=0\relax
+					\global\let\pgfplots@TMP=\pgfutil@empty
+				\else
+					\xdef\pgfplots@TMP{\the\c@pgf@counta}%
+				\fi
+			\endgroup
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\edef\pgfplots@tick@scale@labels{\noexpand\pgfplots@invoke@pgfkeyscode{/pgfplots/tick scale label code/.@cmd}{\pgfplots@TMP}}%
+				\node 
+					[%
+					xshift=\pgfplots@xcoordminTEX,%
+					yshift=\pgfplots@ycoordminTEX,%
+					x=\pgfplots@xcoordmaxTEX-\pgfplots@xcoordminTEX,%
+					y=\pgfplots@ycoordmaxTEX-\pgfplots@ycoordminTEX,%
+					/pgfplots/every tick label,%
+					/pgfplots/every #1 tick label,%
+					/pgfplots/every #1 tick scale label]
+				{\pgfplots@tick@scale@labels};
+			\fi
+		\fi
+	\fi
+}
+
+% Simply invokes the code of PGF key #1 with value #2, that means
+% #1#2\pgfeov
+\def\pgfplots@invoke@pgfkeyscode#1#2{%
+	\pgfkeysgetvalue{#1}\pgfplots@invoke@pgfkeyscode@CODE
+	\pgfplots@invoke@pgfkeyscode@CODE#2\pgfeov
+}
+
+% Check if it does not cross the y-axis
+\def\pgfplots@xtick@check@tickshow{%
+	\pgfplots@tickshowtrue
+	\ifnum\pgfplots@xaxislinesnum=2\relax
+		\ifcase\pgfplots@yaxislinesnum\relax
+			\ifdim\pgfplots@tmpa=\pgfplots@xcoordminTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+			\ifdim\pgfplots@tmpa=\pgfplots@xcoordmaxTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@xcoordminTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@ZERO@x\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\or
+			\ifdim\pgfplots@tmpa=\pgfplots@xcoordmaxTEX\relax
+				\pgfplots@tickshowfalse
+			\fi
+		\fi
+	\fi
+}
+
+\def\pgfplots@drawxaxis@placecomputedtick#1[#2]{%
+	\ifcase\pgfplots@xtickalignnum\relax
+		\def\pgfplots@xtick@offset{0pt}
+	\or
+		\def\pgfplots@xtick@offset{#1}
+	\or
+		\def\pgfplots@xtick@offset{.5*#1}
+	\fi
+	%\pgfplots@xtick@check@tickshow
+	%\ifpgfplots@tickshow
+		\draw[#2]
+		\ifcase\pgfplots@xtickposnum
+			(\pgfplots@tmpa, \pgfplots@ycoordminTEX-\pgfplots@xtick@offset) -- ++(0pt, #1)
+			
+			(\pgfplots@tmpa, \pgfplots@ycoordmaxTEX+\pgfplots@xtick@offset) -- ++(0pt,-#1)
+		\or
+			(\pgfplots@tmpa, \pgfplots@ycoordminTEX-\pgfplots@xtick@offset) -- ++(0pt, #1)
+		\or
+			(\pgfplots@tmpa, \pgfplots@ZERO@y      -\pgfplots@xtick@offset) -- ++(0pt, #1)
+		\or
+			(\pgfplots@tmpa, \pgfplots@ycoordmaxTEX+\pgfplots@xtick@offset) -- ++(0pt,-#1)
+		\fi
+		;
+	%\fi
+}%
+\def\pgfplots@drawxaxis@placecomputedgridline[#1]{%
+	\draw[#1]
+		(\pgfplots@tmpa,	\pgfplots@ycoordminTEX\pgfplots@leftover)
+	--	(\pgfplots@tmpa,	\pgfplots@ycoordmaxTEX\pgfplots@rightover)
+	;
+}%
+
+% #1: axis (x or y)
+% #2: tick position list
+\def\pgfplots@draw@extra@ticks@for#1#2{%
+	\begingroup
+	\edef\pgfplots@TMP{#2}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\pgfplots@scaled@ticksfalse
+		\csname pgfplots@#1minorticksfalse\endcsname
+		\csname pgfplots@#1minorgridsfalse\endcsname
+		\expandafter\let\expandafter\axis@TMP\csname pgfplots@extra@#1ticklabel\endcsname
+		\expandafter\let\csname pgfplots@#1ticklabel\endcsname=\axis@TMP
+		% FIXME: that search path - thing is far from perfect.
+		% In fact, it doesn't even work for choice keys... with
+		% unexpected results.
+		% I have fixed that in PGF CVS - but PGF 2.0 does not yet work
+		% here!
+		\pgfqkeys{/pgfplots/search path for tikz}{/pgfplots/every extra #1 tick}%
+		\csname pgfplots@draw#1axis\endcsname{#2}%
+	\fi
+	\endgroup
+}
+
+\def\pgfplots@drawaxis@innerlines{%
+	\ifnum\pgfplots@yaxislinesnum=2
+		\draw[decorate,ydiscont,decoration={pre length=\ydisstart, post length=\ydisend}] (\pgfplots@ZERO@x,	\pgfplots@ycoordminTEX) -- (\pgfplots@ZERO@x,	\pgfplots@ycoordmaxTEX);
+	\fi
+	\ifnum\pgfplots@xaxislinesnum=2
+		\draw[decorate,xdiscont,decoration={pre length=\xdisstart, post length=\xdisend}] (\pgfplots@xcoordminTEX, \pgfplots@ZERO@y) -- (\pgfplots@xcoordmaxTEX, \pgfplots@ZERO@y);
+	\fi
+}%
+
+\def\pgfplots@drawaxis@outerlines{%
+	\draw
+	(\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX)
+ 	\ifcase\pgfplots@yaxislinesnum
+	    decorate [ydiscont,decoration={pre length=\ydisstart, post length=\ydisend}] { -- (\pgfplots@xcoordminTEX,	\pgfplots@ycoordmaxTEX) }
+	\or decorate [ydiscont,decoration={pre length=\ydisstart, post length=\ydisend}] { -- (\pgfplots@xcoordminTEX,	\pgfplots@ycoordmaxTEX) }
+	\or { (\pgfplots@xcoordminTEX,	\pgfplots@ycoordmaxTEX) }
+	\or { (\pgfplots@xcoordminTEX,	\pgfplots@ycoordmaxTEX) }
+	\fi
+	\ifcase\pgfplots@xaxislinesnum
+	    decorate [xdiscont,decoration={pre length=\xdisstart, post length=\xdisend}] { -- (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX) }
+	\or { (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX) }
+	\or { (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX) }
+	\or decorate [xdiscont,decoration={pre length=\xdisstart, post length=\xdisend}] { -- (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX) }
+	\fi
+	\ifcase\pgfplots@yaxislinesnum
+	    decorate [ydiscont,decoration={pre length=\ydisend, post length=\ydisstart}] { -- (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordminTEX) }
+	\or { (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordminTEX) }
+	\or { (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordminTEX) }
+	\or decorate [ydiscont,decoration={pre length=\ydisend, post length=\ydisstart}] { -- (\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordminTEX) }
+	\fi
+	\ifcase\pgfplots@xaxislinesnum
+	    decorate [xdiscont,decoration={pre length=\xdisend, post length=\xdisstart}] { -- (\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX) }
+	\or decorate [xdiscont,decoration={pre length=\xdisend, post length=\xdisstart}] { -- (\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX) }
+	\or { (\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX) }
+	\or { (\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX) }
+	\fi
+	; %	-- cycle;
+}%
+
+\def\pgfplots@drawaxis@lines{%
+	\begingroup
+	\begingroup
+	% this group employs several temporary dimension registers
+	% and is therefor scoped:
+	\let\ydisstart=\pgf@xa
+	\let\ydisend=\pgf@xb
+	\let\xdisstart=\pgf@ya
+	\let\xdisend=\pgf@yb
+	\ydisend=\pgfplots@ycoordmaxTEX
+	\advance \ydisend by -\pgfplots@ycoordminTEX
+	\ifcase\pgfplots@yaxisdiscontnum\relax
+		\let\ydiscontstyle=\pgfutil@empty
+	\or
+		\def\ydiscontstyle{decoration={zigzag,segment length=12pt, amplitude=4pt}}%
+		\advance \ydisend by -16pt
+	\or
+		\def\ydiscontstyle{decoration={ticks,segment length=4pt, amplitude=8pt}}%
+		\advance \ydisend by -8pt
+	\fi
+	\ifpgfplots@apply@datatrafo@y
+		\advance \pgfplots@ycoordmaxTEX by\pgfplots@data@scale@trafo@SHIFT@y pt
+	\fi
+	\ifdim\pgfplots@ycoordmaxTEX<0pt
+		\ydisstart=\ydisend
+		\ydisend=4pt
+	\else
+		\ydisstart=4pt
+	\fi
+	\ifpgfplots@apply@datatrafo@y
+		\advance \pgfplots@ycoordmaxTEX by-\pgfplots@data@scale@trafo@SHIFT@y pt
+	\fi
+	\xdisend=\pgfplots@xcoordmaxTEX
+	\advance \xdisend by -\pgfplots@xcoordminTEX
+	\ifcase\pgfplots@xaxisdiscontnum\relax
+		\let\xdiscontstyle=\pgfutil@empty
+	\or
+		\def\xdiscontstyle{decoration={zigzag,segment length=12pt, amplitude=4pt}}%
+		\advance \xdisend by -16pt
+	\or
+		\def\xdiscontstyle{decoration={ticks,segment length=4pt, amplitude=8pt}}%
+		\advance \xdisend by -8pt
+	\fi
+	\ifpgfplots@apply@datatrafo@x
+		\advance \pgfplots@xcoordmaxTEX by\pgfplots@data@scale@trafo@SHIFT@x pt
+	\fi
+	\ifdim\pgfplots@xcoordmaxTEX<0pt
+		\xdisstart=\xdisend
+		\xdisend=4pt
+	\else
+		\xdisstart=4pt
+	\fi
+	\ifpgfplots@apply@datatrafo@x
+		\advance \pgfplots@xcoordmaxTEX by-\pgfplots@data@scale@trafo@SHIFT@x pt
+	\fi
+	% carry local computations outside of group:
+	\xdef\pgfplots@TMP{%
+		\noexpand\def\noexpand\xdisstart{\the\xdisstart}%
+		\noexpand\def\noexpand\xdisend{\the\xdisend}%
+		\noexpand\def\noexpand\ydisstart{\the\ydisstart}%
+		\noexpand\def\noexpand\ydisend{\the\ydisend}%
+		\noexpand\pgfkeys{%
+			/tikz/xdiscont/.style={\xdiscontstyle},%
+			/tikz/ydiscont/.style={\ydiscontstyle}}%
+	}%
+	\endgroup
+	\pgfplots@TMP
+	\pgfplots@drawaxis@outerlines%
+	\pgfplots@drawaxis@innerlines%
+	\endgroup
+}%
+
+% X-Achsen und Achsenbeschriftung 
+% 1: Ticks
+\def\pgfplots@drawxaxis#1{%
+	\ifpgfplots@xislinear
+		\ifpgfplots@scaled@ticks
+			\pgfplots@init@scaled@tick@for{x}%
+		\fi
+	\fi
+	\begingroup
+	\global\pgfplots@ticknum=0
+	\edef\pgfplots@TMP{#1}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\ifpgfplots@xminorticks
+			\pgfplots@needsminorlooptrue
+		\fi
+		\ifpgfplots@xminorgrids
+			\pgfplots@needsminorlooptrue
+		\fi
+		\ifpgfplots@needsminorloop
+			\ifpgfplots@xislinear
+				\begingroup
+				\c@pgf@counta=\pgfplots@minor@xtick@num\relax
+				\advance\c@pgf@counta by1\relax
+				\pgfplots@tmpb=\pgfplots@tick@distance@x pt
+				\divide\pgfplots@tmpb by\c@pgf@counta
+				\edef\pgfmathresult{\pgf@sys@tonumber{\pgfplots@tmpb}}%
+				\pgfmath@smuggleone\pgfmathresult
+				\endgroup
+				\let\pgfplots@minor@tick@dist=\pgfmathresult
+			\else
+				\def\pgfplots@minor@xtick@num{9}%
+			\fi
+		\fi
+		\xdef\pgfplots@show@ticklabel@LASTTICK{}%
+		\foreach \x in {#1} {	
+			\pgfextractx{\pgfplots@tmpa}{\pgfpointxy{\x}{0}}%
+			\pgfplots@xtick@check@tickshow
+			%
+			\ifpgfplots@tickshow
+				\ifdim\pgfplots@tmpa<\pgfplots@xcoordminTEX
+				\else
+					\ifdim\pgfplots@tmpa>\pgfplots@xcoordmaxTEX
+					\else
+						\ifcase\pgfplots@xtickalignnum\relax
+							\def\pgfplots@xtick@offset{0pt}
+						\or
+							\def\pgfplots@xtick@offset{\pgfplots@tickwidth}
+						\or
+							\def\pgfplots@xtick@offset{.5*\pgfplots@tickwidth}
+						\fi
+						\ifcase\pgfplots@xtickposnum
+							\def\pgfplots@xtick@origin{\pgfplots@ycoordminTEX}
+						\or
+							\def\pgfplots@xtick@origin{\pgfplots@ycoordminTEX}
+						\or
+							\def\pgfplots@xtick@origin{\pgfplots@ZERO@y}
+						\or
+							\def\pgfplots@xtick@origin{\pgfplots@ycoordmaxTEX}
+						\fi
+						% Axis tick labels:
+						\ifnum\pgfplots@xtickposnum=3
+							\pgfplots@show@ticklabel
+								[above,/pgfplots/every tick label,/pgfplots/every x tick label]%
+								{x}{\x}(\pgfplots@tmpa,\pgfplots@xtick@origin+\pgfplots@xtick@offset)%
+								{\pgfplots@ticknum}%
+						\else
+							\pgfplots@show@ticklabel
+								[below,/pgfplots/every tick label,/pgfplots/every x tick label]%
+								{x}{\x}(\pgfplots@tmpa,\pgfplots@xtick@origin-\pgfplots@xtick@offset)%
+								{\pgfplots@ticknum}%
+						\fi
+					\fi
+				\fi
+			\fi
+			\global\advance\pgfplots@ticknum by1
+			%
+			\scope
+			%\clip 			(\pgfplots@xcoordminTEX\pgfplots@leftover,	\pgfplots@ycoordminTEX\pgfplots@leftover) 
+			%	rectangle	(\pgfplots@xcoordmaxTEX\pgfplots@rightover,	\pgfplots@ycoordmaxTEX\pgfplots@rightover);
+			\pgfinterruptboundingbox%
+			\clip 			(\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX-5cm) 
+				rectangle	(\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX+5cm);
+			\endpgfinterruptboundingbox%
+			% X-Axis ticks bottom and top
+			% in log:
+			%  log( i*10^k ) = log\i + k\log10 -> draw ticks for i=1..9
+			\ifpgfplots@needsminorloop
+				\foreach \i in {1,...,\pgfplots@minor@xtick@num} {
+	%				\pgfextractx{\pgfplots@tmpb}{\pgfpointxy{\logi\i}{0}}%
+					\ifpgfplots@xislinear
+						\pgfextractx{\pgfplots@tmpb}{\pgfpointxy{\i*\pgfplots@minor@tick@dist}{0}}%
+					\else
+						\pgfextractx{\pgfplots@tmpb}{\pgfpointxy{\logi\i}{0}}%
+					\fi
+					\advance\pgfplots@tmpa by\pgfplots@tmpb
+					\ifdim\pgfplots@tmpa<\pgfplots@xcoordminTEX
+					\else
+						\ifdim\pgfplots@tmpa>\pgfplots@xcoordmaxTEX
+						\else
+							\ifpgfplots@xminorgrids
+								\pgfplots@drawxaxis@placecomputedgridline[/pgfplots/every axis grid,/pgfplots/every minor grid]%
+							\fi
+							\ifpgfplots@xminorticks
+								\pgfplots@drawxaxis@placecomputedtick\pgfplots@subtickwidth[/pgfplots/every tick,/pgfplots/every minor tick,/pgfplots/every x tick,/pgfplots/every minor x tick]%
+							\fi
+						\fi
+					\fi
+				}%
+			\fi
+			\ifdim\pgfplots@tmpa<\pgfplots@xcoordminTEX
+			\else
+				\ifdim\pgfplots@tmpa>\pgfplots@xcoordmaxTEX
+				\else
+					\ifpgfplots@xmajorgrids
+						\pgfplots@drawxaxis@placecomputedgridline[/pgfplots/every axis grid,/pgfplots/every major grid,/pgfplots/every axis x grid,/pgfplots/every major x grid]%
+					\fi
+					\ifpgfplots@tickshow
+						\ifpgfplots@xmajorticks
+							\pgfplots@drawxaxis@placecomputedtick\pgfplots@tickwidth[/pgfplots/every tick,/pgfplots/every major tick, /pgfplots/every x tick,/pgfplots/every major x tick]%
+						\fi
+					\fi
+				\fi
+			\fi
+			\endscope
+		}%
+	\fi
+	\pgfplots@draw@tick@scale@label@for x%
+	\endgroup
+}
+
+\def\pgfplots@rememberplotspec#1{%
+	\begingroup
+	\globaldefs=1
+	\pgfplotslistpushback#1\to\pgfplots@plotspeclist
+	\endgroup
+}
+
+\def\pgfplots@getautoplotspec into#1{%
+	\pgfplotslistsize\autoplotspeclist\to\c@pgf@counta
+	\ifnum\c@pgf@counta=0
+		\let#1=\pgfutil@empty
+	\else
+		\c@pgf@countb=\pgfplots@numplots
+		% offset modulo size:
+		\loop
+		\ifnum\c@pgf@countb<\c@pgf@counta
+			\pgfplots@loop@CONTINUEfalse
+		\else
+			\pgfplots@loop@CONTINUEtrue
+		\fi
+		\ifpgfplots@loop@CONTINUE
+			\advance\c@pgf@countb by-\c@pgf@counta
+		\repeat
+		\pgfplotslistselect\c@pgf@countb\of\autoplotspeclist\to#1
+%\pgfplots@message{pgfplots.sty: using \string\autoplotspeclist\ specification no\#\the\c@pgf@countb (of \the\c@pgf@counta): #1}%
+	\fi
+}
+
+% The main interface to draw a plot into an axis.
+%
+% Usage:
+% \addplot 
+% 	plot coordinates {
+% 		(0,0)
+% 		(1,1)
+% 	};
+% 
+% or
+%
+% \addplot[color=blue,mark=*]
+% 	plot coordinates {
+% 		(0,0)
+% 		(1,1)
+% 	};
+% 
+% The first syntax will use the next plot specification in the list
+% \autoplotspeclist
+% and the first will use blue color and * markers. 
+%
+% The linespec. will be used in the legend.
+%
+% Low-level implementation:
+%
+% \pgfplots@addplot 
+% \pgfplots@addplotimpl
+% \pgfplots@start@plot@with@options <--- \begingroup
+% ...
+% ... remember options GLOBALLY
+% ... update limits GLOBALLY
+% ... \pgfplots@addplot@enqueue@coords GLOBALLY
+% ...
+% \pgfplots@end@plot <--- \endgroup
+\long\def\pgfplots@addplot{%
+	\pgfutil@ifnextchar+{%
+		\pgfplots@getautoplotspec into\nextplotspec
+		\pgfplots@addplotimplAPPEND
+	}{%
+		\pgfutil@ifnextchar[{%
+			\pgfplots@addplotimpl%
+		}{%
+			\pgfplots@getautoplotspec into\nextplotspec
+			% the space after ']' is required here:
+			% FIXME: 
+			% - \addplot[]plot coordinates is NOT allowed!?
+			\expandafter\pgfplots@addplotimpl\expandafter[\nextplotspec]
+		}%
+	}%
+}
+
+\long\def\pgfplots@addplotimplAPPEND+[{%
+	\expandafter\pgfplots@addplotimpl\expandafter[\nextplotspec,
+}
+
+\long\def\pgfplots@addplotimpl[#1]{%
+	\pgfutil@ifnextchar p{%
+		\pgfplots@addplotimpl@plot{#1}%
+	}{%
+		\pgfplots@addplotimpl@plot{#1}plot
+	}%
+}
+
+\def\pgfplots@addplotimpl@plot#1plot{%
+	\pgfutil@ifnextchar[{%
+		\pgfplots@addplotimpl@plot@withoptions{#1}%
+	}{%
+		\pgfplots@addplotimpl@plot@withoptions{#1}[]%
+	}%
+}
+
+\def\pgfplots@addplotimpl@plot@withoptions#1[#2]{
+	\pgfplots@start@plot@with@options{#1}{#2}%
+	\pgfutil@ifnextchar c{%
+		\pgfplots@addplotimpl@coordinates{#1}plot 
+	}{%
+		\pgfutil@ifnextchar f{%
+			\pgfplots@addplotimpl@f{#1}%
+		}{%
+			\pgfutil@ifnextchar t{%
+				\pgfplots@addplotimpl@table{#1}%
+			}{%
+				\pgfutil@ifnextchar ({%
+					\pgfplots@addplotimpl@expression{#1}%
+				}{%
+					\pgfplots@error{Sorry, the supplied plot command is unknown or unsupported by pgfplots!}%
+				}%
+			}%
+		}%
+	}%
+}
+
+% Currently, plot expression is really inefficient:
+%
+% 1. it invokes the math parser to get all coordinates. Ok, that's
+% what one expects.
+%
+% 2. It collects the result into one large list instead of calling
+% pgfplots' stream methods. That's because \foreach encapsulates its
+% code in at least one TeX-group.
+%
+% 3. It processes the collected list; applying any floating point
+% parser routines - it does NOT know that any numbers are already in
+% TeX-precision!
+%
+% FIXME : configure pgfplots to finish the data scaling trafo! It's
+% perfectly ok if it is simply the identity!
+\long\def\pgfplots@addplotimpl@expression#1(#2,#3)#4;{%
+	\pgfplots@PREPARE@COORD@STREAM{#1}{#4}%
+	\edef\pgfplots@plot@data{\noexpand\foreach\expandafter\noexpand\tikz@plot@var in {\tikz@plot@samplesat}}%
+	\global\let\pgfplots@TMP=\pgfutil@empty
+	\pgfplots@plot@data{%
+		\pgfmathparse{#2}%
+		\let\pgfplots@current@point@x=\pgfmathresult
+		\pgfmathparse{#3}%
+		\let\pgfplots@current@point@y=\pgfmathresult
+		\pgfplots@toka=\expandafter{\pgfplots@TMP}%
+		\xdef\pgfplots@TMP{\the\pgfplots@toka(\pgfplots@current@point@x,\pgfplots@current@point@y)}%
+	}%
+	\expandafter\pgfplots@coord@stream@foreach\expandafter{\pgfplots@TMP}%
+}%
+
+\def\pgfplots@addplotimpl@expression@limits#1{%
+	%--------------------------------------------------
+	%FIXME
+	% \pgfkeysinstallkeyfilter{/pgf/key filters/equals}{/tikz/domain}%
+	% \pgfkeysinstallkeyfilterhandler{/pgf/key filter handlers/ignore}%
+	% \pgfqkeysfiltered
+	% 	{/tikz}%
+	% 	{#1}%
+	%-------------------------------------------------- 
+	\expandafter\pgfplots@addplotimpl@expression@limits@domain\tikz@plot@domain\relax
+}%
+
+\def\pgfplots@addplotimpl@expression@limits@domain#1:#2\relax{%
+	\ifpgfplots@autocompute@xlim
+		\ifpgfplots@float@numerics@mode@x
+			\pgfmathfloatparsenumber{#1}%
+			\let\pgfplots@current@point@x=\pgfmathresult
+			\pgfmathfloatmin{\pgfplots@xmin}{\pgfplots@current@point@x}%
+			\global\let\pgfplots@xmin=\pgfmathresult
+			\pgfmathfloatmax{\pgfplots@xmax}{\pgfplots@current@point@x}%
+			\global\let\pgfplots@xmax=\pgfmathresult
+			%
+			\pgfmathfloatparsenumber{#2}%
+			\let\pgfplots@current@point@x=\pgfmathresult
+			\pgfmathfloatmin{\pgfplots@xmin}{\pgfplots@current@point@x}%
+			\global\let\pgfplots@xmin=\pgfmathresult
+			\pgfmathfloatmax{\pgfplots@xmax}{\pgfplots@current@point@x}%
+			\global\let\pgfplots@xmax=\pgfmathresult
+		\else
+			\pgfmathmin{\pgfplots@xmin}{#1}%
+			\global\let\pgfplots@xmin=\pgfmathresult
+			\pgfmathmax{\pgfplots@xmax}{#1}%
+			\global\let\pgfplots@xmax=\pgfmathresult
+			\pgfmathmin{\pgfplots@xmin}{#2}%
+			\global\let\pgfplots@xmin=\pgfmathresult
+			\pgfmathmax{\pgfplots@xmax}{#2}%
+			\global\let\pgfplots@xmax=\pgfmathresult
+		\fi
+	\fi
+}
+
+\def\pgfplots@addplotimpl@f#1f{%
+	\pgfutil@ifnextchar i{\pgfplots@addplotimpl@file{#1}}{\pgfplots@addplotimpl@function{#1}}%
+}%
+
+\let\pgfplots@backupof@pgfplotxyfile=\pgfplotxyfile
+
+% #1: args of \addplot[...]
+% #2: file name
+% #3: trailing path commands until ';'
+\def\pgfplots@addplotimpl@function#1unction#2#3;{%
+	\def\tikz@plot@filename{\tikz@plot@prefix\tikz@plot@id}%  
+	\iftikz@plot@raw@gnuplot%
+		\def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{#2}}%
+	\else%
+		\iftikz@plot@parametric%   
+			\def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{%
+				set format "\%.7e";
+				set samples \tikz@plot@samples;
+				set parametric;
+				plot [t=\tikz@plot@domain] #2}}%
+		\else%
+			\def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{%
+				set format "\%.7e";
+				set samples \tikz@plot@samples;
+				plot [x=\tikz@plot@domain] #2}}%
+		\fi%
+	\fi%
+	\def\pgfplotxyfile{\pgfplots@addplotimpl@gnuplotresult{#1}{#3}}%
+	\tikz@plot@data
+	\let\pgfplotxyfile=\pgfplots@backupof@pgfplotxyfile
+}%
+
+\def\pgfplots@addplotimpl@gnuplotresult#1#2#3{%
+	\begingroup
+	\openin1=#3
+	\ifeof1
+		\pgfplots@error{Sorry, the gnuplot-result file '#3' could not be found. Maybe you need to enable the shell-escape feature? For pdflatex, this is '>> pdflatex -shell-escape'. You can also invoke '>> gnuplot #3' manually.}%
+		\aftergroup\pgfplots@loop@CONTINUEfalse
+	\else
+		\aftergroup\pgfplots@loop@CONTINUEtrue
+	\fi
+	\closein1
+	\endgroup
+	\ifpgfplots@loop@CONTINUE
+		\pgfplots@addplotimpl@file{#1}ile{#3}#2;%
+	\fi
+}
+
+\def\pgfplots@addplotimpl@file#1ile{%
+	\pgfplots@addplotimpl@table{#1}table[x index=0,y index=1,header=false]%
+}%
+
+\def\pgfplots@addplotimpl@table#1table{%
+	\pgfutil@ifnextchar[{%
+		\pgfplots@addplotimpl@table@getopts{#1}%
+	}{%
+		\pgfplots@addplotimpl@table@getopts{#1}[x index=0,y index=1]%
+	}%
+}%
+
+\def\pgfplots@addplotimpl@table@f#1#2from{%
+	\pgfplots@addplot@table@from@macrotrue
+	\pgfplots@addplotimpl@table@START{#1}{#2}%
+}
+
+\def\pgfplots@addplotimpl@table@getopts#1[#2]{%
+	\pgfutil@ifnextchar f{%
+		\pgfplots@addplotimpl@table@f{#1}{#2}%
+	}{%
+		\pgfplots@addplot@table@from@macrofalse
+		\pgfplots@addplotimpl@table@START{#1}{#2}%
+	}%
+}
+
+% #1: arguments to \addplot[...]
+% #2: arguments to table[...]
+% #3: the argument of plot table{...}
+% #4: trailing path arguments after plot table{...}#4;
+\long\def\pgfplots@addplotimpl@table@START#1#2#3#4;{%
+	\begingroup
+	\pgfplotstableset{#2}%
+	\ifpgfplots@addplot@table@from@macro
+		\pgfplotstablecopy#3\to\pgfplots@table
+	\else
+		\pgfplotstableread{#3} to \pgfplots@table
+	\fi
+	\ifx\pgfplots@plot@tbl@x\pgfutil@empty
+		\pgfplotstablegetcolumnbyindex\pgfplots@plot@tbl@xindex\of\pgfplots@table\to\addplot@tbl@x
+	\else
+		\pgfplotstablegetcolumnbyname\pgfplots@plot@tbl@x\of\pgfplots@table\to\addplot@tbl@x
+	\fi
+	\ifx\pgfplots@plot@tbl@y\pgfutil@empty
+		\pgfplotstablegetcolumnbyindex\pgfplots@plot@tbl@yindex\of\pgfplots@table\to\addplot@tbl@y
+	\else
+		\pgfplotstablegetcolumnbyname\pgfplots@plot@tbl@y\of\pgfplots@table\to\addplot@tbl@y
+	\fi
+	%
+	\ifpgfplots@errorbars@enabled
+		\let\addplot@tbl@error@x=\pgfutil@empty
+		\let\addplot@tbl@error@y=\pgfutil@empty
+		\pgfkeysgetvalue{/pgfplots/table/x error index}\pgfplots@plot@tbl@error@xindex
+		\pgfkeysgetvalue{/pgfplots/table/x error}\pgfplots@plot@tbl@error@x
+		\pgfkeysgetvalue{/pgfplots/table/y error index}\pgfplots@plot@tbl@error@yindex
+		\pgfkeysgetvalue{/pgfplots/table/y error}\pgfplots@plot@tbl@error@y
+		\ifx\pgfplots@plot@tbl@error@x\pgfutil@empty
+			\ifx\pgfplots@plot@tbl@error@xindex\pgfutil@empty
+			\else
+				\pgfplotstablegetcolumnbyindex\pgfplots@plot@tbl@error@xindex\of\pgfplots@table\to\addplot@tbl@error@x
+			\fi
+		\else
+			\pgfplotstablegetcolumnbyname\pgfplots@plot@tbl@error@x\of\pgfplots@table\to\addplot@tbl@error@x
+		\fi
+		\ifx\pgfplots@plot@tbl@error@y\pgfutil@empty
+			\ifx\pgfplots@plot@tbl@error@yindex\pgfutil@empty
+			\else
+				\pgfplotstablegetcolumnbyindex\pgfplots@plot@tbl@error@yindex\of\pgfplots@table\to\addplot@tbl@error@y
+			\fi
+		\else
+			\pgfplotstablegetcolumnbyname\pgfplots@plot@tbl@error@y\of\pgfplots@table\to\addplot@tbl@error@y
+		\fi
+	\fi
+	%
+	\pgfplots@PREPARE@COORD@STREAM{#1}{#4}%
+	\pgfplots@coord@stream@start
+	\loop
+	\pgfplotslistcheckempty\addplot@tbl@x
+	\ifpgfplotslistempty
+		\pgfplots@loop@CONTINUEfalse
+	\else
+		\pgfplots@loop@CONTINUEtrue
+	\fi
+	\ifpgfplots@loop@CONTINUE
+		\pgfplotslistpopfront\addplot@tbl@x\to\addplot@tbl@cur@x
+		\pgfplotslistpopfront\addplot@tbl@y\to\addplot@tbl@cur@y
+		\ifpgfplots@errorbars@enabled
+			\ifx\addplot@tbl@error@x\pgfutil@empty
+				\let\addplot@tbl@error@cur@x=\pgfutil@empty
+			\else
+				\pgfplotslistpopfront\addplot@tbl@error@x\to\addplot@tbl@error@cur@x
+			\fi
+			\ifx\addplot@tbl@error@y\pgfutil@empty
+				\let\addplot@tbl@error@cur@y=\pgfutil@empty
+			\else
+				\pgfplotslistpopfront\addplot@tbl@error@y\to\addplot@tbl@error@cur@y
+			\fi
+			\edef\pgfplots@TMP{{\addplot@tbl@cur@x}{\addplot@tbl@cur@y}{\addplot@tbl@error@cur@x}{\addplot@tbl@error@cur@y}}%
+			\expandafter\pgfplots@coord@stream@coord\pgfplots@TMP
+		\else
+			\edef\pgfplots@TMP{{\addplot@tbl@cur@x}{\addplot@tbl@cur@y}{}{}}%
+			\expandafter\pgfplots@coord@stream@coord\pgfplots@TMP
+		\fi
+	\repeat
+	\pgfplots@coord@stream@end
+	\endgroup
+}
+
+% #1:  arguments to \addplot[]  (these are used for legend images as well) 
+% #2:  arguments to \addplot plot[] (these are set directly in \addplot)
+\def\pgfplots@start@plot@with@options#1#2{%
+	\begingroup
+	\def\pgfplots@current@point@coordindex{0}% can be used inside of coordinate filters.
+	\def\coordindex{\pgfplots@current@point@coordindex}% valid inside of \addplot
+	\ifx\pgfplots@execute@at@begin@plot\pgfutil@empty
+	\else
+		\pgfplots@execute@at@begin@plot
+	\fi
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@beginplot
+	\fi
+	\pgfplots@rememberplotspec{#1}%
+	\def\pgfplots@addplot@nonlegend@options{#2}%
+	\ifx\pgfplots@addplot@nonlegend@options\pgfutil@empty
+	\else
+		\pgfqkeys{/tikz}{#2}%
+	\fi
+}
+
+% Initialises 
+% \pgfplots@coord@stream@start
+% \pgfplots@coord@stream@coord
+% \pgfplots@coord@stream@end
+% such that a following coordinate stream is processed properly. The
+% following coordinate stream may come from different input methods.
+%
+% Arguments:
+% #1:  all options of \addplot[...] (the plot style)
+% #2:  any trailing path commands after the 'plot' command as such,
+%      for example \addplot plot coordinates {...} -- (0,0);
+%      would yield #2 =' -- (0,0)'
+%
+\long\def\pgfplots@PREPARE@COORD@STREAM#1#2{%
+	\ifpgfplots@errorbars@enabled
+		\pgfplots@streamerrorbar@recordto{\pgfplots@recordederrorbar}%
+		\pgfplots@streamerrorbarstart
+	\else
+		\let\pgfplots@recordederrorbar=\pgfutil@empty
+	\fi
+	\pgfplots@coord@stream@INIT\pgfplots@coord@stream@recorded
+	%
+	% make sure that \pgfplots@coord@stream@end@@ is called at the end
+	% of the lately prepare end-stream method.
+	\expandafter\def\expandafter\pgfplots@coord@stream@end@\expandafter{%
+		\pgfplots@coord@stream@end@
+		\pgfplots@coord@stream@end@@
+		\pgfplots@end@plot
+	}%
+	\def\pgfplots@coord@stream@end@@{%
+		\ifpgfplots@errorbars@enabled
+			\pgfplots@streamerrorbarend
+		\fi
+		% Idea: use
+		%   \scope[plot specification]
+		%   <any paths for error bars>
+		%   \endscope
+		%   \draw plot coordinates {...};
+		% to share plot specifications between error bars and plot
+		% coordinates. Unfortunately, it is NOT sufficient to use
+		% \tikzset{#1}
+		\edef\pgfplots@TMP{/pgfplots/every axis plot,/pgfplots/every axis plot no \the\pgfplots@numplots/.try}%
+		\pgfplotslist@TOK@a=\expandafter{\pgfplots@TMP,#1,/pgfplots/every axis plot post}%
+		% Assemble a
+		% \pgfplots@addplot@enqueue@coords{}{}...{}
+		% statement with correct arguments:
+		\ifx\pgfplots@recordederrorbar\pgfutil@empty
+			\let\pgfplots@TMPB=\pgfutil@empty%
+		\else
+			\pgfplotslist@TOK@b=\expandafter{\pgfplots@recordederrorbar}%
+			\def\pgfplots@TMPB{%
+				\noexpand\pgfplots@errorbars@finishwithstyleoptions[\the\pgfplotslist@TOK@a]{\the\pgfplotslist@TOK@b}%
+			}%
+		\fi
+		\ifpgfplots@datascaletrafo@initialised
+			\pgfplots@addplot@get@named@startendpoints@command\pgfplots@TMP
+			\pgfplots@toka=\expandafter{\pgfplots@TMP}%
+		\else
+			\pgfplots@toka={}%
+		\fi
+		\edef\pgfplots@TMP{%
+			\noexpand\pgfplots@addplot@enqueue@coords
+			{
+				\noexpand\def\noexpand\plotnum{\the\pgfplots@numplots}%
+				\noexpand\pgfplots@initzerolevelhandler
+				\the\pgfplots@toka% named start/end points
+				\noexpand\tikzstyle{current plot style}=[\the\pgfplotslist@TOK@a]%
+				\pgfplots@TMPB% error bar commands
+			}%
+			{%
+				\noexpand\draw[current plot style]%
+			}%
+		}%
+		\expandafter\pgfplots@TMP\expandafter{\pgfplots@coord@stream@recorded #2;}%
+			{}%
+	}%
+}%
+
+\def\pgfplots@end@plot{%
+	\global\advance\pgfplots@numplots by1\relax%
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@endplot
+	\fi
+	\ifx\pgfplots@execute@at@end@plot\pgfutil@empty
+	\else
+		\pgfplots@execute@at@end@plot
+	\fi
+	\global\let\pgfplots@TMP=\relax
+	\ifpgfplots@collect@firstplot@astick
+		\ifnum\pgfplots@numplots=1\relax
+			\pgfplotslist@TOK@a=\expandafter{\pgfplots@firstplot@coords@x}%
+			\pgfplotslist@TOK@b=\expandafter{\pgfplots@firstplot@coords@y}%
+			\xdef\pgfplots@TMP{%
+				\noexpand\def\noexpand\pgfplots@firstplot@coords@x{\the\pgfplotslist@TOK@a}%
+				\noexpand\def\noexpand\pgfplots@firstplot@coords@y{\the\pgfplotslist@TOK@b}%
+			}%
+		\fi
+	\fi
+	\endgroup
+	\pgfplots@TMP% see above
+}
+
+% #1: arguments to \addplot[...]
+% #2: the plot coordinates
+% #3: any trailing path command before the final ';'. It will be used as-is.
+\long\def\pgfplots@addplotimpl@coordinates#1plot coordinates#2#3;{%
+%\tracingmacros=2\tracingcommands=2
+%\pgfplots@message{processing plots coords with trailing path '#3'}%
+	\pgfplots@PREPARE@COORD@STREAM{#1}{#3}%
+	\pgfplots@coord@stream@foreach{#2}%
+}%
+
+\newif\ifpgfplots@update@limits@for@one@point@ISCLIPPED
+\def\pgfplots@math@ONE{1.0}%
+
+\def\pgfplots@streamerrorbarstart{%
+}%
+\def\pgfplots@streamerrorbarend{%
+}%
+\def\pgfplots@streamerrorbarcoords#1#2{%
+}%
+
+\def\pgfplots@streamerrorbar@recordto#1{%
+	\def\pgfplots@streamerrorbarstart{\let#1=\pgfutil@empty}%
+	\def\pgfplots@streamerrorbarend{}%
+	\def\pgfplots@streamerrorbarcoords##1##2{%
+		\expandafter\def\expandafter#1\expandafter{#1%
+			\pgfplots@errorbar@draw{##1}{##2}%
+		}%
+	}%
+}
+\def\pgfplots@streamerrorbar@directdraw{%
+	\def\pgfplots@streamerrorbarstart{}%
+	\def\pgfplots@streamerrorbarend{}%
+	\def\pgfplots@streamerrorbarcoords##1##2{%
+		\pgfplots@errorbar@draw{##1}{##2}%
+	}%
+}
+	
+
+
+% Updates the current x and y limits for point (#1,#2).
+%
+% The point coordinates may be given in floating point format, see
+% below.
+%
+% Please note that if user specified limits are given, automatic
+% limits are only applied to points which fall into the user specified
+% clipping region.
+%
+% PRECONDITIONS:
+%   - 'floating point numerics active' 
+%   		=> coordinate filtering is active
+%   		=> #1 and/or #2 are in floating point format
+%   - no coordinate filters active 
+%   		=> #1 and #2 MAY be macros, but they must be valid TeX
+%   		length (without unit).
+% #3= error for x coord (or empty)
+% #4= error for y coord (or empty)
+\long\def\pgfplots@update@limits@for@one@point#1#2#3#4{%
+%\tracingmacros=2\tracingcommands=2
+%\pgfplots@message{Updating limits for (#1,#2) ...}%
+	\pgfplots@update@limits@for@one@point@ISCLIPPEDfalse
+	\ifpgfplots@clip@limits
+		\ifpgfplots@autocompute@xlim
+		\else
+			\ifpgfplots@float@numerics@mode@x
+				\pgfmathfloatlessthan@{#1}{\pgfplots@xmin}%
+				\ifpgfmathfloatcomparison
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+				\pgfmathfloatlessthan@{\pgfplots@xmax}{#1}%
+				\ifpgfmathfloatcomparison
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+			\else
+				\pgfmathlessthan@{#1}{\pgfplots@xmin}%
+				\ifx\pgfmathresult\pgfplots@math@ONE
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+				\pgfmathlessthan@{\pgfplots@xmax}{#1}%
+				\ifx\pgfmathresult\pgfplots@math@ONE
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+			\fi
+		\fi
+		\ifpgfplots@autocompute@ylim
+		\else
+			\ifpgfplots@float@numerics@mode@y
+				\pgfmathfloatlessthan@{#2}{\pgfplots@ymin}%
+				\ifpgfmathfloatcomparison
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+				\pgfmathfloatlessthan@{\pgfplots@ymax}{#2}%
+				\ifpgfmathfloatcomparison
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+			\else
+				\pgfmathlessthan@{#2}{\pgfplots@ymin}%
+				\ifx\pgfmathresult\pgfplots@math@ONE
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+				\pgfmathlessthan@{\pgfplots@ymax}{#2}%
+				\ifx\pgfmathresult\pgfplots@math@ONE
+					\pgfplots@update@limits@for@one@point@ISCLIPPEDtrue
+				\fi
+			\fi
+		\fi
+	\fi
+	\ifpgfplots@update@limits@for@one@point@ISCLIPPED
+	\else
+		\ifpgfplots@autocompute@xlim
+			\ifpgfplots@float@numerics@mode@x
+				\pgfmathfloatmin@{\pgfplots@xmin}{#1}%
+				\global\let\pgfplots@xmin=\pgfmathresult
+				\pgfmathfloatmax@{\pgfplots@xmax}{#1}%
+				\global\let\pgfplots@xmax=\pgfmathresult
+			\else
+				\pgfmathmin@{\pgfplots@xmin}{#1}%
+				\global\let\pgfplots@xmin=\pgfmathresult
+				\pgfmathmax@{\pgfplots@xmax}{#1}%
+				\global\let\pgfplots@xmax=\pgfmathresult
+			\fi
+		\fi
+		\ifpgfplots@autocompute@ylim
+			\ifpgfplots@float@numerics@mode@y
+				\pgfmathfloatmin@{\pgfplots@ymin}{#2}%
+				\global\let\pgfplots@ymin=\pgfmathresult
+				\pgfmathfloatmax@{\pgfplots@ymax}{#2}%
+				\global\let\pgfplots@ymax=\pgfmathresult
+			\else
+				\pgfmathmin@{\pgfplots@ymin}{#2}%
+				\global\let\pgfplots@ymin=\pgfmathresult
+				\pgfmathmax@{\pgfplots@ymax}{#2}%
+				\global\let\pgfplots@ymax=\pgfmathresult
+			\fi
+		\fi
+		\global\pgfplots@limits@are@computedtrue
+	\fi
+%\pgfplots@message{Updated limits: (\pgfplots@xmin,\pgfplots@ymin) rectangle  (\pgfplots@xmax,\pgfplots@ymax).}%
+%\tracingmacros=0\tracingcommands=0
+}
+
+\def\pgfplots@invoke@filter#1#2{%
+	\pgfkeysvalueof{/pgfplots/#2 filter/.@cmd}#1\pgfeov%
+}%
+
+% #3= error for x coord (or empty)
+% #4= error for y coord (or empty)
+\def\pgfplots@process@one@point#1#2#3#4{%
+	\pgfplots@prepare@xcoord{#1}%
+	\expandafter\pgfplots@invoke@filter\expandafter{\pgfmathresult}{x}%
+	\let\pgfplots@current@point@x=\pgfmathresult
+	%
+	\pgfplots@prepare@ycoord{#2}%
+	\expandafter\pgfplots@invoke@filter\expandafter{\pgfmathresult}{y}%
+	\let\pgfplots@current@point@y=\pgfmathresult
+	%
+	\ifx\pgfplots@current@point@x\pgfutil@empty
+		\ifpgfplots@warn@for@filter@discards
+			\pgfplots@message{NOTE: coordinate (#1,#2) has been dropped because of the x-coordinate filter.}%
+		\fi
+	\else
+		\ifx\pgfplots@current@point@y\pgfutil@empty
+			\ifpgfplots@warn@for@filter@discards
+				\pgfplots@message{NOTE: coordinate (#1,#2) has been dropped because of the y-coordinate filter.}%
+			\fi
+		\else
+			\ifpgfplots@apply@datatrafo
+				\ifpgfplots@apply@datatrafo@x
+					\pgfmathfloatparsenumber{\pgfplots@current@point@x}%
+					\let\pgfplots@current@point@x=\pgfmathresult
+				\fi
+				\ifpgfplots@apply@datatrafo@y
+					\pgfmathfloatparsenumber{\pgfplots@current@point@y}%
+					\let\pgfplots@current@point@y=\pgfmathresult
+				\fi
+				\ifpgfplots@datascaletrafo@initialised
+					% apply data transformation directly.
+					\ifpgfplots@apply@datatrafo@x
+						\pgfplots@datascaletrafo@x\pgfplots@current@point@x
+						\let\pgfplots@current@point@x=\pgfmathresult
+					\fi
+					\ifpgfplots@apply@datatrafo@y
+						\pgfplots@datascaletrafo@y\pgfplots@current@point@y
+						\let\pgfplots@current@point@y=\pgfmathresult
+					\fi
+				\fi
+			\fi
+			% All following routines (limit updating/stacking/error
+			% bars) will use float numerics if necessary (controlled
+			% by ifs).
+			\ifpgfplots@stackedmode
+				\pgfplots@stacked@preparepoint@inmacro{\pgfplots@current@point@x}{\pgfplots@current@point@y}%
+				\ifpgfplots@datascaletrafo@initialised% is also true if there is no scale trafo.
+					\pgfplots@stacked@finishpoint{\pgfplots@current@point@x}{\pgfplots@current@point@y}%
+				\fi
+			\fi
+			\ifpgfplots@autocomputelimits
+				% update also axis limits:
+				\pgfplots@update@limits@for@one@point{\pgfplots@current@point@x}{\pgfplots@current@point@y}{}{}%
+			\fi
+			\ifpgfplots@errorbars@enabled
+				\pgfplots@process@errorbar@for{\pgfplots@current@point@x}{\pgfplots@current@point@y}{#3}{#4}{#1}{#2}%
+			\fi
+			\pgfplots@toka=\expandafter{\pgfplots@coord@stream@recorded}%
+			\edef\pgfplots@coord@stream@recorded{\the\pgfplots@toka (\pgfplots@current@point@x,\pgfplots@current@point@y)}%
+			\ifpgfplots@collect@firstplot@astick
+				\ifnum\pgfplots@numplots=0
+					\ifx\pgfplots@firstplot@coords@x\pgfutil@empty
+						\pgfplots@toka=\expandafter{}%
+					\else
+						\pgfplots@toka=\expandafter{\pgfplots@firstplot@coords@x,}%
+					\fi
+					\edef\pgfplots@firstplot@coords@x{\the\pgfplots@toka\pgfplots@current@point@x}%
+					\ifx\pgfplots@firstplot@coords@y\pgfutil@empty
+						\pgfplots@toka=\expandafter{}%
+					\else
+						\pgfplots@toka=\expandafter{\pgfplots@firstplot@coords@y,}%
+					\fi
+					\edef\pgfplots@firstplot@coords@y{\the\pgfplots@toka\pgfplots@current@point@y}%
+				\fi
+			\fi
+%\pgfplots@message{FILTERING: appended \pgfplots@current@point@x,\pgfplots@current@point@y}%  -> results in \pgfplots@coord@stream@recorded}%
+		\fi
+	\fi
+	%
+	% increase \pgfplots@current@point@coordindex:
+	\begingroup
+	\c@pgf@counta=\pgfplots@current@point@coordindex
+	\advance\c@pgf@counta by1\relax
+	\edef\pgfmathresult{\the\c@pgf@counta}%
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+	\let\pgfplots@current@point@coordindex=\pgfmathresult
+}
+
+% Internal stream methods.
+%
+% Please overwrite \pgfplots@coord@stream@start@,
+% \pgfplots@coord@stream@end@ and \pgfplots@coord@stream@coord@
+% if you implement streams.
+%
+% FIXME: REPLACE THIS HERE WITH METHODS OF THE VISUALIZATION FRAMEWORK
+\newif\ifpgfplots@coord@stream@isfirst
+\def\pgfplots@coord@stream@start{
+	\pgfplots@coord@stream@isfirsttrue
+	\pgfplots@coord@stream@start@}
+\def\pgfplots@coord@stream@end{\pgfplots@coord@stream@end@}
+
+% Will be invoked for every point coordinate.
+%
+% It invokes \pgfplots@coord@stream@coord@.
+% It is expected to assign \pgfplots@current@point@x and
+% \pgfplots@current@point@y
+%
+% It is expected to
+% (#1,#2) : x, y coordinates
+% (#3,#4) : any x, y errors (or empty)
+\def\pgfplots@coord@stream@coord#1#2#3#4{%
+	\pgfplots@coord@stream@coord@{#1}{#2}{#3}{#4}%
+	\ifpgfplots@coord@stream@isfirst
+		\let\pgfplots@currentplot@firstcoord@x=\pgfplots@current@point@x
+		\let\pgfplots@currentplot@firstcoord@y=\pgfplots@current@point@y
+		\pgfplots@coord@stream@isfirstfalse
+	\fi
+	\let\pgfplots@currentplot@lastcoord@x=\pgfplots@current@point@x
+	\let\pgfplots@currentplot@lastcoord@y=\pgfplots@current@point@y
+}%
+
+% A looping method which applies
+% \pgfplots@coord@stream@start
+% for each coordinate '(x,y)'  or '(x,y) +- (ex,ey)', call
+%   \pgfplots@coord@stream@coord{x}{y}{ex}{ey}
+% \pgfplots@coord@stream@end
+%
+% #1 a sequence of coordinates of the form 
+%   '(x,y)'
+%   or
+%   '(x,y) +- (ex,ey)'
+%   separated by white-space.
+\long\def\pgfplots@coord@stream@foreach#1{%
+	\pgfplots@coord@stream@start
+	\pgfplots@foreach@plot@coord@do%
+		\pgfplots@coord@stream@coord
+	\for
+	plot coordinates {#1};%
+	\pgfplots@EOI
+	\pgfplots@coord@stream@end
+}%
+
+% Processes coordinates and writes a new, modified 'plot coordinates'
+% command to macro #1.
+% #1:  macro name for processed coordinates.
+%
+% Please note that it may be necessary to process the same coordinates
+% once more at the end of an axis - see
+% pgfplots@coord@stream@finalize@storedcoords@START
+\def\pgfplots@coord@stream@INIT#1{%
+	\def\pgfplots@coord@stream@start@{%
+		\let\pgfplots@coord@stream@recorded=\pgfutil@empty
+	}%
+	\def\pgfplots@coord@stream@end@{%
+		\pgfplots@toka=\expandafter{\pgfplots@coord@stream@recorded}%
+		\edef#1{plot coordinates {\the\pgfplots@toka}}%
+	}%
+	\let\pgfplots@coord@stream@coord@=\pgfplots@process@one@point
+}
+
+% Takes a sequence of PREPARED coordinates which are given in floating
+% point representation and applies the data scaling trafo.
+%
+% This stream is designed to be done at the end of an axis.
+% See \pgfplots@coord@stream@finalize@storedcoords@START
+\def\pgfplots@coord@stream@INIT@finalize@storedcoords#1{%
+	\def\pgfplots@coord@stream@start@{%
+		\let\pgfplots@data@scaletrafo@result=\pgfutil@empty
+	}%
+	\def\pgfplots@coord@stream@end@{%
+		\let#1=\pgfplots@data@scaletrafo@result
+	}%
+	\let\pgfplots@coord@stream@coord@=\pgfplots@apply@data@scaletrafo@to@one@point
+}
+
+\def\pgfplots@addplot@get@named@startendpoints@command#1{%
+	\edef#1{%
+		\noexpand\path 
+			(\pgfplots@currentplot@firstcoord@x,\pgfplots@currentplot@firstcoord@y) coordinate (current plot begin)
+			(\pgfplots@currentplot@lastcoord@x,\pgfplots@currentplot@lastcoord@y) coordinate (current plot end)
+		;
+	}%
+}%
+
+% INPUT: 
+%   a sequence of points (SMeE,SMeE) (terminated with ';') 
+%   where S=sign, M=mantisse, E = exponent.
+%   Such input is generated in the case pgfplots@apply@datatrafotrue
+%   by the coordinate filters.
+% OUTPUT: 
+%   proper sequence of fixed point coordinates which are the result of the
+%   data scaling transformation (\pgfplots@datascaletrafo@x).
+%
+% The output will be written into the macro #3
+\long\def\pgfplots@coord@stream@finalize@storedcoords@START plot coordinates #1#2;\to#3{%
+	\pgfplots@coord@stream@finalize@storedcoords@START@ plot coordinates {#1}#2;\to#3
+	\ifpgfplots@errorbars@enabled
+		\pgfplots@errorbars@finishwithstyleoptions[current plot style]{\pgfplots@recordederrorbar}%
+	\fi
+	\pgfplots@addplot@get@named@startendpoints@command\pgfplots@TMP
+	\pgfplots@TMP
+}%
+\long\def\pgfplots@coord@stream@finalize@storedcoords@START@ plot coordinates #1#2;\to#3{%
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@beginplot
+	\fi
+	\pgfplots@coord@stream@INIT@finalize@storedcoords#3
+	\ifpgfplots@errorbars@enabled
+		\pgfplots@streamerrorbar@recordto{\pgfplots@recordederrorbar}%
+		\pgfplots@streamerrorbarstart
+	\fi
+	\pgfplots@coord@stream@foreach{#1}%
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@endplot
+	\fi
+	\pgfplots@toka=\expandafter{#3}%
+	\pgfplotslist@TOK@a={#2}%
+	\edef#3{plot coordinates {\the\pgfplots@toka}\the\pgfplotslist@TOK@a;}%
+	\ifpgfplots@errorbars@enabled
+		\pgfplots@streamerrorbarend
+	\fi
+}%
+
+% does the same job, but it does not execute any drawing commands.
+%
+% Instead, it generates a macro #4 which - if used as "precommand"
+% befor a draw operation - restores all required options and performs
+% pre-drawing.
+\long\def\pgfplots@coord@stream@finalize@storedcoords@START@dryrun plot coordinates #1#2;\to#3#4{%
+	\pgfplots@coord@stream@finalize@storedcoords@START@ plot coordinates {#1}#2;\to#3
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@savestateto\pgfplots@TMP
+		\pgfplotslist@TOK@a=\expandafter{\pgfplots@TMP}%
+	\else
+		\pgfplotslist@TOK@a={}%
+	\fi
+	\pgfplots@addplot@get@named@startendpoints@command\pgfplots@TMP
+	\pgfplots@toka=\expandafter{\pgfplots@TMP}%
+	\ifpgfplots@errorbars@enabled
+		\pgfplotslist@TOK@b=\expandafter{\pgfplots@recordederrorbar}%
+		\edef#4{%
+			\the\pgfplots@toka
+			\the\pgfplotslist@TOK@a
+			\noexpand\pgfplots@errorbars@finishwithstyleoptions[current plot style]{\the\pgfplotslist@TOK@b}%
+		}%
+	\else
+		\edef#4{%
+			\the\pgfplots@toka
+			\the\pgfplotslist@TOK@a
+		}%
+	\fi
+}%
+
+% A looping command to loop through plot coordinates.
+% For every point, #1{X}{Y} will be invoked.
+%
+% No scoping is used during this operation, so you can access outer
+% variables.
+\long\def\pgfplots@foreach@plot@coord@do#1\for plot coordinates #2;\pgfplots@EOI{%
+	\def\pgfplots@foreach@plot@coord@do@CMD{#1}%
+	\pgfplots@foreach@plot@coord@ITERATE#2\pgfplots@EOI%
+}
+
+\def\pgfplots@foreach@plot@coord@ITERATE{%
+	\pgfutil@ifnextchar\pgfplots@EOI{%
+		\pgfplots@foreach@plot@coord@FINISH%
+	}{%
+		\pgfplots@foreach@plot@coord@NEXT%
+	}%
+}
+
+\def\pgfplots@foreach@plot@coord@NEXT(#1,#2){%
+	\pgfutil@ifnextchar+{%
+		\pgfplots@foreach@plot@coord@NEXT@WITH@ERRORRANGE{#1}{#2}%
+	}{%
+		\pgfplots@foreach@plot@coord@do@CMD{#1}{#2}{}{}%
+		\pgfplots@foreach@plot@coord@ITERATE
+	}%
+}
+
+% processing something like '(x,y) +- (error_x,error_y)'
+\def\pgfplots@foreach@plot@coord@NEXT@WITH@ERRORRANGE#1#2+-#3({%
+	\pgfplots@foreach@plot@coord@NEXT@WITH@ERRORRANGE@{#1}{#2}%
+}
+\def\pgfplots@foreach@plot@coord@NEXT@WITH@ERRORRANGE@#1#2#3,#4){%
+	\pgfplots@foreach@plot@coord@do@CMD{#1}{#2}{#3}{#4}%
+	\pgfplots@foreach@plot@coord@ITERATE
+}
+
+\def\pgfplots@foreach@plot@coord@FINISH\pgfplots@EOI{}
+
+
+% for use in \ifx:
+\def\pgfplots@EOI{\pgfplots@EOI}%
+	
+% #1= x coord
+% #2= y coord
+% #3= error for x coord (or empty)
+% #4= error for y coord (or empty)
+\def\pgfplots@apply@data@scaletrafo@to@one@point#1#2#3#4{%
+	\ifpgfplots@apply@datatrafo@x
+		\pgfplots@datascaletrafo@x{#1}%
+		\let\pgfplots@current@point@x=\pgfmathresult
+	\else
+		\def\pgfplots@current@point@x{#1}%
+	\fi
+	\ifpgfplots@apply@datatrafo@y
+		\pgfplots@datascaletrafo@y{#2}%
+		\let\pgfplots@current@point@y=\pgfmathresult
+	\else
+		\def\pgfplots@current@point@y{#2}%
+	\fi
+	\ifpgfplots@stackedmode
+		% all these calls work with pgfmath; no more floating point
+		% arithmetics are applied.
+		\pgfplots@stacked@getnextzerolevelpoint
+		\pgfplots@stacked@finishpoint{\pgfplots@current@point@x}{\pgfplots@current@point@y}%
+		\pgfplots@stacked@rememberzerolevelpoint@for@next@plot{(\pgfplots@current@point@x,\pgfplots@current@point@y)}%
+	\fi
+	\pgfplots@toka=\expandafter{\pgfplots@data@scaletrafo@result}%
+	\edef\pgfplots@data@scaletrafo@result{\the\pgfplots@toka(\pgfplots@current@point@x,\pgfplots@current@point@y)}%
+}
+
+% This thing here shall draw all error bar commands listed in '#2'.
+%
+% It will be invoked when any plotting commands take effect (that
+% means all limits are computed; the axis has been drawn,
+% transformations are set up...)
+\def\pgfplots@errorbars@finishwithstyleoptions[#1]#2{%
+	\scope[%/pgfplots/search path for tikz/.cd,
+		#1,/pgfplots/every error bar]%
+	#2%
+	\endscope
+}
+
+\def\pgfplots@errorbar@draw@float(#1,#2)(#3,#4){%
+	\ifpgfplots@apply@datatrafo@x
+		\pgfplots@datascaletrafo@x{#1}%
+		\let\pgfplots@xarg=\pgfmathresult%
+		\pgfplots@datascaletrafo@x{#3}%
+		\let\pgfplots@error@xarg=\pgfmathresult%
+	\else
+		\def\pgfplots@xarg{#1}%
+		\def\pgfplots@error@xarg{#3}%
+	\fi
+	\ifpgfplots@apply@datatrafo@y
+		\pgfplots@datascaletrafo@y{#2}%
+		\let\pgfplots@yarg=\pgfmathresult%
+		\pgfplots@datascaletrafo@y{#4}%
+		\let\pgfplots@error@yarg=\pgfmathresult%
+	\else
+		\def\pgfplots@yarg{#2}%
+		\def\pgfplots@error@yarg{#4}%
+	\fi
+	\edef\pgfplots@TMP{{(\pgfplots@xarg,\pgfplots@yarg)}{(\pgfplots@error@xarg,\pgfplots@error@yarg)}}%
+	\def\pgfplots@TMPB{\pgfkeysvalueof{/pgfplots/error bars/draw error bar/.@cmd}}%
+	\expandafter\pgfplots@TMPB\pgfplots@TMP\pgfeov
+}
+
+\def\pgfplots@errorbar@draw#1#2{%
+	\begingroup
+	\ifpgfplots@apply@datatrafo
+		\pgfplots@errorbar@draw@float#1#2
+	\else
+		\pgfkeysvalueof{/pgfplots/error bars/draw error bar/.@cmd}{#1}{#2}\pgfeov%
+	\fi
+	\endgroup
+}%
+
+% Also provides UNFILTERED arguments x (#5) and y (#6). These are use
+% in case of logplots, because we may need to compute log( x + e_x )
+% or log( y + e_y ).
+\def\pgfplots@process@errorbar@for#1#2#3#4#5#6{%
+%	\begingroup
+	\edef\pgfplots@xarg{#1}%
+	\edef\pgfplots@yarg{#2}%
+	\def\pgfplots@xarg@unfiltered{#5}%
+	\def\pgfplots@yarg@unfiltered{#6}%
+	\edef\pgfplots@error@xarg{#3}%
+	\edef\pgfplots@error@yarg{#4}%
+	\def\pgfplots@TMP{0}%
+	\ifx\pgfplots@TMP\pgfplots@error@xarg
+		\let\pgfplots@error@xarg=\pgfutil@empty
+	\fi
+	\ifx\pgfplots@TMP\pgfplots@error@yarg
+		\let\pgfplots@error@yarg=\pgfutil@empty
+	\fi
+	%  FIXME : INEFFICIENT! This code here does every computation 
+	%  multiple times!
+	\ifcase\pgfplots@errorbars@xdirection
+	\or
+		\pgfplots@process@errorbar@@for{x}{+}1%
+	\or
+		\pgfplots@process@errorbar@@for{x}{-}2%
+	\or
+		\pgfplots@process@errorbar@@for{x}{+}1%
+		\pgfplots@process@errorbar@@for{x}{-}2%
+	\fi
+	\ifcase\pgfplots@errorbars@ydirection
+	\or
+		\pgfplots@process@errorbar@@for{y}{+}1%
+	\or
+		\pgfplots@process@errorbar@@for{y}{-}2%
+	\or
+		\pgfplots@process@errorbar@@for{y}{+}1%
+		\pgfplots@process@errorbar@@for{y}{-}2%
+	\fi
+%	\endgroup
+}
+
+% #1: either 'x' or 'y'
+% #2: either '+' or '-'
+% #3: an integer representing the argument #2. It is '1' if #2='+'
+%     and '2' is #2 = '-'.
+\def\pgfplots@process@errorbar@@for#1#2#3{%
+	\expandafter\let\expandafter\ifpgfplots@is@datascaled\csname ifpgfplots@float@numerics@mode@#1\endcsname
+	\csname ifpgfplots@#1islinear\endcsname
+		\edef\pgfplots@error@src{\csname pgfplots@#1arg\endcsname}%
+		\ifcase\csname pgfplots@errorbars@#1mode\endcsname
+			% fixed absolute error.
+			\ifpgfplots@is@datascaled
+				\edef\pgfplots@error@coord{\csname pgfplots@errorbars@#1fixed\endcsname}%
+				\pgfmathfloatparsenumber{\pgfplots@error@coord}%
+				\let\pgfplots@error@coord=\pgfmathresult
+				\ifnum#3=1
+					\pgfmathfloatadd@{\pgfplots@error@src}{\pgfplots@error@coord}%
+				\else
+					\pgfmathfloatsubtract@{\pgfplots@error@src}{\pgfplots@error@coord}%
+				\fi
+			\else
+				\edef\pgfplots@error@coord{\csname pgfplots@errorbars@#1fixed\endcsname}%
+				\pgfmathparse{\pgfplots@error@src#2 \pgfplots@error@coord}%
+			\fi
+			\let\pgfplots@error@coord=\pgfmathresult
+		\or% fixed relative error:
+			\ifpgfplots@is@datascaled
+				\pgfmathparse{(1#2\csname pgfplots@errorbars@#1rel\endcsname)}%
+				\let\pgfplots@error@coord=\pgfmathresult
+				\pgfmathfloatmultiplyfixed@{\pgfplots@error@src}{\pgfplots@error@coord}%
+			\else
+				\pgfmathparse{\pgfplots@error@src*(1#2\csname pgfplots@errorbars@#1rel\endcsname)}%
+			\fi
+			\let\pgfplots@error@coord=\pgfmathresult
+		\or% explicit absolute:
+			\edef\pgfplots@error@coord{\csname pgfplots@error@#1arg\endcsname}%
+			\ifx\pgfplots@error@coord\pgfutil@empty
+			\else
+				\ifpgfplots@is@datascaled
+					\pgfmathfloatparsenumber{\pgfplots@error@coord}%
+					\let\pgfplots@error@coord=\pgfmathresult
+					\ifnum#3=1
+						\pgfmathfloatadd@{\pgfplots@error@src}{\pgfplots@error@coord}%
+					\else
+						\pgfmathfloatsubtract@{\pgfplots@error@src}{\pgfplots@error@coord}%
+					\fi
+				\else
+					\pgfmathparse{\pgfplots@error@src#2 \pgfplots@error@coord}%
+				\fi
+				\let\pgfplots@error@coord=\pgfmathresult
+			\fi
+		\or% explicit relative:
+			\edef\pgfplots@error@coord{\csname pgfplots@error@#1arg\endcsname}%
+			\ifx\pgfplots@error@coord\pgfutil@empty
+			\else
+				\ifpgfplots@is@datascaled
+					\pgfmathparse{(1#2\pgfplots@error@coord)}%
+					\let\pgfplots@error@coord=\pgfmathresult
+					\pgfmathfloatmultiplyfixed@{\pgfplots@error@src}{\pgfplots@error@coord}%
+				\else
+					\pgfmathparse{\pgfplots@error@src*(1#2\pgfplots@error@coord)}%
+				\fi
+				\let\pgfplots@error@coord=\pgfmathresult
+			\fi
+		\fi
+	\else
+		% LOGARITHMIC scaling. All errors are interpreted as 
+		%   log(x +- e_x)
+		% or
+		%   log( x*(1+-e_x) )
+		\ifcase\csname pgfplots@errorbars@#1mode\endcsname
+			% fixed absolute, log( x +- e_x )
+			\edef\pgfplots@error@src{\csname pgfplots@#1arg@unfiltered\endcsname}%
+			\edef\pgfplots@error@coord{\csname pgfplots@errorbars@#1fixed\endcsname}%
+			\pgfmathfloatparsenumber{\pgfplots@error@coord}%
+			\let\pgfplots@error@coord=\pgfmathresult
+			\pgfmathfloatparsenumber{\pgfplots@error@src}%
+			\let\pgfplots@error@src=\pgfmathresult
+			\ifnum#3=1
+				\pgfmathfloatadd@{\pgfplots@error@src}{\pgfplots@error@coord}%
+			\else
+				\pgfmathfloatsubtract@{\pgfplots@error@src}{\pgfplots@error@coord}%
+			\fi
+			\pgfmathlog@float{\pgfmathresult}%
+			\let\pgfplots@error@coord=\pgfmathresult
+		\or% fixed relative, log( x ( 1+-e_x ) ) = log(x) + log(1+-e_x)
+			\edef\pgfplots@error@src{\csname pgfplots@#1arg\endcsname}%
+			\pgfmathparse{\pgfplots@error@src + ln(1#2\csname pgfplots@errorbars@#1rel\endcsname)}%
+			\let\pgfplots@error@coord=\pgfmathresult%
+		\or% explicit absolute
+			\edef\pgfplots@error@src{\csname pgfplots@#1arg@unfiltered\endcsname}%
+			\edef\pgfplots@error@coord{\csname pgfplots@error@#1arg\endcsname}%
+			\ifx\pgfplots@error@coord\pgfutil@empty
+			\else
+				\pgfmathfloatparsenumber{\pgfplots@error@coord}%
+				\let\pgfplots@error@coord=\pgfmathresult
+				\pgfmathfloatparsenumber{\pgfplots@error@src}%
+				\let\pgfplots@error@src=\pgfmathresult
+				\ifnum#3=1
+					\pgfmathfloatadd@{\pgfplots@error@src}{\pgfplots@error@coord}%
+				\else
+					\pgfmathfloatsubtract@{\pgfplots@error@src}{\pgfplots@error@coord}%
+				\fi
+				\pgfmathlog@float{\pgfmathresult}%
+				\let\pgfplots@error@coord=\pgfmathresult
+			\fi
+		\or% explicit relative:
+			\edef\pgfplots@error@src{\csname pgfplots@#1arg\endcsname}%
+			\edef\pgfplots@error@coord{\csname pgfplots@error@#1arg\endcsname}%
+			\ifx\pgfplots@error@coord\pgfutil@empty
+			\else
+				\pgfmathparse{\pgfplots@error@src + ln(1#2 \pgfplots@error@coord)}%
+				\let\pgfplots@error@coord=\pgfmathresult%
+			\fi
+		\fi
+	\fi
+	\ifx\pgfplots@error@coord\pgfutil@empty
+	\else
+		\def\pgfplots@TMP{#1}%
+		\def\pgfplots@TMPB{x}%
+		\ifx\pgfplots@TMP\pgfplots@TMPB
+			\ifpgfplots@autocomputelimits
+				\pgfplots@update@limits@for@one@point{\pgfplots@error@coord}{\pgfplots@yarg}{}{}%
+			\fi
+			\edef\pgfplots@TMP{%
+				{(\pgfplots@xarg,\pgfplots@yarg)}%
+				{(\pgfplots@error@coord,\pgfplots@yarg)}%
+			}%
+		\else
+			\ifpgfplots@autocomputelimits
+				\pgfplots@update@limits@for@one@point{\pgfplots@xarg}{\pgfplots@error@coord}{}{}%
+			\fi
+			\edef\pgfplots@TMP{%
+				{(\pgfplots@xarg,\pgfplots@yarg)}%
+				{(\pgfplots@xarg,\pgfplots@error@coord)}%
+			}%
+		\fi
+		\expandafter\pgfplots@streamerrorbarcoords\pgfplots@TMP
+	\fi
+}
+
+\long\def\pgfplots@path#1;{%
+	\pgfplots@path@enqueue{#1;}%
+}
+
+% This thing here shall be used to replace any '\path' where \axispath
+% shall be used.
+\long\def\pgfplots@replacement@for@tikz@path#1;{%
+	\axispath\path#1;%
+}
+
+
+% Will be available as \closedcycle command inside of an axis.
+%
+% It closes the current plot by drawing lines to the last "zero
+% level".
+%
+% That means the current plot is connected orthogonally with the
+% x-axis, allowing fill commands.
+%
+% For stacked plots, \closedcycle is special (it connects with the
+% previous \addplot command).
+%
+% Example:
+% \addplot coordinates {(3,0.5) (4,2) (5,1)} \closedcycle;
+\def\pgfplots@path@closed@cycle{%
+	\ifpgfplots@stackedmode
+		\pgfplots@stacked@path@closed@cycle
+	\else
+		\pgfplots@path@closed@cycle@std
+	\fi
+}
+\def\pgfplots@path@closed@cycle@std{%
+	|- (perpendicular cs: 
+		vertical line through={(current plot begin)}, 
+		horizontal line through={(\pgfplots@ZERO@x,\pgfplots@ZERO@y)})
+	-- cycle
+}%
+
+% Remembers the plotting command #2 and '#3=plot coordinates {...} ...';
+% for later postprocessing of the coordinates.
+%
+% #1: commands which should be executed before issueing the plotting
+%        command #2 #3.
+% #2:
+%    the command which is responsable for drawing.
+%    - If #2 is NOT '\pgfutil@empty', we expect #3 to contain only
+%      EXPANDABLE DATA.
+%      That's important for postponed floating point arithmetics in #3.
+%    - If #2='\pgfutil@empty', we don't make any assumption about #3
+%      and process it as-is.
+%
+% #3: see above.
+%
+% #4: commands which should be executed after '#2 #3'.
+%
+\long\def\pgfplots@path@enqueue@coords#1#2#3#4{%
+	\ifpgfplots@draw@at@end
+		\begingroup
+		\globaldefs=1
+		\pgfplotslistpushback{#1}{#2}{#3}{#4}\to\pgfplots@stored@plotlist
+		\endgroup
+	\else
+		\begingroup
+		#1#2#3#4%
+		\endgroup
+	\fi
+}
+
+% The same as \pgfplots@path@enqueue@coords, but this here also stores
+% \pgfplots@addplot@nonlegend@options
+\long\def\pgfplots@addplot@enqueue@coords#1#2#3#4{%
+	\ifpgfplots@draw@at@end
+		\ifx\pgfplots@addplot@nonlegend@options\pgfutil@empty
+			\pgfplots@path@enqueue@coords{#1}{#2}{#3}{#4}%
+		\else
+			\expandafter
+			\pgfplots@path@enqueue@coords
+				\expandafter{%
+				\expandafter\tikzset\expandafter{\pgfplots@addplot@nonlegend@options}%
+				#1}{#2}{#3}{#4}%
+		\fi
+	\else
+		\pgfplots@path@enqueue@coords{#1}{#2}{#3}{#4}%
+	\fi
+}
+
+
+% Remembers the plotting command #1.
+\long\def\pgfplots@path@enqueue#1{%
+	\pgfplots@path@enqueue@coords{}{}{#1}{}%
+}
+
+
+% Assigns a legend.
+% Syntax:
+% \legend{entry 1\\entry2\\entry3}
+\def\pgfplots@command@legend{
+	\pgfutil@ifnextchar[{%
+		\pgfplots@error{Sorry, legend options are now deprecated. Legends are now TikZ-matrizes which provide better alignment and can be placed horizontally. See the manual for details.}%
+	}{%
+		\pgfplots@command@legend@impl
+	}%
+}
+
+\def\pgfplots@command@legend@impl#1{%
+	\pgfplots@assign@list\pgfplots@TMPC{#1}%
+	\global\let\pgfplots@legend=\pgfplots@TMPC
+}
+
+
+\def\pgfplots@addlegendentry{%
+	\pgfutil@ifnextchar[{%
+		\pgfplots@addlegendentry@opts
+	}{%
+		\pgfplots@addlegendentry@opts[]%
+	}%
+}
+\def\pgfplots@addlegendentry@opts[#1]#2{%
+	{%
+	\globaldefs=1% this will ONLY store the options and the legend into global variables
+	\pgfplotslistpushback[#1]#2\to\pgfplots@legend
+	}%
+}
+
+\def\pgfplots@pop@next@legend{{%
+	\globaldefs=1
+	\pgfplotslistcheckempty\pgfplots@plotspeclist
+	\ifpgfplotslistempty
+		\let\pgfplots@curplotlist=\pgfutil@empty
+	\else
+		\pgfplotslistpopfront\pgfplots@plotspeclist\to\pgfplots@curplotlist
+	\fi
+	%
+	\pgfplotslistcheckempty\pgfplots@legend
+	\ifpgfplotslistempty
+		\let\pgfplots@curlegend=\pgfutil@empty
+	\else
+		\pgfplotslistpopfront\pgfplots@legend\to\pgfplots@curlegend
+	\fi
+	\advance\pgfplots@numplots by-1
+}}
+
+% This routine is called at the begin of every plot.
+% It initialised a zero level stream.
+%
+% The default is to use '0' as zero level streams.
+%
+% This method is called as "precommand"; before any Tikz drawing
+% commands have been started.
+\def\pgfplots@initzerolevelhandler{%
+	\ifpgfplots@stackedmode
+		% ATTENTION: this thing here says:
+		%    "draw zero level coordinates from list XYZ."
+		% But at the time of this initialisation, the list will be EMPTY!
+		%
+		% It will be filled later. That's ok, because 
+		% \pgfplots@initzerolevelhandler will be
+		% used as 'precommand', that means before Tikz sees any
+		% coordinates.
+		\pgfplots@stacked@initzerolevelhandler
+	\else
+		\pgfplotxzerolevelstreamconstant{\pgfplots@ZERO@x}%
+		\pgfplotyzerolevelstreamconstant{\pgfplots@ZERO@y}%
+	\fi
+}
+
+\def\pgfplots@try@mirror@plot@handler{%
+	\pgfutil@ifundefined{tikz@plot@handler}{}{%
+		\ifx\tikz@plot@handler\pgfplothandlerconstantlineto
+			\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkright
+		\else
+			\ifx\tikz@plot@handler\pgfplothandlerconstantlinetomarkright
+				\let\tikz@plot@handler=\pgfplothandlerconstantlineto
+			\fi
+		\fi
+	}%
+}
+
+\long\def\pgfplots@show@small@legendplots#1#2{
+	\begingroup
+	\def\pgfplots@TMPB{#1}%
+	\ifx\pgfplots@TMPB\pgfutil@empty
+	\else
+		\pgfqkeys{/pgfplots/search path for tikz}{#1}%
+	\fi
+	\pgfkeysvalueof{/pgfplots/legend image code/.@cmd}#2\pgfeov
+	\endgroup
+}
+
+\def\pgfplots@split@opts{%
+	\pgfutil@ifnextchar[{%
+		\pgfplots@split@opts@opts
+	}{%
+		\pgfplots@split@opts@opts[]%
+	}%
+}
+\def\pgfplots@split@opts@opts[#1]#2\pgfplots@result@to#3#4{%
+	\def#3{#2}%
+	\def#4{#1}%
+}
+
+% Typesets a legend node.
+%
+% It will either typeset a previously computed legend (which needs to be
+% stored in the macro \pgfplots@already@computed@legend@node)
+%
+% or it creates a legend, stores the commands into the macro named
+% above and typesets it.
+\def\pgfplots@createlegend{%
+	\ifx\pgfplots@already@computed@legend@node\pgfutil@empty
+		\pgfplotslistcheckempty\pgfplots@legend
+		\ifpgfplotslistempty
+		\else
+		%
+		% 
+		\begingroup
+			% assemble a 
+			% \matrix {
+			% 	small plot  & legend1\\
+			% 	small plot  & legend2\\
+			% 	...
+			% };
+			% command [and using the 'legend columns' option]
+			%
+			% \pgfplotslist@TOK@a={
+			% 	small plot  & legend1\\
+			% 	small plot  & legend2\\
+			% 	...
+			% }
+			% ( I have allocated the token registers in my
+			% liststructure.sty)
+			% 
+			% \global\def\pgfplots@TMP{
+			% 	\matrix {
+			% 		\TOKL@TA
+			% 	};
+			% }
+			% -> finally, \pgfplots@TMP will contain the complete command.
+			\pgfplotslist@TOK@a={}%
+			\let\curcolumnNum=\c@pgf@counta
+			\let\maxcolumnCount=\c@pgf@countb
+			\let\legendplotpos=\c@pgf@countc
+			\legendplotpos\expandafter=\pgfplots@legend@plot@pos
+			\curcolumnNum=0
+			\maxcolumnCount=\pgfplots@legend@columns\relax
+			%
+			\loop
+			\ifnum0<\pgfplots@numplots\relax
+				\pgfplots@pop@next@legend
+				\ifx\pgfplots@curlegend\pgfutil@empty
+				\else
+					\advance\curcolumnNum by1
+					\begingroup
+					\expandafter\pgfplots@split@opts\pgfplots@curlegend\pgfplots@result@to{\pgfplots@curlegend}{\pgfplots@curlegend@opts}%
+					\ifcase\legendplotpos
+						% legend plot pos=left 
+						\pgfplotslist@TOK@b=\expandafter{%
+								\expandafter\pgfplots@show@small@legendplots
+								\expandafter{\pgfplots@curlegend@opts}}%
+						\pgfplotslist@TOK@b=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfplotslist@TOK@b\expandafter{\pgfplots@curplotlist}%
+								\pgfmatrixnextcell\node}%
+						\pgfplotslist@TOK@b=\expandafter\expandafter\expandafter{%
+							\expandafter\the\expandafter\pgfplotslist@TOK@b
+							\expandafter{\pgfplots@curlegend};}%
+					\or
+						% legend plot pos=right
+						\pgfplotslist@TOK@b=\expandafter{%
+							\expandafter\node
+							\expandafter{\pgfplots@curlegend};%
+							\pgfmatrixnextcell
+							\pgfplots@show@small@legendplots}%
+						\pgfplotslist@TOK@b=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfplotslist@TOK@b\expandafter{\pgfplots@curlegend@opts}}%
+						\pgfplotslist@TOK@b=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfplotslist@TOK@b\expandafter{\pgfplots@curplotlist}}%
+					\or
+						% legend plot pos=none
+						\pgfplotslist@TOK@b=\expandafter{\expandafter\node\expandafter{\pgfplots@curlegend};}%
+					\fi
+					\ifnum\curcolumnNum=\maxcolumnCount
+						\pgfplotslist@TOK@b=\expandafter{\the\pgfplotslist@TOK@b\\}%
+					\else
+						\ifnum\pgfplots@numplots=0
+							\pgfplotslist@TOK@b=\expandafter{\the\pgfplotslist@TOK@b\\}%
+						\else
+							\pgfplotslist@TOK@b=\expandafter{\the\pgfplotslist@TOK@b\pgfmatrixnextcell}%
+						\fi
+					\fi
+					\xdef\pgfplots@TMP{%
+						\the\pgfplotslist@TOK@a
+						\the\pgfplotslist@TOK@b
+					}%
+					\endgroup
+					\ifnum\curcolumnNum=\maxcolumnCount
+						\curcolumnNum=0
+					\fi
+					\expandafter\pgfplotslist@TOK@a\expandafter{\pgfplots@TMP}%
+				\fi
+			\repeat
+			\pgfplotslist@TOK@b={\matrix[/pgfplots/every axis legend]}%
+			\xdef\pgfplots@TMP{%
+				\noexpand\def\noexpand\plotnum{0}%
+				\the\pgfplotslist@TOK@b {%
+					\the\pgfplotslist@TOK@a
+				};%
+			}%
+		\endgroup
+		\let\pgfplots@already@computed@legend@node=\pgfplots@TMP
+		\fi
+	\fi
+%\pgfplots@message{Vor legende: \meaning\pgfplots@already@computed@legend@node}%
+	\pgfplots@already@computed@legend@node
+}
+
+\newif\ifpgfplots@checkuniform@isfirst
+% Checks whether the argument to xtick or ytick is a UNIFORM tick
+% sequence.
+%
+% A uniform tick sequence is 0,...,10 and 3,4,5 and -5,-4,-2 but 
+% NOT 0,2,4 or 4,10.
+%
+% Furthermore, any NON-integer tick arguments are also assumed to be
+% NOT uniform.
+%
+% INPUT:
+% #1: a tick argument (i.e. something which can be put to 
+%     \foreach \x in {#1})
+%
+% OUTPUT:
+%    \pgfplots@isuniformticktrue
+%    or
+%    \pgfplots@isuniformtickfalse
+% depending on the check.
+% This variable will be set globally.
+\def\pgfplots@checkisuniformLOGtick#1{%
+	\begingroup
+	\global\pgfplots@isuniformticktrue
+	\pgfplots@checkuniform@isfirsttrue
+	\foreach \x in {#1}{%
+		\pgfmathmultiply@\x\reciproclogten
+		\let\cur=\pgfmathresult
+		% check whether
+		%  \cur - last == 1 (last = \pgfplots@TMPB)
+		\ifpgfplots@checkuniform@isfirst
+			\global\pgfplots@checkuniform@isfirstfalse
+		\else
+			\pgfmathsubtract@\cur\pgfplots@TMPB%
+			\pgfmathapproxequalto@\pgfmathresult{1.0}%
+			\ifpgfmathcomparison
+			\else
+				\global\pgfplots@isuniformtickfalse
+				\breakforeach
+			\fi
+		\fi
+		\global\let\pgfplots@TMPB=\cur
+	}%
+	\endgroup
+}
+
+% Checks whether the linear tick sequence #1 is a uniform tick.
+%
+% It also assigns pgfplots@tick@distance@#1  as the distance.
+%
+% see \pgfplots@checkisuniformLOGtick for details.
+\def\pgfplots@checkisuniformLINEARtick#1{%
+	\begingroup
+	\global\pgfplots@isuniformticktrue
+	\pgfplots@checkuniform@isfirsttrue
+	\global\let\pgfplots@TMPB=\pgfutil@empty
+	\global\let\pgfplots@TMP=\relax
+	\foreach \x in {#1}{%
+		\ifx\pgfplots@TMPB\pgfutil@empty
+		\else
+			\pgfmathsubtract@\x\pgfplots@TMPB
+			\ifpgfplots@checkuniform@isfirst
+				% remember first distance h = x_1 - x_0
+				\global\let\pgfplots@TMP=\pgfmathresult
+				\global\pgfplots@checkuniform@isfirstfalse
+			\else
+				% check whether x_i - x_{i-1} = h
+				\pgfmathapproxequalto@\pgfmathresult\pgfplots@TMP%
+				\ifpgfmathcomparison
+				\else
+					\global\pgfplots@isuniformtickfalse
+					\breakforeach
+				\fi
+			\fi
+		\fi
+		\global\let\pgfplots@TMPB=\x%
+	}%
+	\endgroup
+	\expandafter\let\csname pgfplots@tick@distance@#1\endcsname=\pgfplots@TMP
+}
+
+\def\skipsuffixzero#1.#2|{
+	{%
+	\def\pgfplots@TMP{#2}%
+	\def\pgfplots@TMPB{0}%
+	\ifx\pgfplots@TMP\pgfplots@TMPB
+		\global\def\pgfmathresult{#1}%
+	\else
+		\global\def\pgfmathresult{#1.#2}%
+	\fi
+	}%
+}
+
+\def\pgfmathlogtologten#1{%
+	\pgfmathparse{#1}%
+	\expandafter\pgfmathlogtologten@\expandafter{\pgfmathresult}%
+}
+
+% Simply divides #1 by log(10).
+\def\pgfmathlogtologten@#1{%
+	\pgfmathmultiply@{#1}\reciproclogten%
+}%
+
+% DEPRECATED.
+\def\logtologtentomacro#1#2{%
+	\pgfmathmultiply@{#1}\reciproclogten%
+	\expandafter\skipsuffixzero\pgfmathresult|%
+	\let#2=\pgfmathresult
+}
+
+% DEPRECATED.
+\def\logtologten#1{%
+	\pgfmathmultiply@{#1}\reciproclogten%
+	\expandafter\skipsuffixzero\pgfmathresult|%
+	\pgfmathresult
+}
+
+% helper method which computes log10*\x foreach \x in {#1}.
+% The result will be \xdef'ed into #2.
+\def\pgfplots@compute@tick@times@logten#1\to#2{%
+	\global\let#2=\pgfutil@empty
+	\foreach \pgfplots@TMPB in {#1} {%
+		\pgfmathmultiply@\pgfplots@TMPB\logten%
+		\ifx#2\pgfutil@empty
+			\xdef#2{\pgfmathresult}%
+		\else
+			\xdef#2{#2,\pgfmathresult}%
+		\fi
+	}%
+}
+
+\def\pgfplots@init@enlarge@limit@booleans{%
+	\pgfplots@enlargelimits@autofalse
+	\pgfplots@enlargelimitsfalse
+	\pgfplots@enlargelimits@rel@threshfalse
+	\edef\pgfplots@TMP{\pgfplots@enlargelimits}%
+	%
+	\def\pgfplots@TMPB{true}%
+	\ifx\pgfplots@TMP\pgfplots@TMPB
+		\pgfplots@enlargelimitstrue
+	\else
+		\def\pgfplots@TMPB{false}%
+		\ifx\pgfplots@TMP\pgfplots@TMPB
+		\else
+			\def\pgfplots@TMPB{auto}%
+			\ifx\pgfplots@TMP\pgfplots@TMPB
+				\pgfplots@enlargelimits@autotrue
+			\else
+				\begingroup
+				% try to read it as number:
+				\expandafter\pgf@xa\pgfplots@enlargelimits pt\relax
+				\endgroup
+				\pgfplots@enlargelimitstrue
+				\pgfplots@enlargelimits@rel@threshtrue
+			\fi
+		\fi
+	\fi
+}
+
+\def\pgfplots@enlarge@limit@for#1{%
+	\begingroup
+	\expandafter\let\expandafter\min\expandafter=\csname pgfplots@#1min\endcsname
+	\expandafter\let\expandafter\max\expandafter=\csname pgfplots@#1max\endcsname
+	\ifpgfplots@enlargelimits@rel@thresh
+		\edef\enlargepercent{\pgfplots@enlargelimits}%
+	\else
+		\def\enlargepercent{0.1}% FIXME : pack 10% as default into option 'enlargelimits' or so
+	\fi
+	\pgfmathsubtract@\max\min%
+	\pgf@xa\pgfmathresult pt
+	\pgf@xb\enlargepercent\pgf@xa
+	\ifdim\pgf@xb>0.001pt
+		% the case with 
+		%   enlargeabsolute ~= 0
+		% means that \min ~= \max.
+		% It is handled in another method.
+		\edef\enlargeabsolute{\pgf@sys@tonumber{\pgf@xb}}%
+		%
+		% compute xmin := xmin - enlargeabsolute
+		\pgfmathsubtract@\min\enlargeabsolute%
+		\let\min=\pgfmathresult
+		\pgfmathadd@\max\enlargeabsolute%
+		\let\max=\pgfmathresult
+	\fi
+	\xdef\pgfplots@TMP{\min}%
+	\xdef\pgfplots@TMPB{\max}%
+	\endgroup
+	\expandafter\global\expandafter\let\csname pgfplots@#1min\endcsname=\pgfplots@TMP
+	\expandafter\global\expandafter\let\csname pgfplots@#1max\endcsname=\pgfplots@TMPB
+}
+
+% Computes tick positions using the current axis limits.
+%
+% Parameters:
+% /pgfplots/max space between ticks
+%    Determines the maximum space which is not filled by at least one
+%    tick label (approximate, there is some rounding internally)
+% /pgfplots/try min ticks
+%    see manual
+%
+% Idea:
+% We want ticks at each 
+%    { i*H, i in \Z }.
+% Of course, there shouldn't be TOO MUCH ticks. 
+%
+% Our heuristics is to set
+%    desirednumticks = round(ACTUAL WIDTH / (max space between ticks) )
+% and generate H = (axis range) / (desirednumticks).
+%
+% Since not all step sizes H look well, restrict H to a set of allowed 
+% step sizes such as 
+%   { 1, 1/2, 1/5, 1/10 },
+% or, to be more precise:
+%   { 1*10^e, 2*10^e, 5*10^e }
+% -> round to the nearest matching number!
+%
+% For log-plots, 
+% 	H in { j*log(10), j=1,2,3,... }
+% where the usual case should be j = 1.
+%
+% Then, the resulting tick is
+% TICK={MIN,MIN+H,...,MAX}
+% where
+%    MIN = I*H
+% is chosen such that 
+%    axis minimum limit = I*H + rest; |rest| < H.
+%
+% Again, log plots follow a slightly different approach: here,
+%   MIN = I * log(10)
+% is chosen such that
+%    axis minimum limit = I*log(10) + rest; |rest| < log(10)
+% while H = j*log(10), j>=1.
+%
+%
+% PRECONDITION:
+% - limits are correct
+% - axis width/height is set correctly
+%
+% POSTCONDITION:
+% - Tick for axis #1 is assigned
+% - \ifpgfplots@determinedefaultvalues@needs@check@uniformtick is set
+%
+% REMARKS:
+% - this algorithms works also if the data range has been transformed
+%   with a LINEAR transformation.
+%   ATTENTION: as of 2008-05-15, the scaling trafo is AFFINE LINEAR.
+%   That means we have to eliminate the 'affine' shifting before the
+%   algorithms works correctly.
+\def\pgfplots@assign@default@tick@foraxis#1{%
+	\begingroup
+	% Shortcut-names:
+	\expandafter\let\expandafter\ifpgfplots@is@datascaled\csname ifpgfplots@apply@datatrafo@#1\endcsname
+	% Attention here: use UNSHIFTET scalings, see remark above
+	\expandafter\let\expandafter\pgfplots@data@scale@trafo\csname pgfplots@datascaletrafo@#1@noshift\endcsname
+	\expandafter\let\expandafter\pgfplots@data@scale@inverse@trafo\csname pgfplots@inverse@datascaletrafo@#1@noshift\endcsname
+	\expandafter\let\expandafter\ifpgfplots@cur@is@linear\csname ifpgfplots@#1islinear\endcsname
+	%
+	\let\desirednumticks=\c@pgf@countd
+	\let\Wr=\pgf@xc
+	\Wr=\csname pgfplots@#1coordmaxTEX\endcsname
+	\advance\Wr by-\csname pgfplots@#1coordminTEX\endcsname
+	% r = max place without ticks in pt -> choose desirednumticks >= W/r
+	\expandafter\expandafter\divide\Wr\axisdefaulttickwidth
+	\pgfmathsetcount{\desirednumticks}{\Wr}%
+	\advance\desirednumticks by1
+	\csname ifpgfplots@#1islinear\endcsname
+		\expandafter\ifnum\axisdefaulttryminticks>\desirednumticks
+			\expandafter\desirednumticks\axisdefaulttryminticks
+		\fi
+	\else
+		\expandafter\ifnum\pgfplots@default@try@minticks@log>\desirednumticks
+			\expandafter\desirednumticks\pgfplots@default@try@minticks@log\relax
+		\fi
+		\expandafter\ifx\csname pgfplots@#1tickten\endcsname\pgfutil@empty
+		\else
+			% log plot and tickten-option: provide special processing.
+			\edef\pgfplots@TMP{\csname pgfplots@#1tickten\endcsname}%
+			\expandafter\pgfplots@compute@tick@times@logten\pgfplots@TMP\to\pgfplots@TMP
+			\expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplots@TMP
+			\aftergroup\pgfplots@determinedefaultvalues@needs@check@uniformticktrue
+		\fi
+	\fi
+	%
+	\expandafter\ifx\csname pgfplots@#1tick\endcsname\pgfutil@empty
+		% Ok, we have either log or linear axis and need default
+		% ticks MIN,MIN+H,...,MAX.
+		\let\MINH=\pgf@xa
+		\let\H=\pgf@xb
+		\let\MAX=\pgfplots@tmpa
+		\let\MIN=\pgfplots@tmpb
+		% compute step size 'H':
+		\expandafter\MAX\csname pgfplots@#1max\endcsname pt
+		\advance\MAX by0.001pt% avoid round errors
+		%\expandafter\MIN\the\c@pgf@counta pt
+		\expandafter\MIN\csname pgfplots@#1min\endcsname pt
+		\H=\MAX
+		\advance\H by-\MIN
+		\c@pgf@counta=\desirednumticks
+		\advance\c@pgf@counta by-1
+		\divide\H by\c@pgf@counta
+%\message{determining ticks for #1-axis: Wr := (width/max space between ticks) = \the\Wr, desirednumticks=max(\axisdefaulttryminticks, trunc(Wr)) = \the\desirednumticks, H#1=(axis range/(desirednumticks-1)) = \the\H}%
+		%
+		% SEARCH for the NEXT FEASABLE H.
+		\edef\Hmacro{\pgf@sys@tonumber\H}%
+		\ifpgfplots@cur@is@linear
+			% CASE LINEAR AXIS
+			\ifpgfplots@is@datascaled
+				% This here works if the scaling trafo is linear.
+				\expandafter\pgfplots@data@scale@inverse@trafo\expandafter{\Hmacro}%
+				\let\Hmacro=\pgfmathresult
+			\else
+				\pgfmathfloatparsenumber{\Hmacro}%
+				\let\Hmacro=\pgfmathresult
+			\fi
+			\expandafter\pgfmathfloat@decompose\pgfmathresult\relax\pgfmathfloat@a@S\H\pgfmathfloat@a@E
+%\message{Got T^{-1}(H#1) = \Hmacro}%
+			% modify the mantisse:
+			\ifdim\H<2pt
+				\ifdim\H<1.5pt
+					\H=1.0pt
+				\else
+					\H=2.0pt
+				\fi
+			\else
+				\ifdim\H<4.9999pt
+					\ifdim\H<3.5pt
+						\H=2.0pt\relax
+					\else
+						\H=5.0pt\relax
+					\fi
+				\else
+					\ifdim\H<7.5pt
+						\H=5.0pt\relax
+					\else
+						\H=1.0pt\relax
+						\advance\pgfmathfloat@a@E by1
+					\fi
+				\fi
+			\fi
+%\message{Computed H#1=\the\H [unscaled]; transforming ... }%
+			\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgf@sys@tonumber{\H}}{\the\pgfmathfloat@a@E}%
+			\let\Hmacro=\pgfmathresult
+			\ifpgfplots@is@datascaled
+				\pgfplots@data@scale@trafo\Hmacro
+			\else
+				\pgfmathfloattofixed\Hmacro
+			\fi
+			\let\Hmacro=\pgfmathresult
+%\message{got H#1=\Hmacro\ [transformed]}%
+			\expandafter\H\Hmacro pt
+			\expandafter\aftergroup\csname pgfplots@determinedefaultvalues@#1isuniformtrue\endcsname
+			%
+			% Now, we want to activate the Tick set {i*H, i in \Z}
+			% compute I such that
+			%   xmin = I * H + rest;  |rest| < H
+			% -> I = round(xmin/H)
+			% -> MIN = I * H
+			%
+			% but first: eliminate any 'affine' data scaling!
+			\ifpgfplots@is@datascaled
+				\advance\MIN by\csname pgfplots@data@scale@trafo@SHIFT@#1\endcsname pt
+			\fi
+			\pgfmathlog@invoke@expanded\pgfmathdivide@{%
+				{\pgf@sys@tonumber\MIN}%
+				{\pgf@sys@tonumber\H}%
+			}%
+			\pgfmathsetcount{\c@pgf@counta}{\pgfmathresult}%
+			\ifdim\MIN<0pt
+				% the truncation rounds TOWARDS 0 which is not what I want.
+				\advance\c@pgf@counta by-1
+			\fi
+			\MIN=\H
+			\multiply\MIN by\c@pgf@counta
+			\ifpgfplots@is@datascaled
+				\advance\MIN by-\csname pgfplots@data@scale@trafo@SHIFT@#1\endcsname pt
+			\fi
+		\else
+			% CASE LOG AXIS
+			%
+			% search for the "best" H= j* log(10),  j an integer.
+			%
+			% And prefer j=1 if that is possible (otherwise minor
+			% ticks are not useful).
+			\pgfmathmultiply@{\Hmacro}{\reciproclogten}%
+			\expandafter\H\pgfmathresult pt
+%\message{ [ H / log(10) = \pgfmathresult}%
+			\ifdim\H<2pt
+				\H=1pt
+			\else
+				\ifnum\H<1pt
+					\H=1pt
+				\else
+					\expandafter\pgfmathfloor\expandafter{\pgfmathresult}%
+					\expandafter\H\pgfmathresult pt
+				\fi
+			\fi
+			\ifdim\H=1pt
+				\expandafter\aftergroup\csname pgfplots@determinedefaultvalues@#1isuniformtrue\endcsname
+				\pgfplots@isuniformticktrue
+			\else
+				\expandafter\aftergroup\csname pgfplots@determinedefaultvalues@#1isuniformfalse\endcsname
+				\pgfplots@isuniformtickfalse
+			\fi
+%\message{final H=\pgf@sys@tonumber{\H} * log(10)}%
+			\H=\logten\H\relax
+			% Now, we want to activate the Tick set 
+			%   {lowest, lowest+H, ..., highest}
+			%
+			% Where 
+			% 	lowest =  I * log(10) + rest, |rest| < log(10).
+			% this is conceptionally different from the approach for
+			% linear axes, because H = j*log(10).
+			%
+			% remember the original xmin in MINH:
+			\MINH=\MIN
+			%
+			% and compute I and I*log(10) here:
+			\expandafter\MIN\reciproclogten\MIN\relax
+			\edef\pgfmathresult{\pgf@sys@tonumber{\MIN}}%
+			\pgfmathsetcount{\c@pgf@counta}{\pgfmathresult}%
+			\ifdim\MIN<0pt
+				% the truncation rounds TOWARDS 0 which is not what I want.
+				\advance\c@pgf@counta by-1
+			\fi
+			\expandafter\MIN\logten pt
+			\multiply\MIN by\c@pgf@counta
+			\ifpgfplots@isuniformtick
+			\else
+				% This here is a special case to move the first tick
+				% near the lower axis limit.
+				%
+				% "Near" means either directly above or directly below ymin.
+				% 
+				% My application example is as follows:
+				% Let H = 2*log(10).
+				% Furthermore, ymin = 3e-6, ymax= 8e-2. That means we can choose either
+				%    10^{-5}, 10^{-3}, 10^{-1}
+				% or
+				%    10^{-4}, 10^{-2}
+				% as ticks. Well, I prefer the first one.
+				%
+				% HEURISTICS: start as near to ymin as possible!
+				%
+				% We check here if we can come nearer to ymin if we
+				% shift the current tick by log(10):
+				%  if( ymin - I * log(10) < 0.5*H ->  use I+1, that means add log(10).
+				%
+				% that's equivalent to 
+				%  2*(ymin - I * log(10)) - H < 0.
+				\advance\MINH by-\MIN
+				\multiply\MINH by2
+				\advance\MINH by-\H
+				% 
+				\ifdim\MINH<0pt
+					\expandafter\advance\expandafter\MIN\logten pt
+				\fi
+			\fi
+		\fi
+		\MINH=\MIN
+		\advance\MINH by\H
+%\pgfplots@message{final H=\the\H}%
+		\xdef\pgfplots@TMP{\pgf@sys@tonumber{\MIN},\pgf@sys@tonumber{\MINH},...,\pgf@sys@tonumber{\MAX}}%
+		\xdef\pgfplots@TMPB{\pgf@sys@tonumber{\H}}%
+		\aftergroup\pgfplots@determinedefaultvalues@needs@check@uniformtickfalse
+	\fi
+	\endgroup
+	\expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplots@TMP
+	\expandafter\let\csname pgfplots@tick@distance@#1\endcsname=\pgfplots@TMPB
+%\pgfplots@message{pgfplots.sty: #1tick set to \csname pgfplots@#1tick\endcsname [#1mode=\the\csname pgfplots@#1mode\endcsname,  #1min=\csname pgfplots@#1min\endcsname, #1max=\csname pgfplots@#1max\endcsname].}%
+}
+
+% Helper method for 
+%  \pgfplots@apply@data@scale@trafo@to@options@for
+% #1: the ticks
+% #2: the trafo macro name 
+% #3: the output macro name
+\long\def\pgfplots@apply@data@scale@trafo@to@user@ticks#1#2\to#3{%
+	\let#3=\pgfutil@empty
+	\foreach \pgfplots@TMPB in {#1} {%
+		\pgfmathfloatparsenumber{\pgfplots@TMPB}%
+		\expandafter#2\expandafter{\pgfmathresult}%
+		\ifx#3\pgfutil@empty
+			\xdef#3{\pgfmathresult}%
+		\else
+			\xdef#3{#3,\pgfmathresult}%
+		\fi
+	}%
+	%
+}%
+
+% Helper method for 
+%  \pgfplots@apply@data@scale@trafo@to@options@for
+% #1: the ticks ALREADY IN FLOAT FORMAT
+% #2: the trafo macro name 
+% #3: the output macro name
+\long\def\pgfplots@apply@data@scale@trafo@to@user@ticks@isfloat#1#2\to#3{%
+	\let#3=\pgfutil@empty
+	\foreach \pgfplots@TMPB in {#1} {%
+		#2{\pgfplots@TMPB}%
+		\ifx#3\pgfutil@empty
+			\xdef#3{\pgfmathresult}%
+		\else
+			\xdef#3{#3,\pgfmathresult}%
+		\fi
+	}%
+	%
+}%
+
+% helper for \pgfplots@apply@data@scale@trafo@to@options@for.
+\def\pgfplots@compute@number@order@for@trafo@isdimen#1\tocount#2{%
+	\edef\pgfplots@TMP{\pgf@sys@tonumber{#1}}%
+	\pgfmathfloatparsenumber{\pgfplots@TMP}%
+	\expandafter\pgfmathfloat@decompose@E\pgfmathresult\relax#2
+	\advance#2 by1
+}
+
+% helper for \pgfplots@apply@data@scale@trafo@to@options@for.
+% 
+\def\pgfplots@compute@number@order@for@trafo@isfloat#1\tocount#2{%
+	\expandafter\pgfmathfloat@decompose@E#1\relax#2
+	\advance#2 by1
+}
+
+% Initialises the data scale transformation and applies it to any
+% user specified options.
+%
+% PRECONDITION:
+%   - all axis limits are available in float representation
+%   - \pgfplots@set@default@size@options has been called before
+% POSTCONDITION:
+%   - the scaling transformation is set up,
+%   - all axis limits are transformed,
+%   - any user input (like ticks and tick labels)
+%     will reflect the changes.
+\def\pgfplots@apply@data@scale@trafo@to@options@for#1{%
+	% initialise data scale transformation 
+	%   T(x) = 10^{q-m} * x
+	%
+	\begingroup
+	\let\data@max@order=\c@pgf@counta
+	\let\data@cur@order=\c@pgf@countb
+	\let\data@dimen=\pgf@xa
+	\let\data@tmp=\pgf@xb
+	\let\data@dimen@order=\c@pgf@countc
+	\let\data@EXPONENT=\c@pgf@countd
+	\expandafter\let\expandafter\pgfplots@min@float\csname pgfplots@#1min\endcsname
+	\expandafter\let\expandafter\pgfplots@max@float\csname pgfplots@#1max\endcsname
+	\expandafter\let\expandafter\pgfplots@actual@trafo\csname pgfplots@datascaletrafo@#1\endcsname
+	%
+	% Step 1: compute 'm', the data order
+	\pgfplots@compute@number@order@for@trafo@isfloat
+		\pgfplots@min@float
+		\tocount\data@cur@order
+	%
+	\data@max@order=\data@cur@order
+	%
+	\pgfplots@compute@number@order@for@trafo@isfloat
+		\pgfplots@max@float
+		\tocount\data@cur@order
+	%
+	\ifnum\data@cur@order>\data@max@order
+		\data@max@order=\data@cur@order
+	\fi
+	%
+	% Step 2: compute 'q', the #1-size of the axis.
+	\expandafter\ifx\csname pgfplots@#1\endcsname\pgfutil@empty
+		% We have 'width' or 'height'.
+		%
+		% Use the order of these parameters.
+		\def\pgfplots@TMP{#1}%
+		\def\pgfplots@TMPB{x}%
+		\ifx\pgfplots@TMP\pgfplots@TMPB
+			\expandafter\data@dimen\pgfplots@width\relax
+		\else
+			\def\pgfplots@TMPB{y}%
+			\ifx\pgfplots@TMP\pgfplots@TMPB
+				\expandafter\data@dimen\pgfplots@height\relax
+			\fi
+		\fi
+		\pgfplots@compute@number@order@for@trafo@isdimen
+			\data@dimen
+			\tocount\data@dimen@order
+		% This here is to avoid inaccuracies in the final
+		% axis rectangle size, see \pgfplots@initsizes:
+		%\advance\data@dimen@order by-1
+	\else
+		% FIXME:
+		% we have either the 'x=1cm' or 'y=1cm' option!
+		% How should I initialise the trafo!?
+		\data@dimen@order=3
+	\fi
+	%
+%\message{Direction #1: data max order=\the\data@max@order;  data dimen order=\the\data@dimen@order. }%
+	\data@EXPONENT=\data@dimen@order
+	\advance\data@EXPONENT by-\data@max@order
+	% Now, I introduce a loop which shall avoid cancellation of
+	% significant digits.
+	%
+	% Harmless Example: 
+	%  if we have data shift = -3 and 
+	%  max = 2e6, min = 1e6, then max-min = 1e6; T(max)-T(min) = 1e3 which is ok.
+	%  In this case, the loop won't change anything.
+	%
+	% Critical Example:
+	%  if we have data shift = -3 and
+	%  max = 1980, min = 1930 then 
+	%    T(max) = 1.98 and T(min) = 1.93
+	%  and thus T(max)-T(min) = 0.05 . 
+	%  Considering that this is the axis range
+	%  in which tick labels and plot points need to be computed, we
+	%  only have two or three digits left! That happens because the
+	%  prefix '19' is common and is cancelled in the subtraction.
+	%  Idea: while T(max)-T(min) < O(10^2) -> increase shift by +1
+	%  (and make sure that T(max) < MAX_VALID_TEX_NUMBER).
+	%
+	\pgfplots@loop@CONTINUEtrue
+	\expandafter\edef\csname pgfplots@data@scale@trafo@SHIFT@#1\endcsname{0}%
+	\loop
+	\expandafter\edef\csname pgfplots@data@scale@trafo@EXPONENT@#1\endcsname{\the\data@EXPONENT}%
+	\pgfplots@actual@trafo{\pgfplots@min@float}%
+	\let\pgfplots@min@fixed=\pgfmathresult
+	\ifpgfplots@loop@CONTINUE
+		\pgfplots@actual@trafo{\pgfplots@max@float}%
+		\let\pgfplots@max@fixed=\pgfmathresult
+		\expandafter\data@tmp\pgfplots@max@fixed pt
+%\message{Current trafo SHIFT for #1 direction: \the\data@EXPONENT; original #1 limits: [\pgfplots@min@float:\pgfplots@max@float]; current transformed #1 limits: [\pgfplots@min@fixed:\pgfplots@max@fixed]; cancellation check max-min running...}%
+		\ifdim\data@tmp<0pt
+			% I need absolute values here:
+			\multiply\data@tmp by-1\relax
+		\fi
+		\pgfplots@loop@CONTINUEfalse
+		\ifdim\data@tmp<1500pt% a multiplication with '10' results in max = 15000 which is the upper limit.
+			\pgfmathsubtract@{\pgfplots@max@fixed}{\pgfplots@min@fixed}%
+			\expandafter\data@dimen\pgfmathresult pt
+			\ifdim\data@dimen<100pt% I guess if max-min = O(100), we have quite good accuracy
+				\ifdim\data@dimen<0.0001pt
+				\else
+					\advance\data@EXPONENT by1
+					\pgfplots@loop@CONTINUEtrue
+				\fi
+			\fi
+		\fi
+	\repeat
+	\xdef\pgfplots@TMP{\csname pgfplots@data@scale@trafo@EXPONENT@#1\endcsname}%
+	\xdef\pgfplots@TMPB{\pgfplots@min@fixed}%
+	\endgroup
+%\message{Initialising the data scale transformation in direction #1 to 10^\pgfplots@TMP*#1 - \pgfplots@TMPB...}%
+	% COMPLETE INITIALISATION:
+	\ifpgfplots@EMERGENCY@FORCE@DATA@TRAFO@TO@IDENTITY
+		\pgfplots@warning{WARNING: the automatic scaling of input data has been DISABLED to allow unscalable commands. DISABLING THE DATA SCALING LIMITS THE DATA RANGE! I hope I can fix this issue as soon as possible. Please take a look at the manual for more information. If you get 'OVERFLOW' or 'UNDERFLOW' errors, you may need to disable the axispath.}%
+		\def\pgfplots@TMP{0}%
+		\def\pgfplots@TMPB{0}%
+	\fi
+	\expandafter\let\csname pgfplots@data@scale@trafo@EXPONENT@#1\endcsname\pgfplots@TMP
+	\expandafter\let\csname pgfplots@data@scale@trafo@SHIFT@#1\endcsname\pgfplots@TMPB%
+	%
+	% ... and apply transformation to any user input
+	%
+	% Transform axis limits:
+%\message{#1-limits BEFORE data transformation: [\csname pgfplots@#1min\endcsname:\csname pgfplots@#1max\endcsname]}%
+	\expandafter\expandafter\csname pgfplots@datascaletrafo@#1\endcsname\expandafter{\csname pgfplots@#1min\endcsname}%
+	\expandafter\global\expandafter\let\csname pgfplots@#1min\endcsname=\pgfmathresult
+	%
+	\expandafter\expandafter\csname pgfplots@datascaletrafo@#1\endcsname\expandafter{\csname pgfplots@#1max\endcsname}%
+	\expandafter\global\expandafter\let\csname pgfplots@#1max\endcsname=\pgfmathresult
+%\message{#1-limits after data transformation: [\csname pgfplots@#1min\endcsname:\csname pgfplots@#1max\endcsname]}%
+	%
+	% Convert any user-specified ticks:
+	\edef\pgfplots@TMP{\csname pgfplots@#1tick\endcsname}%
+	% this here should also work with 'xtick=\pgfutil@empty', the "No tick" command.
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\pgfplots@toka=\expandafter{\csname pgfplots@datascaletrafo@#1\endcsname}%
+		\def\pgfplots@TMPB{data}%
+		\ifx\pgfplots@TMP\pgfplots@TMPB
+			% we have #1tick = data
+			%
+			% Since we have entered this method, we know that these
+			% coordinate ARE ALREADY in floating point representation.
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@firstplot@coords@#1\endcsname
+			\pgfplotslist@TOK@a=\expandafter{\pgfplots@TMP}%
+			\edef\pgfplots@TMP{{\the\pgfplotslist@TOK@a}\the\pgfplots@toka}%
+			\expandafter\pgfplots@apply@data@scale@trafo@to@user@ticks@isfloat\pgfplots@TMP\to\pgfplots@TMPC
+		\else
+			\pgfplotslist@TOK@a=\expandafter{\pgfplots@TMP}%
+%\message{Converting #1tick='\csname pgfplots@#1tick\endcsname'}%
+			\edef\pgfplots@TMP{{\the\pgfplotslist@TOK@a}\the\pgfplots@toka}%
+			\expandafter\pgfplots@apply@data@scale@trafo@to@user@ticks\pgfplots@TMP\to\pgfplots@TMPC
+		\fi
+		\expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplots@TMPC
+	\fi
+	%
+	% Convert any extra-ticks, see above.
+	\edef\pgfplots@TMP{\csname pgfplots@extra@#1tick\endcsname}%
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\pgfplots@toka=\expandafter{\csname pgfplots@datascaletrafo@#1\endcsname}%
+		\edef\pgfplots@TMP{{\csname pgfplots@extra@#1tick\endcsname}\the\pgfplots@toka}%
+		\expandafter\pgfplots@apply@data@scale@trafo@to@user@ticks\pgfplots@TMP\to\pgfplots@TMPC
+		\expandafter\let\csname pgfplots@extra@#1tick\endcsname=\pgfplots@TMPC
+	\fi
+	%
+	% Transform any explicit axis unit scalings:
+	\expandafter\ifx\csname pgfplots@#1\endcsname\pgfutil@empty
+	\else
+%\message{Converting #1 unit scale='\csname pgfplots@#1\endcsname' ... }%
+		\expandafter\pgfmathparse\expandafter{\csname pgfplots@#1\endcsname}%
+		\expandafter\expandafter\csname pgfplots@inverse@datascaletrafo@tofixed@#1@noshift\endcsname\expandafter{\pgfmathresult}%
+		\expandafter\edef\csname pgfplots@#1\endcsname{\pgfmathresult pt}%
+%\message{to #1='\csname pgfplots@#1\endcsname'.}%
+	\fi
+}
+
+\newif\ifpgfplots@determinedefaultvalues@xisuniform
+\newif\ifpgfplots@determinedefaultvalues@yisuniform
+\newif\ifpgfplots@determinedefaultvalues@needs@check@uniformtick
+
+\def\pgfplots@determinedefaultvalues{%
+	\ifpgfplots@limits@are@computed
+	\else
+		% EMPTY AXIS:
+		\pgfplots@warning{WARNING: You have a plot with empty range. This may produce errors!}%
+	\fi
+	%
+	\pgfplots@set@default@size@options
+	%
+	\ifpgfplots@apply@datatrafo@x
+		\let\pgfplots@xmin@unscaled@as@float=\pgfplots@xmin
+		\let\pgfplots@xmax@unscaled@as@float=\pgfplots@xmax
+		\pgfplots@apply@data@scale@trafo@to@options@for x%
+	\else
+		\def\pgfplots@TMPB{data}%
+		\ifx\pgfplots@xtick\pgfplots@TMPB
+			\let\pgfplots@xtick=\pgfplots@firstplot@coords@x
+		\fi
+		\let\pgfplots@xmin@unscaled@as@float=\pgfutil@empty
+		\let\pgfplots@xmax@unscaled@as@float=\pgfutil@empty
+	\fi
+	\ifpgfplots@apply@datatrafo@y
+		\let\pgfplots@ymin@unscaled@as@float=\pgfplots@ymin
+		\let\pgfplots@ymax@unscaled@as@float=\pgfplots@ymax
+		\pgfplots@apply@data@scale@trafo@to@options@for y%
+	\else
+		\def\pgfplots@TMPB{data}%
+		\ifx\pgfplots@ytick\pgfplots@TMPB
+			\let\pgfplots@ytick=\pgfplots@firstplot@coords@y
+		\fi
+		\let\pgfplots@ymin@unscaled@as@float=\pgfutil@empty
+		\let\pgfplots@ymax@unscaled@as@float=\pgfutil@empty
+	\fi
+	\pgfplots@datascaletrafo@initialisedtrue
+	%
+	% From now on, we can always work with pgfmath.
+	% We simply need to apply the data scaling trafo before doing so.
+	\pgfplots@float@numerics@mode@xfalse
+	\pgfplots@float@numerics@mode@yfalse
+	%
+	\pgfkeysgetvalue{/pgfplots/minor x tick num}\pgfplots@minor@xtick@num
+	\pgfkeysgetvalue{/pgfplots/minor y tick num}\pgfplots@minor@ytick@num
+	\ifpgfplots@xislinear
+		\ifnum\pgfplots@minor@xtick@num=0\relax
+			\pgfplots@xminorticksfalse
+			\pgfplots@xminorgridsfalse
+		\else
+			\pgfplots@xminortickstrue
+		\fi
+	\fi
+	\ifpgfplots@yislinear
+		\ifnum\pgfplots@minor@ytick@num=0\relax
+			\pgfplots@yminorticksfalse
+			\pgfplots@yminorgridsfalse
+		\else
+			\pgfplots@yminortickstrue
+		\fi
+	\fi
+	%
+	\pgfplots@init@enlarge@limit@booleans
+	\ifpgfplots@enlargelimits
+		% relax the sizes.
+		%
+		% Idea: if the user chose his xmin,xmax tight to his data,
+		% this here will look better.
+		\pgfplots@enlarge@limit@for x
+		\pgfplots@enlarge@limit@for y
+	\else
+		\ifpgfplots@enlargelimits@auto
+			\ifpgfplots@hide
+				% there is no axis, so skip this enlargement (unless
+				% the user explizitly requests it)
+			\else
+				% FIXME : this here should be user-configurable!
+				\ifpgfplots@autocompute@xlim
+					\pgfplots@enlarge@limit@for x
+				\fi
+				\ifpgfplots@autocompute@ylim
+					\pgfplots@enlarge@limit@for y
+				\fi
+			\fi
+		\fi
+	\fi
+	%
+	\pgfplots@avoid@empty@axis@range@for x%
+	\pgfplots@avoid@empty@axis@range@for y%
+	%
+	\pgfplots@initsizes
+	%
+	\pgfplots@determinedefaultvalues@xisuniformtrue
+	\pgfplots@determinedefaultvalues@yisuniformtrue
+	\pgfplots@determinedefaultvalues@needs@check@uniformticktrue
+	\ifx\pgfplots@xtick\pgfutil@empty
+		\pgfplots@assign@default@tick@foraxis{x}%
+	\fi
+	\ifpgfplots@determinedefaultvalues@needs@check@uniformtick
+		\ifpgfplots@xislinear
+			\expandafter\pgfplots@checkisuniformLINEARtick\expandafter{\pgfplots@xtick}%
+			\ifpgfplots@isuniformtick
+				\pgfplots@determinedefaultvalues@xisuniformtrue
+			\else
+				\pgfplots@determinedefaultvalues@xisuniformfalse
+			\fi
+		\else
+			\expandafter\pgfplots@checkisuniformLOGtick\expandafter{\pgfplots@xtick}%
+			\ifpgfplots@isuniformtick
+				\pgfplots@determinedefaultvalues@xisuniformtrue
+			\else
+				\pgfplots@determinedefaultvalues@xisuniformfalse
+			\fi
+		\fi
+	\fi
+	\ifpgfplots@determinedefaultvalues@xisuniform
+	\else
+		\pgfplots@xminorticksfalse
+	\fi
+	%
+	%
+	%
+	\pgfplots@determinedefaultvalues@needs@check@uniformticktrue
+	\ifx\pgfplots@ytick\pgfutil@empty
+		\pgfplots@assign@default@tick@foraxis{y}%
+	\fi
+	\ifpgfplots@determinedefaultvalues@needs@check@uniformtick
+		\ifpgfplots@yislinear
+			\expandafter\pgfplots@checkisuniformLINEARtick\expandafter{\pgfplots@ytick}%
+			\ifpgfplots@isuniformtick
+				\pgfplots@determinedefaultvalues@yisuniformtrue
+			\else
+				\pgfplots@determinedefaultvalues@yisuniformfalse
+			\fi
+		\else
+			\expandafter\pgfplots@checkisuniformLOGtick\expandafter{\pgfplots@ytick}%
+			\ifpgfplots@isuniformtick
+				\pgfplots@determinedefaultvalues@yisuniformtrue
+			\else
+				\pgfplots@determinedefaultvalues@yisuniformfalse
+			\fi
+		\fi
+	\fi
+	\ifpgfplots@determinedefaultvalues@yisuniform
+	\else
+		\pgfplots@yminorticksfalse
+	\fi
+	%
+	\ifx\pgfplots@xticklabel\pgfutil@empty
+		\ifpgfplots@xislinear
+			\def\pgfplots@xticklabel{\axisdefaultticklabel}%
+		\else
+			\def\pgfplots@xticklabel{\axisdefaultticklabellog}%
+		\fi
+	\fi
+	\ifx\pgfplots@extra@xticklabel\pgfutil@empty
+		\let\pgfplots@extra@xticklabel=\pgfplots@xticklabel
+	\fi
+	\ifx\pgfplots@yticklabel\pgfutil@empty
+		\ifpgfplots@yislinear
+			\def\pgfplots@yticklabel{\axisdefaultticklabel}%
+		\else
+			\def\pgfplots@yticklabel{\axisdefaultticklabellog}%
+		\fi
+	\fi
+	\ifx\pgfplots@extra@yticklabel\pgfutil@empty
+		\let\pgfplots@extra@yticklabel=\pgfplots@yticklabel
+	\fi
+	%
+	%
+	\pgfplots@prepare@ZERO@coordinates
+}
+
+% This code is mainly interesting for bar plots.
+%
+% It precomputes x = 0 and y = 0 - which is not necessarily
+% trivial in case of data scaling. Furthermore, it applies
+% coordinate clipping to the resulting values and multiplies them
+% with x- and y scale vectors.
+\def\pgfplots@prepare@ZERO@coordinates{%
+	\ifpgfplots@apply@datatrafo@x
+		\pgfplots@datascaletrafo@fromfixed@x{0}%
+		\global\let\pgfplots@ZERO@x=\pgfmathresult
+	\else
+		\gdef\pgfplots@ZERO@x{0}%
+	\fi
+	\pgfmathmax@{\pgfplots@ZERO@x}{\pgfplots@xmin}%
+	\global\let\pgfplots@ZERO@x=\pgfmathresult
+	%
+	\ifpgfplots@apply@datatrafo@y
+		\pgfplots@datascaletrafo@fromfixed@y{0}%
+		\global\let\pgfplots@ZERO@y=\pgfmathresult
+	\else
+		\gdef\pgfplots@ZERO@y{0}%
+	\fi
+	\pgfmathmax@{\pgfplots@ZERO@y}{\pgfplots@ymin}%
+	\global\let\pgfplots@ZERO@y=\pgfmathresult
+	\pgfinterruptboundingbox%
+	\pgfpointxy{\pgfplots@ZERO@x}{\pgfplots@ZERO@y}%
+	\xdef\pgfplots@ZERO@x{\the\pgf@x}%
+	\xdef\pgfplots@ZERO@y{\the\pgf@y}%
+	\endpgfinterruptboundingbox%
+}%
+
+
+% Helper method for initsizes.
+%
+% It computes a scaling such that \pgfplots@width = SCALE * ACTUAL WIDTH.
+% 
+% The actual width is 
+% 	c + x*(xmax-xmin)
+% based on
+% - x*xmax = \pgfplots@xcoordmaxTEX
+% - x*xmin = \pgfplots@xcoordminTEX
+% - c = estimated, a constant for the axis label/tick labels
+%
+% Arguments: 
+% #1: the output argument for the SCALE.
+\def\pgfplots@initsizes@getXscale\into#1{%
+	\expandafter\pgfplots@tmpa\pgfplots@width\relax
+	% EXPECTED WIDTH = X = \pgfplots@width
+	% ACTUAL WIDTH = c + x * (xmax-xmin)
+	% where c is a CONSTANT (for the axis labels/tick labels).
+	% -> \pgfplots@tmpXscale = (X - c) / (x *(xmax-xmin))
+	%
+	% \pgfplots@tmpa := X-c:
+	\ifpgfplots@scale@only@axis
+	\else
+		\advance\pgfplots@tmpa by-45pt% FIXME determine 'c' correctly!
+	\fi
+	\ifdim\pgfplots@tmpa<0pt
+		\pgfplots@error{Error: Plot width `\pgfplots@width' is too small. This can't be realised while maintaining constant width for y-labels. Sorry, label width are only approximate. You will need to adjust your width.}%
+		\pgfplots@tmpa=0pt
+	\fi
+	% \pgfplots@tmpb := x*(xmax-xmin):
+	\pgfplots@tmpb=\pgfplots@xcoordmaxTEX
+	\advance\pgfplots@tmpb by-\pgfplots@xcoordminTEX
+	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
+		{\pgf@sys@tonumber\pgfplots@tmpa}%
+		{\pgf@sys@tonumber\pgfplots@tmpb}%
+	}%
+	\let#1=\pgfmathresult
+%\pgfplots@message{pgfplots.sty: Computing 'x' such that 'width = c + x*(xmax-xmin)';
+%	c=estimated, 
+%	width-c =\the\pgfplots@tmpa,  
+%	x*(xmax[=\the\pgfplots@xcoordmaxTEX] - xmin[=\the\pgfplots@xcoordminTEX)]) = \the\pgfplots@tmpb  
+%	-> x-scale =#1 }%
+}
+
+% The same as \pgfplots@initsizes@getXscale, just for the height.
+\def\pgfplots@initsizes@getYscale\into#1{%
+	\expandafter\pgfplots@tmpa\pgfplots@height\relax
+	% EXPECTED WIDTH = X = \pgfplots@width
+	% ACTUAL WIDTH = c + x * (xmax-xmin)
+	% where c is a CONSTANT (for the axis labels/tick labels).
+	% -> \pgfplots@tmpXscale = (X - c) / (x *(xmax-xmin))
+	%
+	% \pgfplots@tmpa := X-c:
+	\ifpgfplots@scale@only@axis
+	\else
+		\advance\pgfplots@tmpa by-45pt\relax% FIXME determine 'c' correctly!
+	\fi
+	\ifdim\pgfplots@tmpa<0pt
+		\pgfplots@error{Error: Plot height `\pgfplots@height' is too small. This can't be realised while maintaining constant height for x-labels. Sorry, label heights are only approximate. You will need to adjust your height.}%
+		\pgfplots@tmpa=0pt
+	\fi
+	% \pgfplots@tmpb := x*(xmax-xmin):
+	\pgfplots@tmpb=\pgfplots@ycoordmaxTEX
+	\advance\pgfplots@tmpb by-\pgfplots@ycoordminTEX
+	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
+		{\pgf@sys@tonumber\pgfplots@tmpa}%
+		{\pgf@sys@tonumber\pgfplots@tmpb}%
+	}%
+	\let#1=\pgfmathresult
+%\pgfplots@message{pgfplots.sty: Computing 'y' such that 'height = c + y*(ymax-ymin)';
+%	height=\pgfplots@height,
+%	c=estimated,
+%	height-c =\the\pgfplots@tmpa,  
+%	y*(ymax[=\the\pgfplots@ycoordmaxTEX] - ymin[=\the\pgfplots@ycoordminTEX)]) = \the\pgfplots@tmpb  
+%	-> y-scale =#1 }%
+}
+
+
+\newif\ifpgfplots@avoid@emptyrange@@range@is@approx@equal
+% Checks whether axis limits in coordinate #1 are approximately equal.
+%
+% If that is the case, force a non-zero width of the range.
+%
+\def\pgfplots@avoid@empty@axis@range@for#1{%
+	% Check if axis limits are empty:
+	\begingroup
+	\expandafter\let\expandafter\if@cur@is@scaled\csname ifpgfplots@apply@datatrafo@#1\endcsname
+	\expandafter\let\expandafter\min\csname pgfplots@#1min\endcsname
+	\expandafter\let\expandafter\max\csname pgfplots@#1max\endcsname
+	\let\min@d=\pgf@xa
+	\let\max@d=\pgf@xb
+	\let\diff=\pgf@xc
+	\expandafter\min@d\min pt
+	\expandafter\max@d\max pt
+	\diff=\max@d
+	\advance\diff by-\min@d
+	% FIXME : I need a RELATIVE check here!
+	% but: real number point division is expensive
+	\if@cur@is@scaled
+		% this here should be sufficient because the axis
+		% has absolute values of order O( 10^3 ) or so.
+		\ifdim\diff<0.01pt
+			\pgfplots@avoid@emptyrange@@range@is@approx@equaltrue
+		\fi
+	\else
+		% there is no data scaling, so I should be much more defensive
+		% with absolute thresholds...
+		\ifdim\diff<0.01pt
+			\pgfplots@avoid@emptyrange@@range@is@approx@equaltrue
+		\fi
+	\fi
+	\ifpgfplots@avoid@emptyrange@@range@is@approx@equal
+		\pgfplots@warning{WARNING: Axis range for axis #1 (transformed: [\min:\max]) is approximately equal; enlargeing it.}%
+		% the case \min ~= \max
+		%
+		% enlarge \max and shrink \min:
+		\ifdim\max@d<0pt
+			\ifdim\max@d<-1pt
+				\max@d=0.8\max@d
+				\min@d=1.2\min@d
+			\else
+				\advance\max@d by-1pt
+				\advance\min@d by1pt
+			\fi
+		\else
+			\ifdim\max@d>1pt
+				\max@d=1.2\max@d
+				\min@d=0.8\min@d
+			\else
+				\ifdim\max@d=0pt
+					\if@cur@is@scaled
+						% we can't simply add a constant in the
+						% transformed range.
+						%
+						% So: set limits to [-1,1] = [-1.0e0,+1.0e0]
+						\pgfmathfloatcreate{2}{1.0}{0}%
+						\csname pgfplots@datascaletrafo@#1\endcsname{\pgfmathresult}%
+						\let\min=\pgfmathresult
+						\pgfmathfloatcreate{1}{1.0}{0}%
+						\csname pgfplots@datascaletrafo@#1\endcsname{\pgfmathresult}%
+						\let\max=\pgfmathresult
+%\pgfplots@message{[trafo shift = \csname pgfplots@data@scale@trafo@EXPONENT@#1\endcsname; setting limits -1:1]}%
+						\expandafter\min@d\min pt
+						\expandafter\max@d\max pt
+					\else
+						\advance\max@d by1pt
+						\advance\min@d by-1pt
+					\fi
+				\else
+					\advance\max@d by1pt
+					\advance\min@d by-1pt
+				\fi
+			\fi
+		\fi
+		\xdef\pgfplots@TMP{\pgf@sys@tonumber{\min@d}}%
+		\xdef\pgfplots@TMPB{\pgf@sys@tonumber{\max@d}}%
+%\pgfplots@message{ -> #1 = \pgfplots@TMP : \pgfplots@TMPB;}%
+	\else
+		\global\let\pgfplots@TMP=\min%
+		\global\let\pgfplots@TMPB=\max%
+	\fi
+	\endgroup
+	\expandafter\global\expandafter\let\csname pgfplots@#1min\endcsname=\pgfplots@TMP
+	\expandafter\global\expandafter\let\csname pgfplots@#1max\endcsname=\pgfplots@TMPB
+}
+
+% PRECONDITION:
+% 	none
+% POSTCONDITION:
+% 	\pgfplots@default@aspect@ratio is set.
+\def\pgfplots@compute@default@aspect@ratio{%
+	\expandafter\pgfmath@x\axisdefaultwidth
+	\expandafter\pgfmath@y\axisdefaultheight
+	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
+		{\pgf@sys@tonumber{\pgfmath@x}}%
+		{\pgf@sys@tonumber{\pgfmath@y}}%
+	}%
+	\let\pgfplots@default@aspect@ratio=\pgfmathresult
+}
+
+\def\pgfplots@set@default@size@options{%
+	% The axes 'x' and 'y' vectors will be scaled such that the total
+	% size is (\axisdefaultwidth, \axisdefaultheight).
+	%
+	% If the user specifies ONE of width OR height, 
+	% the plot will be resized; keeping the aspect ratio.
+	%
+	\let\pgfplots@default@aspect@ratio=\pgfutil@empty
+	% CASES:
+	% hasx := 'x' option non-empty
+	% hasy := 'y' option non-empty
+	% W := 'width' option non-empty
+	% H := 'height' option non-empty
+	%
+	% hasx = 1 -> width is not interesting; we use 'x' option.
+	% hasx = 0 -> determine final width:
+	% 		W H
+	% 		0 0 -> \axisdefaultwidth 
+	% 		0 1 -> determine width out of H and the default aspect ratio
+	% 		1 X -> ok, use the user parameter.
+	%
+	% hasy = 1 -> height is not interesting, we use 'y' option.
+	% hasy = 0 -> determine final height:
+	% 		W H
+	% 		0 0 -> \axisdefaultheight
+	% 		X 1 -> ok, use the user parameter
+	% 		1 0 -> determine height out of W and the default aspect ratio
+	%
+	\ifx\pgfplots@x\pgfutil@empty
+		\ifx\pgfplots@y\pgfutil@empty
+			% hasx=0, hasy=0 
+			%
+			% -> KEEP ASPECT RATIO if just one W, or H is given!
+			\ifx\pgfplots@width\pgfutil@empty
+				\ifx\pgfplots@height\pgfutil@empty
+					% The case hasx=0, hasy=0,  W=0 H=0:
+					\let\pgfplots@width=\axisdefaultwidth
+					\let\pgfplots@height=\axisdefaultheight
+				\else
+					% The case hasx=0, hasy=0,  W=0 H=1:
+					\pgfplots@compute@default@aspect@ratio
+					\expandafter\pgfmath@y\pgfplots@height
+					\pgfmathlog@invoke@expanded\pgfmathmultiply@{%
+						{\pgf@sys@tonumber{\pgfmath@y}}%
+						{\pgfplots@default@aspect@ratio}%
+					}%
+					\edef\pgfplots@width{\pgfmathresult pt}%
+				\fi
+			\else
+				\ifx\pgfplots@height\pgfutil@empty
+					% The case hasx=0, hasy=0,  W=1 H=0:
+					\pgfplots@compute@default@aspect@ratio
+					\expandafter\pgfmath@x\pgfplots@width
+					\pgfmathlog@invoke@expanded\pgfmathdivide@{%
+						{\pgf@sys@tonumber{\pgfmath@x}}%
+						{\pgfplots@default@aspect@ratio}%
+					}%
+					\edef\pgfplots@height{\pgfmathresult pt}%
+				\else
+					% The case hasx=0, hasy=0,  W=1 H=1:
+				\fi
+			\fi
+		\else
+			% hasx=0, hasy=1, W=0:
+			\ifx\pgfplots@width\pgfutil@empty
+				\let\pgfplots@width=\axisdefaultwidth
+			\fi
+		\fi
+	\else
+		\ifx\pgfplots@y\pgfutil@empty
+			% hasx=1, hasy=0, H=0
+			\ifx\pgfplots@height\pgfutil@empty
+				\let\pgfplots@height=\axisdefaultheight
+			\fi
+		\fi
+	\fi
+}
+
+% PRECONDITION: 
+% 	- final axis limits are given in transformed range
+% 	-  \pgfplots@set@default@size@options has been invoked before
+% POSTCONDITION: 
+% 	- the current x- and y unit vectors are changed;
+% 	- \pgfplots@[xy]coord{min,max}TEX  are set
+%
+\def\pgfplots@initsizes{%
+	% INIT.
+	%
+	%
+	\pgfpointxy{\pgfplots@xmin}{\pgfplots@ymin}%
+	\pgfplots@xcoordminTEX=\pgf@x
+	\pgfplots@ycoordminTEX=\pgf@y
+	\pgfpointxy{\pgfplots@xmax}{\pgfplots@ymax}%
+	\pgfplots@xcoordmaxTEX=\pgf@x
+	\pgfplots@ycoordmaxTEX=\pgf@y
+	%
+	%
+	%-----------------------------------------
+	% PROCESS THE 'width' and 'height' options
+	%-----------------------------------------
+	%
+	% FIXME: make these variables LOCAL:
+	%
+	\let\pgfplots@rectangle@width=\pgfutil@empty
+	\let\pgfplots@rectangle@height=\pgfutil@empty
+	%
+	\ifx\pgfplots@x\pgfutil@empty
+		\ifx\pgfplots@width\pgfutil@empty
+			\pgfplots@error{INTERNAL LOGIC ERROR! WIDTH NOT SET}%
+		\fi
+		\pgfplots@initsizes@getXscale\into\pgfplots@tmpXscale
+		\ifpgfplots@scale@only@axis
+			\let\pgfplots@rectangle@width=\pgfplots@width
+		\fi
+	\else
+		\def\pgfplots@tmpXscale{1}%
+	\fi
+	%
+	\ifx\pgfplots@y\pgfutil@empty
+		\ifx\pgfplots@height\pgfutil@empty
+			\pgfplots@error{INTERNAL LOGIC ERROR! HEIGHT NOT SET}%
+		\fi
+		\pgfplots@initsizes@getYscale\into\pgfplots@tmpYscale
+		\ifpgfplots@scale@only@axis
+			\let\pgfplots@rectangle@height=\pgfplots@height
+		\fi
+	\else
+		\def\pgfplots@tmpYscale{1}%
+	\fi
+	%
+	% 
+	% assert( \pgfplots@tmpXscale != \pgfutil@empty && \pgfplots@tmpYscale != \pgfutil@empty )
+	%
+	% Apply scaling:
+	\pgfpointxy{\pgfplots@tmpXscale}{\pgfplots@tmpYscale}%
+	\pgfplots@tmpa=\pgf@x
+	\pgfplots@tmpb=\pgf@y
+%\message{initscaling: got x-scaling \the\pgfplots@tmpa, and y-scaling \the\pgfplots@tmpb}%
+	\ifx\pgfplots@x\pgfutil@empty
+		\pgfsetxvec{\pgfqpoint{\pgfplots@tmpa}{0pt}}%
+	\else
+		\pgfsetxvec{\pgfpoint{\pgfplots@x}{0pt}}%
+	\fi
+	\ifx\pgfplots@y\pgfutil@empty
+		\pgfsetyvec{\pgfqpoint{0pt}{\pgfplots@tmpb}}%
+	\else
+		\pgfsetyvec{\pgfpoint{0pt}{\pgfplots@y}}%
+	\fi
+	%
+	% Determine final rectangle dimensions.
+	% There are the following cases: 
+	% 1. the user really wants a fixed dimension,
+	%    i.e. he used 'scale only axis'.
+	%    Then, we have to work to get the correct dimension!
+	%
+	%    Up to now, the scaling mechanism looses to many significant
+	%    digits such that the final width/height differs by 1-2 pt.
+	%
+	%    If I am not mistaken, this does ONLY affect the final size,
+	%    not the relative plot precision.
+	%    
+	%    FIXME : really compute the plot precision!
+	% 
+	% 2. The use specified width and/or height, but not 'scale only
+	%    axis'. Accept inaccurate final widths/heights (see above).
+	%
+	% 3. The user supplied 'x' and or 'y'. Simply use them, its
+	% accurate.
+	%
+	\pgfpointxy{\pgfplots@xmin}{\pgfplots@ymin}%
+	\pgfplots@xcoordminTEX=\pgf@x
+	\pgfplots@ycoordminTEX=\pgf@y
+	\pgfpointxy{\pgfplots@xmax}{\pgfplots@ymax}%
+	\ifx\pgfplots@rectangle@width\pgfutil@empty
+		\pgfplots@xcoordmaxTEX=\pgf@x
+	\else
+		% this 'if' here should only make a difference of about
+		% 1-2pt, not more.
+		%
+		% and I am quite sure that this inaccuracy (and this
+		% work-around) only affects the
+		% final size, not the relative plot accuracy.
+		\pgfplots@xcoordmaxTEX=\pgfplots@xcoordminTEX
+		\expandafter\advance\expandafter\pgfplots@xcoordmaxTEX\pgfplots@width
+	\fi
+	\ifx\pgfplots@rectangle@height\pgfutil@empty
+		\pgfplots@ycoordmaxTEX=\pgf@y
+	\else
+		\pgfplots@ycoordmaxTEX=\pgfplots@ycoordminTEX
+		\expandafter\advance\expandafter\pgfplots@ycoordmaxTEX\pgfplots@height
+	\fi
+%--------------------------------------------------
+% \begingroup
+% \pgf@x=\pgfplots@xcoordmaxTEX\advance\pgf@x by-\pgfplots@xcoordminTEX
+% \pgf@y=\pgfplots@ycoordmaxTEX\advance\pgf@y by-\pgfplots@ycoordminTEX
+% \message{Axis scaling x=\pgfplots@tmpXscale, y=\pgfplots@tmpYscale\ yields lower-left-corner (\pgfplots@xmin,\pgfplots@ymin) = (\the\pgfplots@xcoordminTEX,\the\pgfplots@ycoordminTEX) and upper right (\pgfplots@xmax,\pgfplots@ymax) = (\the\pgfplots@xcoordmaxTEX,\the\pgfplots@ycoordmaxTEX).   Axis dimensions are width=\the\pgf@x, height=\the\pgf@y.}%
+% \endgroup
+%-------------------------------------------------- 
+}
+
+
+% This is the main axis shape.
+%
+% It has one node part, which is the complete image. It provides a lot
+% of anchors.
+\pgfdeclareshape{pgfplots@low@level@shape}{%
+	\savedanchor\upperrightcorner{
+		\pgf@x=\wd\pgfnodepartimagebox
+		\pgf@y=\ht\pgfnodepartimagebox
+	}%
+	\savedanchor\lowerleftinnercorner{%
+		\pgfpoint{\pgfplots@savedanchor@inner@lowerleft@x}{\pgfplots@savedanchor@inner@lowerleft@y}%
+	}%
+	\savedanchor\upperrightinnercorner{%
+		\pgfpoint{\pgfplots@savedanchor@inner@upperright@x}{\pgfplots@savedanchor@inner@upperright@y}%
+	}%
+	%
+	\nodeparts{image}%
+	\anchor{image}{%
+		\pgf@x=0pt
+		\pgf@y=0pt
+	}%
+	%
+	\anchor{outer north}{%
+		\upperrightcorner
+		\pgf@x=.5\pgf@x
+	}%
+	\anchor{outer north east}{\upperrightcorner}%
+	\anchor{outer east}{%
+		\upperrightcorner
+		\pgf@y=.5\pgf@y
+	}%
+	\anchor{outer south east}{%
+		\upperrightcorner
+		\pgf@y=0pt
+	}%
+	\anchor{outer south}{%
+		\upperrightcorner
+		\pgf@x=.5\pgf@x
+		\pgf@y=0pt
+	}%
+	\anchor{outer south west}{%
+		\pgf@x=0pt
+		\pgf@y=0pt
+	}%
+	\anchor{outer west}{%
+		\upperrightcorner
+		\pgf@x=0pt
+		\pgf@y=.5\pgf@y
+	}%
+	\anchor{outer north west}{%
+		\upperrightcorner
+		\pgf@x=0pt
+	}%
+	\anchor{outer center}{%
+		\upperrightcorner
+		\pgf@x=.5\pgf@x
+		\pgf@y=.5\pgf@y
+	}%
+	%
+	%
+	\anchor{center}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\advance\pgf@xa by\pgf@x
+		\pgf@x=.5\pgf@xa
+		\advance\pgf@xb by\pgf@y
+		\pgf@y=.5\pgf@xb
+	}%
+	\anchor{north}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\advance\pgf@xa by\pgf@x
+		\pgf@x=.5\pgf@xa
+	}%
+	\anchor{north east}{\upperrightinnercorner}%
+	\anchor{east}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\advance\pgf@xb by\pgf@y
+		\pgf@y=.5\pgf@xb
+	}%
+	\anchor{south east}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\pgf@y=\pgf@xb
+	}%
+	\anchor{south}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\advance\pgf@xa by\pgf@x
+		\pgf@x=.5\pgf@xa
+		\pgf@y=\pgf@xb
+	}%
+	\anchor{south west}{\lowerleftinnercorner}%
+	\anchor{west}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\pgf@x=\pgf@xa
+		\advance\pgf@xb by\pgf@y
+		\pgf@y=.5\pgf@xb
+	}%
+	\anchor{north west}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\upperrightinnercorner
+		\pgf@x=\pgf@xa
+	}%
+	%%
+	%%
+	\anchor{above north}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@y
+		\lowerleftinnercorner
+		\pgf@xb=\pgf@x
+		\upperrightinnercorner
+		\advance\pgf@xb by\pgf@x
+		\pgf@x=.5\pgf@xb
+		\pgf@y=\pgf@xa
+	}%
+	\anchor{above north east}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@y
+		\upperrightinnercorner
+		\pgf@y=\pgf@xa
+	}%
+	\anchor{right of north east}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@x
+		\upperrightinnercorner
+		\pgf@x=\pgf@xa
+	}%
+	\anchor{right of east}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@x
+		\upperrightinnercorner
+		\pgf@xb=\pgf@y
+		\lowerleftinnercorner
+		\advance\pgf@xb by\pgf@y
+		\pgf@x=\pgf@xa
+		\pgf@y=.5\pgf@xb
+	}%
+	\anchor{right of south east}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@x
+		\lowerleftinnercorner
+		\pgf@x=\pgf@xa
+	}%
+	\anchor{below south east}{%
+		\upperrightinnercorner
+		\pgf@y=0pt
+	}%
+	\anchor{below south}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@x
+		\upperrightinnercorner
+		\pgf@y=0pt
+		\advance\pgf@xa by\pgf@x
+		\pgf@x=.5\pgf@xa
+	}%
+	\anchor{below south west}{%
+		\lowerleftinnercorner
+		\pgf@y=0pt
+	}%
+	\anchor{left of south west}{%
+		\lowerleftinnercorner
+		\pgf@x=0pt
+	}%
+	\anchor{left of west}{%
+		\lowerleftinnercorner
+		\pgf@xa=\pgf@y
+		\upperrightinnercorner
+		\advance\pgf@xa by\pgf@y
+		\pgf@y=.5\pgf@xa
+		\pgf@x=0pt
+	}%
+	\anchor{left of north west}{%
+		\upperrightinnercorner
+		\pgf@x=0pt
+	}%
+	\anchor{above north west}{%
+		\upperrightcorner
+		\pgf@xa=\pgf@y
+		\lowerleftinnercorner
+		\pgf@y=\pgf@xa
+	}%
+	%%
+	%%
+	%%
+	\anchorborder{%
+		% Call a function that computes a border point. Since this
+		% function will modify dimensions like \pgf@x, we must move them to
+		% other dimensions.
+		\@tempdima=\pgf@x
+		\@tempdimb=\pgf@y
+		\pgfpointborderrectangle%
+			{\pgfpoint{\@tempdima}{\@tempdimb}}%
+			{\pgfpointadd{\upperrightcorner}{\pgfpoint{\width}{\height}}}
+	}%
+	\backgroundpath{\pgfpathrectangle{\pgfpointorigin}{\upperrightcorner}}%
+	\foregroundpath{}%
+	\behindbackgroundpath{}%
+	\beforebackgroundpath{}%
+	\behindforegroundpath{}%
+	\beforeforegroundpath{}%
+}
+
+\def\pgfplots@BEGIN@init@and@draw@axis{%
+	\pgfplots@determinedefaultvalues
+	\setbox\pgfnodepartimagebox=\hbox\bgroup\bgroup
+		\pgfinterruptpicture
+		\tikzpicture[/pgfplots/every axis]%
+		%\pgfqkeys{/tikz}{every axis}%
+		% set baseline for sub-picture to default value.
+		% the baseline option will be applied to the OUTER picture.
+		\pgfsetbaseline{\pgf@picminy}%
+		%
+		\scope
+		\ifpgfplots@hide
+		\else
+			\pgfplots@drawaxis@lines
+			\expandafter\pgfplots@drawxaxis\expandafter{\pgfplots@xtick}%
+			\expandafter\pgfplots@draw@extra@ticks@for\expandafter x\expandafter{\pgfplots@extra@xtick}%
+			\expandafter\pgfplots@drawyaxis\expandafter{\pgfplots@ytick}%
+			\expandafter\pgfplots@draw@extra@ticks@for\expandafter y\expandafter{\pgfplots@extra@ytick}%
+		\fi
+		\clip
+						(\pgfplots@xcoordminTEX,	\pgfplots@ycoordminTEX) 
+			rectangle	(\pgfplots@xcoordmaxTEX,	\pgfplots@ycoordmaxTEX);
+}
+
+
+\def\pgfplots@END@init@and@draw@axis{%
+	\endscope%
+}
+
+% Writes output to \pgfplots@TMP
+\def\pgfplots@filter@input@ticks@with@log#1{%
+	\let\pgfplots@TMP=\pgfutil@empty
+	\foreach \pgfplots@TMPB in {#1} {%
+		\expandafter\pgfmathlog@\expandafter{\pgfplots@TMPB}%
+		\ifx\pgfplots@TMP\pgfutil@empty
+			\xdef\pgfplots@TMP{\pgfmathresult}%
+		\else
+			\xdef\pgfplots@TMP{\pgfplots@TMP,\pgfmathresult}%
+		\fi
+	}%
+}
+
+\tikzdeclarecoordinatesystem{axis}{\pgfplots@evalute@tikz@coord@system@interface#1\pgfplots@coord@end}
+
+
+% Assigns \pgfmathresult := canvas coordinate (#2) for axis #1.
+\long\def\pgfplots@evalute@tikz@coord@system@interface@for#1#2{%
+	\expandafter\let\expandafter\if@datascaled@cur\csname ifpgfplots@apply@datatrafo@#1\endcsname
+	\csname ifpgfplots@#1islinear\endcsname
+		\if@datascaled@cur
+			\csname pgfplots@datascaletrafo@fromfixed@#1\endcsname{#2}%
+		\else
+			\def\pgfmathresult{#2}%
+		\fi
+	\else
+		\pgfmathlog@{#2}%
+	\fi
+}
+
+\long\def\pgfplots@evalute@tikz@coord@system@interface#1,#2\pgfplots@coord@end{%
+	\begingroup
+	\pgfplots@evalute@tikz@coord@system@interface@for{x}{#1}%
+	\let\pgfplots@evaluate@tikz@coord@x=\pgfmathresult
+	\pgfplots@evalute@tikz@coord@system@interface@for{y}{#2}%
+	\xdef\pgfplots@TMP{\pgfplots@evaluate@tikz@coord@x pt}%
+	\xdef\pgfplots@TMPB{\pgfmathresult pt}%
+	\endgroup
+	\pgfpointxy{\pgfplots@TMP}{\pgfplots@TMPB}%
+}
+
+% In case of (semi-) logplots, this command will 
+% - assign a filter which invokes \pgfmathlog@{} for each coordinate
+% - replace any user-specified coordinate by its log.
+%
+% All subsequent commands will then work with logarithmic coordinates.
+%
+% @see pgfmathlog.sty for details about the implementation of log().
+%
+% PRECONDITION: 
+% - The user input options have been set correctly, 
+% - the option processing has not yet begun
+%
+% POSTCONDITION: 
+% - any user input for log-axis has been replaced by its log
+% - coordinate filters to compute logs are installed
+%
+% See also:
+%     \pgfplots@apply@data@scale@trafo@to@options@for
+\def\pgfplots@prepare@coord@filtering@for#1{%
+	\expandafter\def\csname pgfplots@prepare@#1coord\endcsname##1{%
+		\def\pgfmathresult{##1}%
+	}%
+	\pgfkeysgetvalue{/pgfplots/#1filter}\pgfplots@TMP
+	\ifx\pgfplots@TMP\pgfutil@empty
+	\else
+		\expandafter\let\csname pgfplots@#1filter@backwcompat\endcsname=\pgfplots@TMP
+		\pgfplots@toka={WARNING: /pgfplots/#1filter is deprecated. Please use /pgfplots/#1 filter/.code={\def\pgfmathresult{\#1}}}%
+		\pgfplots@warning{\the\pgfplots@toka}%
+		\pgfkeys{/pgfplots/#1 filter/.code={\csname pgfplots@#1filter@backwcompat\endcsname{##1}\to\pgfmathresult}}%
+	\fi
+	\csname pgfplots@float@numerics@mode@#1false\endcsname
+	\csname ifpgfplots@#1islinear\endcsname
+		\ifpgfplots@disabledatascaling
+			\csname pgfplots@apply@datatrafo@#1false\endcsname
+			\pgfplots@apply@datatrafofalse
+		\else
+			\csname pgfplots@apply@datatrafo@#1true\endcsname
+			\csname pgfplots@float@numerics@mode@#1true\endcsname
+			\pgfplots@apply@datatrafotrue
+		\fi
+		\ifpgfplots@apply@datatrafo
+			% Check for any existing axis limits:
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1min\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@TMP}%
+				\expandafter\global\expandafter\let\csname pgfplots@#1min\endcsname=\pgfmathresult
+			\fi
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1max\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@TMP}%
+				\expandafter\global\expandafter\let\csname pgfplots@#1max\endcsname=\pgfmathresult
+			\fi
+		\fi
+	\else
+		\ifpgfplots@disablelogfilter
+		\else
+			% any user-specified axis limits:
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1min\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\expandafter\pgfmathlog@\expandafter{\pgfplots@TMP}%
+				\expandafter\global\expandafter\let\csname pgfplots@#1min\endcsname=\pgfmathresult
+			\fi
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1max\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\expandafter\pgfmathlog@\expandafter{\pgfplots@TMP}%
+				\expandafter\global\expandafter\let\csname pgfplots@#1max\endcsname=\pgfmathresult
+			\fi
+			%
+			% any user specified axis ticks:
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1tick\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\def\pgfplots@TMPB{data}%
+				\ifx\pgfplots@TMP\pgfplots@TMPB
+				\else
+					\expandafter\pgfplots@filter@input@ticks@with@log\expandafter{\pgfplots@TMP}%
+					\expandafter\edef\csname pgfplots@#1tick\endcsname{\pgfplots@TMP}%
+				\fi
+			\fi
+			\expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@extra@#1tick\endcsname
+			\ifx\pgfplots@TMP\pgfutil@empty
+			\else
+				\expandafter\pgfplots@filter@input@ticks@with@log\expandafter{\pgfplots@TMP}%
+				\expandafter\edef\csname pgfplots@extra@#1tick\endcsname{\pgfplots@TMP}%
+			\fi
+			%
+			\expandafter\def\csname pgfplots@prepare@#1coord\endcsname##1{%
+				\pgfmathlog@{##1}%
+			}%
+			%--------------------------------------------------
+			% \expandafter\let\expandafter\pgfplots@TMP\csname pgfplots@#1filter\endcsname
+			% \ifx\pgfplots@TMP\pgfutil@empty
+			% 	\expandafter\def\csname addplot@log@compute@#1filter\endcsname##1\to##2{%
+			% 		\pgfmathlog@{##1}%
+			% 		\let##2=\pgfmathresult
+			% 	}%
+			% \else
+			% 	\expandafter\let\csname pgfplots@#1filter@orig\endcsname=\pgfplots@TMP
+			% 	\expandafter\def\csname addplot@log@compute@#1filter\endcsname##1\to##2{%
+			% 		\pgfmathlog@{##1}%
+			% 		\ifx\pgfmathresult\pgfutil@empty
+			% 			\let##2=\pgfutil@empty
+			% 		\else
+			% 			\expandafter\expandafter\csname pgfplots@#1filter@orig\endcsname\pgfmathresult\to##2\relax
+			% 		\fi
+			% 	}%
+			% \fi
+			% \expandafter\let\expandafter\pgfplots@TMP\csname addplot@log@compute@#1filter\endcsname
+			% \expandafter\let\csname pgfplots@#1filter\endcsname\pgfplots@TMP
+			%-------------------------------------------------- 
+		\fi
+	\fi
+}
+
+\def\pgfplots@create@axis@descriptions{%
+	\ifpgfplots@hide
+	\else
+		\ifx\pgfplots@xlabel\pgfutil@empty
+		\else
+			\pgfplots@show@label{x}%
+		\fi
+		\ifx\pgfplots@ylabel\pgfutil@empty
+		\else
+			\pgfplots@show@label{y}%
+		\fi
+	\fi
+	\ifx\pgfplots@title\pgfutil@empty
+	\else
+		\pgfplots@show@title
+	\fi
+	\pgfplots@createlegend
+}
+
+\def\pgfplots@datascaletrafo@undoshift@x#1{%
+	\pgfmathsubtract@{#1}{\pgfplots@data@scale@trafo@SHIFT@x}%
+}%
+\def\pgfplots@datascaletrafo@redoshift@x#1{%
+	\pgfmathadd@{#1}{\pgfplots@data@scale@trafo@SHIFT@x}%
+}%
+\def\pgfplots@datascaletrafo@undoshift@y#1{%
+	\pgfmathsubtract@{#1}{\pgfplots@data@scale@trafo@SHIFT@y}%
+}%
+\def\pgfplots@datascaletrafo@redoshift@y#1{%
+	\pgfmathadd@{#1}{\pgfplots@data@scale@trafo@SHIFT@y}%
+}%
+
+% DATA TRANSFORMATION T(x) = X - xmin
+%
+% Input: 
+%    a number in the original data range, given in **floating** point representation
+% Output: 
+%    a fixed point number in transformed range
+%    stored in \pgfmathresult
+% @see
+% \pgfplots@datascaletrafo@fromfixed@x
+\def\pgfplots@datascaletrafo@x#1{%
+	\pgfmathfloatshift{#1}{\pgfplots@data@scale@trafo@EXPONENT@x}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+	\expandafter\pgfmathsubtract@\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@SHIFT@x}%
+}
+\def\pgfplots@datascaletrafo@x@noshift#1{%
+	\pgfmathfloatshift{#1}{\pgfplots@data@scale@trafo@EXPONENT@x}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+
+% Overloaded function.
+% Input:
+%     a FIXED point number instead of a floating point one.
+% @see \pgfplots@datascaletrafo@x
+\def\pgfplots@datascaletrafo@fromfixed@x#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfplots@datascaletrafo@x\expandafter{\pgfmathresult}%
+}
+
+\def\pgfplots@datascaletrafo@y#1{%
+	\pgfmathfloatshift{#1}{\pgfplots@data@scale@trafo@EXPONENT@y}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+	\expandafter\pgfmathsubtract@\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@SHIFT@y}%
+}
+\def\pgfplots@datascaletrafo@fromfixed@y#1{%
+	\pgfmathfloatparsenumber{#1}%
+	\expandafter\pgfplots@datascaletrafo@y\expandafter{\pgfmathresult}%
+}
+\def\pgfplots@datascaletrafo@y@noshift#1{%
+	\pgfmathfloatshift{#1}{\pgfplots@data@scale@trafo@EXPONENT@y}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+
+% INVERSE transformation x = T^{-1}( X )
+% Input: 
+%    a fixed point number in transformed domain
+% Output:
+%    a number in the data domain, given in floating point
+%    representation
+%
+% If the input number is approximately X=0, we will return x=0 as
+% well.
+%
+% This allows to handle rounding inaccuracies and should not pose any
+% problems.
+\def\pgfplots@inverse@datascaletrafo@x#1{%
+	\begingroup
+	\pgfmathadd@{#1}{\pgfplots@data@scale@trafo@SHIFT@x}%
+	\let\pgfplots@inverse@datascaletrafo@@shifted=\pgfmathresult
+	\pgfmathapproxequalto@{\pgfplots@inverse@datascaletrafo@@shifted}{0.0}%
+	\ifpgfmathcomparison
+		\pgfmathfloatcreate{0}{0.0}{0}%
+	\else
+		\pgfmathfloatparsenumber{\pgfplots@inverse@datascaletrafo@@shifted}%
+		\edef\pgfplots@data@scale@trafo@EXPONENT@x{-\pgfplots@data@scale@trafo@EXPONENT@x}%
+		\expandafter\pgfmathfloatshift\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@EXPONENT@x}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+\def\pgfplots@inverse@datascaletrafo@x@noshift#1{%
+	\begingroup
+	\pgfmathapproxequalto@{#1}{0.0}%
+	\ifpgfmathcomparison
+		\pgfmathfloatcreate{0}{0.0}{0}%
+	\else
+		\pgfmathfloatparsenumber{#1}%
+		\edef\pgfplots@data@scale@trafo@EXPONENT@x{-\pgfplots@data@scale@trafo@EXPONENT@x}%
+		\expandafter\pgfmathfloatshift\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@EXPONENT@x}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+\def\pgfplots@inverse@datascaletrafo@y#1{%
+	\begingroup
+	\pgfmathadd@{#1}{\pgfplots@data@scale@trafo@SHIFT@y}%
+	\let\pgfplots@inverse@datascaletrafo@@shifted=\pgfmathresult
+	\pgfmathapproxequalto@{\pgfplots@inverse@datascaletrafo@@shifted}{0.0}%
+	\ifpgfmathcomparison
+		\pgfmathfloatcreate{0}{0.0}{0}%
+	\else
+		\pgfmathfloatparsenumber{\pgfplots@inverse@datascaletrafo@@shifted}%
+		\edef\pgfplots@data@scale@trafo@EXPONENT@y{-\pgfplots@data@scale@trafo@EXPONENT@y}%
+		\expandafter\pgfmathfloatshift\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@EXPONENT@y}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+% Overloaded function. This one does only apply the scaling, no shift.
+\def\pgfplots@inverse@datascaletrafo@y@noshift#1{%
+	\begingroup
+	\pgfmathapproxequalto@{#1}{0.0}%
+	\ifpgfmathcomparison
+		\pgfmathfloatcreate{0}{0.0}{0}%
+	\else
+		\pgfmathfloatparsenumber{#1}%
+		\edef\pgfplots@data@scale@trafo@EXPONENT@y{-\pgfplots@data@scale@trafo@EXPONENT@y}%
+		\expandafter\pgfmathfloatshift\expandafter{\pgfmathresult}{\pgfplots@data@scale@trafo@EXPONENT@y}%
+	\fi
+	\pgfmath@smuggleone\pgfmathresult
+	\endgroup
+}
+
+% Overloaded function.
+%
+% In contrast to \pgfplots@inverse@datascaletrafo@x, this method
+% returns a number in FIXED point representation.
+% @see \pgfplots@inverse@datascaletrafo@x
+\def\pgfplots@inverse@datascaletrafo@tofixed@x#1{%
+	\pgfplots@inverse@datascaletrafo@x{#1}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+\def\pgfplots@inverse@datascaletrafo@tofixed@y#1{%
+	\pgfplots@inverse@datascaletrafo@y{#1}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+
+% Overloaded function.
+%
+% This one does only apply the scale, no shift.
+\def\pgfplots@inverse@datascaletrafo@tofixed@x@noshift#1{%
+	\pgfplots@inverse@datascaletrafo@x@noshift{#1}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+\def\pgfplots@inverse@datascaletrafo@tofixed@y@noshift#1{%
+	\pgfplots@inverse@datascaletrafo@y@noshift{#1}%
+	\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
+}
+
+% Parses all options in #1 which are known in the currently active families.
+%
+% The result will be stored back into the TikZ-style named #1 without 
+% further processing.
+%
+% Example:
+% \tikzstyle{every axis}=[xmin=0,xmax=1,line width=1pt
+% \pgfplots@set@keys@from@tikz@style\tmpmacro{every axis}{/pgfplots}
+% 
+% - sets axis options 'xmin' and 'xmax'
+% - calls \tikzstyle{every axis}={line width=1pt}
+% 
+% I assume that this method is called within local TeX groups so
+% nothing will be destroyed outside.
+%
+% #1:  A style name.
+\def\pgfplots@set@keys@from@tikz@style#1{%
+	\let\pgfplots@rmopts=\pgfutil@empty
+	\pgfqkeysfiltered{/pgfplots}{/pgfplots/#1}%
+	\pgfplots@set@keymacro@to@style\pgfplots@rmopts{#1}%
+}
+
+% The same as \pgfplots@set@keys@from@tikz@style  but this one appends
+% unmatched options to style #2.
+%
+% #1:  A style name.
+% #2:  A style name which will be filled with unprocessed options.
+\def\pgfplots@set@keys@from@tikz@style@append@to#1#2{%
+	\let\pgfplots@rmopts=\pgfutil@empty
+	\pgfqkeysfiltered{/pgfplots}{/pgfplots/#1}%
+	\pgfplots@append@keymacro@to@style\pgfplots@rmopts{#2}%
+}
+
+% #1:  A sequence of options.
+% #2:  A style name which will be filled with unprocessed options.
+\def\pgfplots@set@keys@and@append@remaining@to@style#1#2{%
+	\let\pgfplots@rmopts=\pgfutil@empty
+	\pgfqkeysfiltered{/pgfplots}{#1}%
+	\pgfplots@append@keymacro@to@style\pgfplots@rmopts{#2}%
+}%
+
+% #1: input macro
+\def\pgfplots@setkeys@from@macro#1{%
+	\let\pgfplots@rmopts=\pgfutil@empty
+	\def\pgfplots@TMP{\pgfqkeysfiltered{/pgfplots}}%
+	\expandafter\pgfplots@TMP\expandafter{#1}%
+}
+
+% #1: macro
+% #2: style name
+\long\def\pgfplots@append@keymacro@to@style#1#2{%
+	\pgfplotslist@TOK@a={#2/.append style=}%
+	\pgfplotslist@TOK@b=\expandafter{#1}%
+	\edef\pgfplots@setkeys@TMP{\the\pgfplotslist@TOK@a{\the\pgfplotslist@TOK@b}}%
+	\expandafter\pgfplotsset\expandafter{\pgfplots@setkeys@TMP}%
+%\pgfplots@message{tikzstyle{#2}+=[#1]}%
+}
+
+% #1: macro
+% #2: style name
+\long\def\pgfplots@set@keymacro@to@style#1#2{%
+	\pgfplotslist@TOK@a={#2/.style=}%
+	\pgfplotslist@TOK@b=\expandafter{#1}%
+	\edef\pgfplots@setkeys@TMP{\the\pgfplotslist@TOK@a{\the\pgfplotslist@TOK@b}}%
+	\expandafter\pgfplotsset\expandafter{\pgfplots@setkeys@TMP}%
+%\pgfplots@message{tikzstyle{#2}=[#1]}%
+}
+
+\def\pgfplots@preset@keys{%
+  \def\pgfplots@at{\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
+}
+
+% backwards compatibility:
+\let\prettyprintnumber=\pgfmathprintnumber%
+
+\def\pgfplots@set@options#1{%
+	\pgfplots@preset@keys
+	%
+	% Temporarily assign families to 'name' and 'alias' options.
+	% This allows to get the names - they should not be appended to
+	% 'every axis'!
+	\pgfkeys{%
+		/tikz/domain/.belongs to family=/pgfplots,
+		/pgfplots/domain/.code={\pgfkeysalso{/tikz/domain=##1}},
+		/tikz/name/.belongs to family=/pgfplots/naming commands,
+		/tikz/alias/.belongs to family=/pgfplots/naming commands,
+		% and provide aliases in the '/pgfplots/' tree to avoid 
+		% search path problems just for these two options:
+		/pgfplots/name/.belongs to family=/pgfplots/naming commands,
+		/pgfplots/alias/.belongs to family=/pgfplots/naming commands,
+		/pgfplots/name/.code={\pgfkeysalso{/tikz/name=##1}},
+		/pgfplots/alias/.code={\pgfkeysalso{/tikz/alias=##1}},
+		%
+		%
+		/pgf/key filter handlers/append filtered to/.install key filter handler=\pgfplots@rmopts,
+	}%
+	\let\tikz@alias=\pgfutil@empty
+	\let\tikz@fig@name=\pgfutil@empty
+	%
+	% Step 1: acquire ONLY 'xmode' and 'ymode' (necessary to decide
+	% which axis style shall be loaded):
+		\let\pgfplots@rmopts=\pgfutil@empty
+		\pgfkeysinstallkeyfilter
+			{/pgf/key filters/active families or no family}
+			{{/pgf/key filters/false}{/pgf/key filters/false}}
+		%
+		\pgfqkeysactivatesinglefamilyandfilteroptions{/pgfplots/scale}%
+			{/pgfplots}
+			{#1}%
+	\let\pgfplots@remaining@input=\pgfplots@rmopts
+	%
+	% Step 2: parse any pgfplots options out of styles.
+	\pgfkeysactivatefamily{/pgfplots/style commands}%
+	\pgfkeysinstallkeyfilter
+		{/pgf/key filters/active families or no family}% DEBUG}
+		{{/pgf/key filters/is descendant of=/pgfplots}% for keys without family
+		 {/pgf/key filters/false}% for unknown keys
+		}%
+	%
+	\pgfkeysactivatefamilies
+		{/pgfplots,/pgfplots/naming commands,/pgfplots/tick,/pgfplots/legend,/pgfplots/descriptions,/pgfplots/scale}
+		{\pgfplots@deactivefamiliescmd}%
+		\pgfplots@set@keys@from@tikz@style{every axis}%
+		\pgfkeysdeactivatefamily{/pgfplots/scale}%
+		%
+		\ifpgfplots@xislinear
+			\ifpgfplots@yislinear
+				\pgfplots@set@keys@from@tikz@style@append@to{every linear axis}{every axis}%
+			\else
+				\pgfplots@set@keys@from@tikz@style@append@to{every semilogy axis}{every axis}%
+			\fi
+		\else
+			\ifpgfplots@yislinear
+				\pgfplots@set@keys@from@tikz@style@append@to{every semilogx axis}{every axis}%
+			\else
+				\pgfplots@set@keys@from@tikz@style@append@to{every loglog axis}{every axis}%
+			\fi
+		\fi
+	\pgfplots@deactivefamiliescmd
+	%
+	% Acquire style commands and nameing commands from direct input
+	% options '#1' BEFORE the 'every' styles are processed:
+	\pgfkeysactivatefamily{/pgfplots/naming commands}%
+		\pgfplots@setkeys@from@macro\pgfplots@remaining@input%
+		\let\pgfplots@remaining@input=\pgfplots@rmopts
+	\pgfkeysdeactivatefamily{/pgfplots/naming commands}%
+	%
+	% Now, any 'name' and 'alias' options have been processed. 
+	%
+	% Remember their current meaning and reset the tikz options!
+	\let\pgfplots@fig@name=\tikz@fig@name
+	\let\pgfplots@fig@alias=\tikz@alias
+	\let\tikz@alias=\pgfutil@empty
+	\let\tikz@fig@name=\pgfutil@empty
+	%
+	% And protocol all named sub-nodes! Their positions need to be
+	% updated later.
+	\let\pgfplots@named@child@node@list=\pgfutil@empty
+	\pgfkeysgetvalue{/tikz/name/.@cmd}\pgfplots@old@name@impl
+	\pgfkeysgetvalue{/tikz/alias/.@cmd}\pgfplots@old@alias@impl
+	\pgfkeysdef{/tikz/name}{%
+		\xdef\pgfplots@named@child@node@list{\pgfplots@named@child@node@list,{##1}}%
+		\pgfplots@old@name@impl##1\pgfeov
+	}%
+	\pgfkeysdef{/tikz/alias}{%
+		\xdef\pgfplots@named@child@node@list{\pgfplots@named@child@node@list,{##1}}%
+		\pgfplots@old@alias@impl##1\pgfeov
+	}%
+	%
+	% Now, continue to process the 'every' styles. Please note that
+	% the 'legend style={}' like options have already been processed;
+	% their values are already inside of the associated 'every'
+	% styles.
+	%
+	% What I am doing here is: set every pgfplots-option directly, and
+	% discard it from the every-style. Any non-pgfplots-option will
+	% be set in its context.
+	%
+	\pgfkeysactivatefamily{/pgfplots/legend}%
+		\pgfplots@set@keys@from@tikz@style{every axis legend}%
+	\pgfkeysdeactivatefamily{/pgfplots/legend}%
+	%
+	%
+	\pgfkeysactivatefamily{/pgfplots/descriptions}%
+		\pgfplots@set@keys@from@tikz@style{every axis label}%
+		\pgfplots@set@keys@from@tikz@style{every axis x label}%
+		\pgfplots@set@keys@from@tikz@style{every axis y label}%
+		\pgfplots@set@keys@from@tikz@style{every axis title}%
+	\pgfkeysdeactivatefamily{/pgfplots/descriptions}%
+	%
+	\pgfkeysactivatefamily{/pgfplots/tick}%
+		\pgfplots@set@keys@from@tikz@style{every tick}%
+		\pgfplots@set@keys@from@tikz@style{every minor tick}%
+		\pgfplots@set@keys@from@tikz@style{every major tick}%
+		\pgfplots@set@keys@from@tikz@style{every axis grid}%
+		\pgfplots@set@keys@from@tikz@style{every minor grid}%
+		\pgfplots@set@keys@from@tikz@style{every major grid}%
+	\pgfkeysdeactivatefamily{/pgfplots/tick}%
+	%
+	\pgfkeysactivatefamily{/pgfplots}%
+		\pgfplots@set@keys@from@tikz@style{every axis plot}%
+	\pgfkeysdeactivatefamily{/pgfplots}%
+	%
+	\pgfkeysactivatefamily{/pgfplots/descriptions}%
+	\pgfkeysactivatefamily{/pgfplots/tick}%
+		\pgfplots@set@keys@from@tikz@style{every x tick label}%
+		\pgfplots@set@keys@from@tikz@style{every y tick label}%
+		\pgfplots@set@keys@from@tikz@style{every tick label}%
+	\pgfkeysdeactivatefamily{/pgfplots/tick}%
+	\pgfkeysdeactivatefamily{/pgfplots/descriptions}%
+	%
+	% Step 3: Set all remaining options of '#1'. They should have
+	% highest precedence.
+	\pgfkeysactivatefamilies
+		{/pgfplots,/pgfplots/tick,/pgfplots/legend,/pgfplots/descriptions}%
+		{\pgfplots@deactivefamiliescmd}%
+		\expandafter
+			\pgfplots@set@keys@and@append@remaining@to@style
+		\expandafter
+			{\pgfplots@remaining@input}%
+			{every axis}%
+	\pgfplots@deactivefamiliescmd
+%\pgfkeysgetvalue{/tikz/every axis/.@cmd}\pgfplots@TMP
+%\message{every axis is now '\meaning\pgfplots@TMP'}%
+	%
+	\pgfkeysdeactivatefamily{/pgfplots/style commands}%
+	\global\pgfkeysgetvalue{/pgfplots/xmin}{\pgfplots@xmin}%
+	\global\pgfkeysgetvalue{/pgfplots/xmax}{\pgfplots@xmax}%
+	\global\pgfkeysgetvalue{/pgfplots/ymin}{\pgfplots@ymin}%
+	\global\pgfkeysgetvalue{/pgfplots/ymax}{\pgfplots@ymax}%
+	%
+	\def\pgfplots@TMP{data}%
+	\pgfplots@collect@firstplot@astickfalse
+	\ifx\pgfplots@xtick\pgfplots@TMP
+		\pgfplots@collect@firstplot@asticktrue
+	\fi
+	\ifx\pgfplots@ytick\pgfplots@TMP
+		\pgfplots@collect@firstplot@asticktrue
+	\fi
+	\ifpgfplots@collect@firstplot@astick
+		\let\pgfplots@firstplot@coords@x=\pgfutil@empty
+		\let\pgfplots@firstplot@coords@y=\pgfutil@empty
+	\fi
+}
+
+\def\pgfplots@install@abbrev@commands{
+	\let\pgfplots@orig@path=\path
+	\let\pgfplots@orig@plot=\plot
+	%
+	\let\axispath=\pgfplots@path
+	%
+	\let\addplot=\pgfplots@addplot
+	\let\plot=\addplot
+	%
+	\def\logten{2.3025851}%
+	\def\reciproclogten{0.434294}%
+	%
+	\def\logi##1{%
+		\ifcase##1
+		\or0
+		\or0.693147
+		\or1.098612
+		\or1.386294
+		\or1.60943791
+		\or1.7917594
+		\or1.94591014
+		\or2.07944154
+		\or2.197224
+		\fi
+	}%
+	%
+	\let\legend=\pgfplots@command@legend
+	\let\addlegendentry=\pgfplots@addlegendentry
+}
+
+\def\pgfplots@environment{%
+	\pgfutil@ifnextchar[{%
+		\pgfplots@environment@opt
+	}{%
+		\pgfplots@environment@opt[]%
+	}%
+}%
+
+% temporary (local) variables inside of axis
+\newif\ifpgfplots@autocomputelimits
+\newif\ifpgfplots@autocompute@xlim
+\newif\ifpgfplots@autocompute@ylim
+\newif\ifpgfplots@apply@datatrafo@x
+\newif\ifpgfplots@apply@datatrafo@y
+\newif\ifpgfplots@apply@datatrafo
+\newif\ifpgfplots@float@numerics@mode@x
+\newif\ifpgfplots@float@numerics@mode@y
+\newif\ifpgfplots@datascaletrafo@initialised
+\newif\ifpgfplots@draw@at@end
+\newif\ifpgfplots@limits@are@computed
+\newif\ifpgfplots@EMERGENCY@FORCE@DATA@TRAFO@TO@IDENTITY
+
+% Extracts single components of an entry of
+% \pgfplots@stored@plotlist
+%
+% They are defined as
+% \pgfplots@stored@current@precmd
+% \pgfplots@stored@current@cmd
+% \pgfplots@stored@current@data
+% \pgfplots@stored@current@postcmd
+\def\pgfplots@stored@plotlist@EXTRACTENTRY#1#2#3#4{%
+	\def\pgfplots@stored@current@precmd{#1}%
+	\def\pgfplots@stored@current@cmd{#2}%
+	\def\pgfplots@stored@current@data{#3}%
+	\def\pgfplots@stored@current@postcmd{#4}%
+}
+
+\def\pgfplots@environment@opt[#1]{%
+	\begingroup
+	\pgfplots@install@abbrev@commands
+	\pgfplots@stacked@initialise
+	%
+	%
+	% The explicit specification of 'x' and 'y' as 1pt is to avoid
+	% numeric overflow/underflow during scale computations:
+	%
+	% The scaling (i.e. proper values for 'x' and 'y') will be
+	% determined later-on, dependend on the axis limits.  Since axis
+	% limits are implicitly in units of 1pt, it is reasonable to use
+	% '1pt' here as well.
+	\pgfsetxvec{\pgfqpoint{1pt}{0pt}}%
+	\pgfsetyvec{\pgfqpoint{0pt}{1pt}}%
+	%
+	\pgfplots@set@options{#1}%
+	%
+	% --------------------
+	% Allocations:
+	% --------------------
+	\global\pgfplots@EMERGENCY@FORCE@DATA@TRAFO@TO@IDENTITYfalse
+	\global\pgfplotslistnewempty\pgfplots@plotspeclist
+	\global\pgfplotslistnewempty\pgfplots@legend
+	\global\pgfplotslistnewempty\pgfplots@stored@plotlist
+	\global\pgfplots@numplots=0
+	\let\pgfplots@already@computed@legend@node=\pgfutil@empty
+	%
+	% --------------------
+	% Option preprocessing
+	% --------------------
+	\pgfplots@prepare@coord@filtering@for x
+	\pgfplots@prepare@coord@filtering@for y
+	\ifpgfplots@apply@datatrafo
+		\pgfplots@datascaletrafo@initialisedfalse
+	\else
+		\pgfplots@datascaletrafo@initialisedtrue% there is no trafo.
+	\fi
+	%
+	\ifx\pgfplots@xmin\pgfutil@empty
+		\pgfplots@autocompute@xlimtrue
+		\gdef\pgfplots@xmin{16300}%
+		\ifpgfplots@float@numerics@mode@x
+			\pgfmathfloatcreate{1}{1.0}{324}%
+			\global\let\pgfplots@xmin=\pgfmathresult
+		\fi
+	\fi
+	\ifx\pgfplots@xmax\pgfutil@empty
+		\pgfplots@autocompute@xlimtrue
+		\gdef\pgfplots@xmax{-16300}%
+		\ifpgfplots@float@numerics@mode@x
+			\pgfmathfloatcreate{2}{1.0}{324}%
+			\global\let\pgfplots@xmax=\pgfmathresult
+		\fi
+	\fi
+	\ifx\pgfplots@ymin\pgfutil@empty
+		\pgfplots@autocompute@ylimtrue
+		\gdef\pgfplots@ymin{16300}%
+		\ifpgfplots@float@numerics@mode@y
+			\pgfmathfloatcreate{1}{1.0}{324}%
+			\global\let\pgfplots@ymin=\pgfmathresult
+		\fi
+	\fi
+	\ifx\pgfplots@ymax\pgfutil@empty
+		\pgfplots@autocompute@ylimtrue
+		\gdef\pgfplots@ymax{-16300}%
+		\ifpgfplots@float@numerics@mode@y
+			\pgfmathfloatcreate{2}{1.0}{324}%
+			\global\let\pgfplots@ymax=\pgfmathresult
+		\fi
+	\fi
+	%
+	\global\pgfplots@limits@are@computedtrue
+	\ifpgfplots@autocompute@xlim
+		\pgfplots@draw@at@endtrue
+		\pgfplots@autocomputelimitstrue
+		\global\pgfplots@limits@are@computedfalse
+	\fi
+	\ifpgfplots@autocompute@ylim
+		\pgfplots@draw@at@endtrue
+		\pgfplots@autocomputelimitstrue
+		\global\pgfplots@limits@are@computedfalse
+	\fi
+	%
+	%
+	% --------------------
+	% Start axis:
+	% either postponed to \end or directly.
+	% --------------------
+	%
+	% Since I've introduced a public \numplots macro, I should 
+	% make sure it's filled correctly:
+	\pgfplots@draw@at@endtrue
+	%
+	\ifpgfplots@collect@firstplot@astick
+		\pgfplots@draw@at@endtrue
+	\fi
+	\ifpgfplots@apply@datatrafo
+		% ALWAYS TRUE. This allows to use inline plots because the data
+		% scale transformation will be applied after I know that it should
+		% be disabled.
+		\pgfplots@draw@at@endtrue
+	\fi
+	\ifpgfplots@stackedmode
+		% Stacked plots require special attention: they are drawn in
+		% REVERSE order.
+		\pgfplots@draw@at@endtrue
+	\else
+		% we have no stacked plots and thus no reversing.
+		\pgfplots@stacked@reversefalse
+	\fi
+	%
+	% any \path command is invalid inside of an axis.
+	% Use \axispath instead:
+	\def\numplots{\the\pgfplots@numplots}%
+	\let\path=\pgfplots@replacement@for@tikz@path
+	\let\closedcycle=\pgfplots@path@closed@cycle
+	\ifpgfplots@draw@at@end
+		\let\pgfplots@nextcommand=\relax
+	\else
+		\def\pgfplots@nextcommand{\pgfplots@BEGIN@init@and@draw@axis}%
+	\fi
+	\pgfplots@nextcommand
+}
+\def\endpgfplots@environment@opt{%
+	\pgfkeysvalueof{/pgfplots/before end axis/.@cmd}\pgfeov%
+	\xdef\numplots{\the\pgfplots@numplots}%
+	%
+	% restore old \path command:
+	\let\path=\pgfplots@orig@path
+	\let\plot=\pgfplots@orig@plot
+	%
+	%\end{axis}:
+	% --------------------
+	%  All plotting commands have been read.
+	%  -> apply postponed drawing commands!
+	% --------------------
+	\ifpgfplots@draw@at@end
+		\def\pgfplots@nextcommand{%
+			\pgfplots@BEGIN@init@and@draw@axis
+			\pgfplots@stacked@initialise
+			\ifpgfplots@stacked@reverse
+				% This here applies any scaling trafos and assembles a
+				% NEW \pgfplots@stored@plotlist!
+				\pgfplots@stacked@finalize@stored@plots
+			\fi
+			\pgfplotslistforeach\pgfplots@stored@plotlist\as\pgfplots@TMP{%
+				\expandafter\pgfplots@stored@plotlist@EXTRACTENTRY\pgfplots@TMP
+%\message{Processing stored plot with precommand '\meaning\pgfplots@stored@current@precmd';  pgfplots@plotcmd '\meaning\pgfplots@stored@current@cmd' postcommand '\meaning\pgfplots@stored@current@postcmd'}%
+				\pgfplots@stored@current@precmd
+				\ifx\pgfplots@stored@current@cmd\pgfutil@empty
+					\pgfplots@stored@current@data%
+				\else
+					% this code here means we REALLY have a plotting
+					% command!
+					\ifpgfplots@stacked@reverse
+						% has already been processed above, in \pgfplots@stacked@finalize@stored@plots.
+					\else
+						\ifpgfplots@apply@datatrafo
+							% Apply the data scaling transformation
+							\expandafter\pgfplots@coord@stream@finalize@storedcoords@START\pgfplots@stored@current@data\to\pgfplots@stored@current@data%
+						\fi
+					\fi
+%\message{calling plotcmd and plotdata: pgfplots@plotcmd '\meaning\pgfplots@stored@current@cmd' data '\meaning\pgfplots@stored@current@data'}%
+					\expandafter\pgfplots@stored@current@cmd\pgfplots@stored@current@data
+				\fi
+				\pgfplots@stored@current@postcmd
+			}%
+			\global\pgfplotslistnewempty\pgfplots@stored@plotlist% delete contents.
+		}%
+	\else
+		\let\pgfplots@nextcommand=\relax
+	\fi
+	\pgfplots@nextcommand
+	\pgfplots@END@init@and@draw@axis
+	%
+	\begingroup
+	\pgfkeysvalueof{/pgfplots/after end axis/.@cmd}\pgfeov%
+	\endgroup
+	%
+	\begingroup
+		% set coordinate system to (0,0) rectangle (1,1) for descriptions:
+		\pgftransformxshift{\pgfplots@xcoordminTEX}%
+		\pgftransformyshift{\pgfplots@ycoordminTEX}%
+		%
+		\pgfplots@tmpa=\pgfplots@xcoordmaxTEX
+		\advance\pgfplots@tmpa by-\pgfplots@xcoordminTEX
+		\pgfsetxvec{\pgfqpoint{\pgfplots@tmpa}{0cm}}%
+		%
+		\pgfplots@tmpa=\pgfplots@ycoordmaxTEX
+		\advance\pgfplots@tmpa by-\pgfplots@ycoordminTEX
+		\pgfsetyvec{\pgfqpoint{0cm}{\pgfplots@tmpa}}%
+		%
+		\pgfplots@create@axis@descriptions
+		\pgfkeysvalueof{/pgfplots/extra description/.@cmd}\pgfeov%
+	\endgroup
+	\endtikzpicture%
+	\begingroup
+		% Protocol sizes for the axis-shape.
+		% I fear that needs to be done globally, do avoid all those
+		% \endgroup's in and after \endpgfinterruptpicture ...
+		\ifdim\pgf@picmaxx=-16000pt\relax%
+			\pgf@picmaxx=0pt\relax%
+			\pgf@picminx=0pt\relax%
+			\pgf@picmaxy=0pt\relax%
+			\pgf@picminy=0pt\relax%
+		\fi%
+		%
+		\xdef\pgfplots@saveddimen@picminx{\the\pgf@picminx}%
+		\xdef\pgfplots@saveddimen@picminy{\the\pgf@picminy}%
+		%
+		\pgf@xa=\pgfplots@xcoordmaxTEX
+		\advance\pgf@xa by-\pgf@picminx
+		\xdef\pgfplots@savedanchor@inner@upperright@x{\the\pgf@xa}%
+		%
+		\pgf@xa=\pgfplots@xcoordminTEX
+		\advance\pgf@xa by-\pgf@picminx
+		\xdef\pgfplots@savedanchor@inner@lowerleft@x{\the\pgf@xa}%
+		%
+		\pgf@xa=\pgfplots@ycoordmaxTEX
+		\advance\pgf@xa by-\pgf@picminy
+		\xdef\pgfplots@savedanchor@inner@upperright@y{\the\pgf@xa}%
+		%
+		\pgf@xa=\pgfplots@ycoordminTEX
+		\advance\pgf@xa by-\pgf@picminy
+		\xdef\pgfplots@savedanchor@inner@lowerleft@y{\the\pgf@xa}%
+	\endgroup
+	\endpgfinterruptpicture
+	\egroup\egroup% end of pgfnodepartimagebox
+	%
+	\let\tikz@fig@name=\pgfplots@fig@name
+	\tikz@fig@mustbenamed
+    \pgftransformshift{\pgfplots@at}%
+	\pgfmultipartnode{pgfplots@low@level@shape}{\pgfplots@anchorname}{\tikz@fig@name}{\pgfusepath{discard}}%
+	\pgfplots@fig@alias
+	%
+	\pgfplots@finally@correct@child@node@positions
+	\pgfplots@stacked@finalize
+	\endgroup
+}
+
+% Now, we need to process all named nodes inside of our
+% axis-image.
+%
+% The situation at this point is as follows:
+% 1. the complete axis image has been "typeset" into a box. That
+% means its coordinate system is LOST up to those variables
+% which have been saved explicitly.
+%
+% 2. the \pgfmultipartnode above knows about all axis anchors and
+% saved dimensions.
+%
+% 3. All sub-nodes don't know about their position any more. Any
+% saved anchors are wrong.
+%
+% The approach:
+% 1. we shift each named node's saved anchors such that it's
+% coordinate is valid inside of the TeX box.
+%
+% 2. we also shift each named node's saved anchors to reflect the
+% axis' anchor.
+%
+% Afterwards, everything should be fine.
+\def\pgfplots@finally@correct@child@node@positions{%
+   \ifx\pgfplots@named@child@node@list\pgfutil@empty%
+   \else%
+      	\begingroup
+		\pgftransformreset% FIXME: what's that for!? Copied from matrix code...
+		%
+		% Use the 'image' anchor here - the internal anchor
+		% transformation matrix already has the shift for
+		% \pgfplots@anchorname.
+		\pgfpointanchor{\tikz@fig@name}{image}%
+		\pgf@xa=\pgf@x
+		\pgf@xb=\pgf@y
+		\pgf@process{\pgfqpoint{\pgfplots@saveddimen@picminx}{\pgfplots@saveddimen@picminy}}%
+		\advance\pgf@xa by-\pgf@x
+		\advance\pgf@xb by-\pgf@y
+		\pgf@x=\pgf@xa
+		\pgf@y=\pgf@xb
+		\edef\pgfplots@offset{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+		%
+		\pgfutil@for\pgfplots@child@node@name:=\pgfplots@named@child@node@list\do{%
+			\ifx\pgfplots@child@node@name\pgfutil@empty
+			\else
+				\expandafter\ifx\csname pgfplots@child@node@visited@\pgfplots@child@node@name\endcsname\relax%
+					\pgfutil@ifundefined{pgf@sh@nt@\pgfplots@child@node@name}{%
+						\pgfplots@warning{Package pgfplots WARNING: could not adjust coordinates of named node '\pgfplots@child@node@name' for reasons I do not understand! After finishing the image, it did no longer exist!? Sorry.}%
+					}{%
+						\pgf@shift@node{\pgfplots@child@node@name}{\pgfplots@offset}%
+						\expandafter\let\csname pgfplots@child@node@visited@\pgfplots@child@node@name\endcsname=\pgfutil@empty%
+					}%
+				\fi
+			\fi
+		}%
+		\endgroup
+    \fi%
+}%
+
+\def\pgfplots@environment@axis{%
+	\pgfutil@ifnextchar[{\pgfplots@@environment@axis}{\pgfplots@@environment@axis[]}%
+}
+\let\endpgfplots@environment@axis=\endpgfplots@environment@opt
+\def\pgfplots@@environment@axis[#1]{%
+	\pgfplots@environment@opt[/pgfplots/xmode=linear,/pgfplots/ymode=linear,#1]%
+}
+
+\def\pgfplots@environment@semilogxaxis{%
+	\pgfutil@ifnextchar[{\pgfplots@@environment@semilogxaxis}{\pgfplots@@environment@semilogxaxis[]}%
+}
+\let\endpgfplots@environment@semilogxaxis=\endpgfplots@environment@opt
+\def\pgfplots@@environment@semilogxaxis[#1]{%
+	\pgfplots@environment@opt[/pgfplots/xmode=log,/pgfplots/ymode=linear,#1]%
+}
+
+\def\pgfplots@environment@semilogyaxis{%
+	\pgfutil@ifnextchar[{\pgfplots@@environment@semilogyaxis}{\pgfplots@@environment@semilogyaxis[]}%
+}
+\let\endpgfplots@environment@semilogyaxis=\endpgfplots@environment@opt
+\def\pgfplots@@environment@semilogyaxis[#1]{%
+	\pgfplots@environment@opt[/pgfplots/xmode=linear,/pgfplots/ymode=log,#1]%
+}
+
+\def\pgfplots@environment@loglogaxis{%
+	\pgfutil@ifnextchar[{\pgfplots@@environment@loglogaxis}{\pgfplots@@environment@loglogaxis[]}%
+}
+\let\endpgfplots@environment@loglogaxis=\endpgfplots@environment@opt
+\def\pgfplots@@environment@loglogaxis[#1]{%
+	\pgfplots@environment@opt[/pgfplots/xmode=log,/pgfplots/ymode=log,#1]%
+}
+
+
+\pgfutil@ifundefined{tikzaddtikzonlycommandshortcutlet}{%
+	\def\tikzaddtikzonlycommandshortcutlet#1#2{%
+		\expandafter\def\expandafter\tikz@installcommands\expandafter{\tikz@installcommands
+			\let#1=#2
+		}%
+	}%
+}{}
+
+\tikzaddtikzonlycommandshortcutlet\axis\pgfplots@environment@axis
+\tikzaddtikzonlycommandshortcutlet\endaxis\endpgfplots@environment@axis
+
+\tikzaddtikzonlycommandshortcutlet\semilogxaxis\pgfplots@environment@semilogxaxis
+\tikzaddtikzonlycommandshortcutlet\endsemilogxaxis\endpgfplots@environment@semilogxaxis
+
+\tikzaddtikzonlycommandshortcutlet\semilogyaxis\pgfplots@environment@semilogyaxis
+\tikzaddtikzonlycommandshortcutlet\endsemilogyaxis\endpgfplots@environment@semilogyaxis
+
+\tikzaddtikzonlycommandshortcutlet\loglogaxis\pgfplots@environment@loglogaxis
+\tikzaddtikzonlycommandshortcutlet\endloglogaxis\endpgfplots@environment@loglogaxis
diff --git a/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.stackedplots.code.tex b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.stackedplots.code.tex
new file mode 100644
index 00000000000..1612ca8c7f5
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgfplots/pgfplots/pgfplots.stackedplots.code.tex
@@ -0,0 +1,365 @@
+%--------------------------------------------
+%
+% Package pgfplots
+%
+% Provides a user-friendly interface to create function plots (normal
+% plots, semi-logplots and double-logplots).
+% 
+% It is based on Till Tantau's PGF package.
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+
+%
+% This file contains the implementation for stacked plots.
+%
+% Stacked plots always keep record of the last plotted coordinates.
+% Any new plot will be ADDED on top of the last plotted coordinates.
+% 
+% Terminology: "last plotted coordinates" are called "zero levels"
+% because they actually work like shifts.
+%
+% Programming Structure:
+%
+% 1. We keep TWO lists of coordinates: a list of CURRENT zero level
+% coordinates and a list of NEXT zero level coordinates.
+%
+% The first one will be queried whenever a zero level coordinate is
+% requested.
+%
+% The second one will be used to form zero levels for the next plot.
+%
+% 2. At the beginning and end of each plot, the lists in 1.) are
+% initialised properly.
+%
+% 3. While plot coordinates are processed, the following methods
+% interact with the stacked API:
+% \pgfplots@stacked@preparepoint@inmacro
+% 	-> compute the 'stacked' sum.
+% 	This may need to be done with floating point arithmetics because
+% 	the data scaling trafo is not yet initialised
+%
+% \pgfplots@stacked@finishpoint
+% 	-> takes coordinates as they will be given to Tikz. This method is
+% 	used to 
+% 		- communicate zero level coordinates to Tikz
+% 		- implement the 'closed paths' option (allows filled stacked plots).
+%
+% \pgfplots@stacked@rememberzerolevelpoint@for@next@plot
+% \pgfplots@stacked@getnextzerolevelpoint
+%
+% 4. Zero levels are communicated to Tikz by
+% \pgfplots@stacked@initzerolevelhandler. This routine initialises an
+% input stream for Tikz plot handlers which produces a sequence of
+% zero levels. It is used by [xy]comb and [xy]bar.
+%
+%
+% REMARK:
+% the state of the boolean \ifpgfplots@datascaletrafo@initialised
+% determines whether these routines expect and return floating point
+% numbers or fixed point numbers.
+
+\let\pgfplots@stacked@zerolevelpoint@x=\pgfutil@empty
+\let\pgfplots@stacked@zerolevelpoint@y=\pgfutil@empty
+\newif\ifpgfplots@stacked@isfirstplot
+\newif\ifpgfplots@stacked@isinitialised
+
+% Pre-initialisation.
+% Needs to be called before the first call to
+% \pgfplots@stacked@beginplot.
+\def\pgfplots@stacked@initialise{%
+	\pgfplots@stacked@isfirstplottrue
+	\pgfplots@stacked@isinitialisedtrue
+}%
+
+% Cleanup method. Truncates any global variables to reduce string
+% space.
+\def\pgfplots@stacked@finalize{%
+	\global\pgfplotslistnewempty\pgfplots@stacked@zerolevellist
+	\global\pgfplotslistnewempty\pgfplots@stacked@nextzerolevellist
+	\pgfplots@stacked@isinitialisedfalse
+}%
+
+% (Re)defines the macro \pgfplots@stacked@getnextzerolevelpoint
+% at the beginning of each plot.
+%
+% The macro \pgfplots@stacked@getnextzerolevelpoint fills
+% \pgfplots@stacked@zerolevelpoint@[xy].
+%
+% ATTENTION: call \pgfplots@stacked@initialise before the first call
+% to beginplot!
+\def\pgfplots@stacked@beginplot{%
+%\message{pgfplots@stacked@beginplot: PLOT STARTED.}%
+	\ifpgfplots@stacked@isinitialised
+	\else
+		\pgfplots@error{LOGIC ERROR: please call \string\pgfplots@stacked@initialise.}%
+	\fi
+	\global\pgfplotslistnewempty\pgfplots@stacked@PGFzerolevels
+	% accumulate this command here for \closedcycle:
+	\let\pgfplots@stacked@closedcycle@impl=\pgfutil@empty
+	\ifpgfplots@stacked@isfirstplot
+		\global\pgfplotslistnewempty\pgfplots@stacked@zerolevellist
+		\def\pgfplots@stacked@zerolevelpoint@x{0}%
+		\def\pgfplots@stacked@zerolevelpoint@y{0}%
+		\ifpgfplots@datascaletrafo@initialised
+			% work with pgfmath if possible - its faster.
+		\else
+			% only work with float if its really necessary - for
+			% example if the scaling trafo which maps to pgfmath is
+			% not yet initialised.
+			\ifpgfplots@float@numerics@mode@x
+				\pgfmathfloatcreate{0}{0.0}{0}%
+				\let\pgfplots@stacked@zerolevelpoint@x=\pgfmathresult
+			\fi
+			\ifpgfplots@float@numerics@mode@y
+				\pgfmathfloatcreate{0}{0.0}{0}%
+				\let\pgfplots@stacked@zerolevelpoint@y=\pgfmathresult
+			\fi
+		\fi
+		\def\pgfplots@stacked@getnextzerolevelpoint{}% will remain constant anyway.
+	\else
+		{\globaldefs=1
+		\pgfplotslistcopy\pgfplots@stacked@nextzerolevellist\to\pgfplots@stacked@zerolevellist
+		}%
+		\def\pgfplots@stacked@getnextzerolevelpoint{%
+			{\globaldefs=1
+			\pgfplotslistpopfront\pgfplots@stacked@zerolevellist\to\pgfmathresult
+			}%
+			\expandafter\pgfplots@stacked@parsezerolevelpoint\pgfmathresult
+		}%
+	\fi
+	\global\pgfplotslistnewempty\pgfplots@stacked@nextzerolevellist
+}%
+
+\def\pgfplots@stacked@parsezerolevelpoint(#1,#2){%
+	\def\pgfplots@stacked@zerolevelpoint@x{#1}%
+	\def\pgfplots@stacked@zerolevelpoint@y{#2}%
+}
+
+\def\pgfplots@stacked@endplot{%
+	\ifpgfplots@stacked@isfirstplot
+		\let\pgfplots@stacked@closedcycle@impl=\pgfplots@path@closed@cycle@std
+	\else
+		\pgfplots@toka=\expandafter{\pgfplots@stacked@closedcycle@impl}%
+		\edef\pgfplots@stacked@closedcycle@impl{%
+			[mark=none,/utils/exec=\noexpand\pgfplots@try@mirror@plot@handler]
+			--plot coordinates{\the\pgfplots@toka}
+			--cycle
+		}%
+	\fi
+	\global\pgfplots@stacked@isfirstplotfalse
+%\message{pgfplots@stacked@endplot: PLOT ENDED}%
+}%
+
+% WARNING: when this method is called, NEITHER
+% \ifpgfplots@stacked@isfirstplot NOR the zero level lists are
+% initialised!
+\def\pgfplots@stacked@initzerolevelhandler{%
+	\ifpgfplots@stacked@x
+		\pgfplotxzerolevelstream@@list
+		\pgfplotyzerolevelstreamconstant{\pgfplots@ZERO@y}%
+	\else
+		\pgfplotxzerolevelstreamconstant{\pgfplots@ZERO@x}%
+		\pgfplotyzerolevelstream@@list
+	\fi
+}%
+
+\def\pgfplots@stacked@rememberzerolevelpoint@for@next@plot#1{%
+	\edef\pgfplots@TMP{#1}%
+	{\globaldefs=1
+	\expandafter\pgfplotslistpushback\pgfplots@TMP\to\pgfplots@stacked@nextzerolevellist
+	}%
+}
+
+\def\pgfplots@stacked@finishpoint#1#2{%
+	\ifpgfplots@stacked@isfirstplot
+	\else
+		\pgfpointxy{\pgfplots@stacked@zerolevelpoint@x}{\pgfplots@stacked@zerolevelpoint@y}%
+		\ifpgfplots@stacked@x
+			\edef\pgfplots@TMP{\the\pgf@x}%
+		\else
+			\edef\pgfplots@TMP{\the\pgf@y}%
+		\fi
+		{\globaldefs=1
+		\expandafter\pgfplotslistpushback\pgfplots@TMP\to\pgfplots@stacked@PGFzerolevels
+		}%
+		\pgfplotslist@TOK@a=\expandafter{\pgfplots@stacked@closedcycle@impl}%
+		\edef\pgfplots@stacked@closedcycle@impl{%
+			(\pgfplots@stacked@zerolevelpoint@x,\pgfplots@stacked@zerolevelpoint@y)%
+			\the\pgfplotslist@TOK@a}%
+	\fi
+}%
+
+\def\pgfplots@stacked@preparepoint@inmacro#1#2{%
+	\pgfplots@stacked@getnextzerolevelpoint
+	\ifpgfplots@stacked@x
+		\ifpgfplots@stacked@plus
+			\let\pgfplots@stacked@op=\pgfmathadd@
+		\else
+			\let\pgfplots@stacked@op=\pgfmathsubtract@
+		\fi
+		\ifpgfplots@float@numerics@mode@x
+			\ifpgfplots@datascaletrafo@initialised
+			\else
+				\ifpgfplots@stacked@plus
+					\let\pgfplots@stacked@op=\pgfmathfloatadd@
+				\else
+					\let\pgfplots@stacked@op=\pgfmathfloatsubtract@
+				\fi
+			\fi
+		\fi
+		\pgfplots@stacked@op{\pgfplots@stacked@zerolevelpoint@x}{#1}%
+		\let#1=\pgfmathresult
+	\else
+		\ifpgfplots@stacked@plus
+			\let\pgfplots@stacked@op=\pgfmathadd@
+		\else
+			\let\pgfplots@stacked@op=\pgfmathsubtract@
+		\fi
+		\ifpgfplots@float@numerics@mode@y
+			\ifpgfplots@datascaletrafo@initialised
+			\else
+				\ifpgfplots@stacked@plus
+					\let\pgfplots@stacked@op=\pgfmathfloatadd@
+				\else
+					\let\pgfplots@stacked@op=\pgfmathfloatsubtract@
+				\fi
+			\fi
+		\fi
+		\pgfplots@stacked@op{\pgfplots@stacked@zerolevelpoint@y}{#2}%
+		\let#2=\pgfmathresult
+	\fi
+	\pgfplots@stacked@rememberzerolevelpoint@for@next@plot{(#1,#2)}%
+}
+
+% This here is a re-implementation of the stored plot processing.
+%
+% The idea is simply, although it requires quite some work:
+%
+% If we stack plots on top of each other, early drawing commands
+% (early plots) will be OVERDRAWN by later drawing commands (later
+% plots). This is especially unfortunate if we use filled bar plots
+% or comb plots.
+%
+% IDEA: draw plots in REVERSE order. The positioning, styles and
+% whatever must not be affected, only the sequence of drawing commands
+% shall change.
+%
+% So, this command here does all numerics which is to be done and
+% assembles a NEW, REVERSED STORED PLOT LIST.
+\def\pgfplots@stacked@finalize@stored@plots{%
+	\pgfplotslistnewempty\pgfplots@stored@plotlist@reversed
+	\begingroup
+	\pgfplotslistforeachungrouped\pgfplots@stored@plotlist\as\pgfplots@TMP{%
+		\expandafter\pgfplots@stored@plotlist@EXTRACTENTRY\pgfplots@TMP
+		\ifx\pgfplots@stored@current@cmd\pgfutil@empty
+		\else
+			\ifpgfplots@apply@datatrafo
+				% Apply the data scaling transformation, but do NOT
+				% issue any drawing commands (-> use the ...@dryrun
+				% version)
+				\expandafter\pgfplots@coord@stream@finalize@storedcoords@START@dryrun\pgfplots@stored@current@data\to\pgfplots@stored@current@data\pgfplots@stored@current@precmdapp%
+				% save any intermediate results as "precmd":
+				\pgfplotslist@TOK@b=\expandafter{\pgfplots@stored@current@precmd}%
+				\pgfplotslist@TOK@a=\expandafter{\pgfplots@stored@current@precmdapp}%
+				\edef\pgfplots@stored@current@precmd{\the\pgfplotslist@TOK@b\the\pgfplotslist@TOK@a}%
+			\fi
+		\fi
+		% Now, we need to insert all stored entities into the new,
+		% reversed list. We only expand them ONCE.
+		\pgfplotslist@TOK@a=\expandafter{\pgfplots@stored@current@precmd}%
+		\pgfplotslist@TOK@b=\expandafter{\pgfplots@stored@current@cmd}%
+		\edef\pgfplots@TMP{%
+			{\the\pgfplotslist@TOK@a}{\the\pgfplotslist@TOK@b}}%
+		\pgfplots@toka=\expandafter{\pgfplots@TMP}%
+		\pgfplotslist@TOK@a=\expandafter{\pgfplots@stored@current@data}%
+		\pgfplotslist@TOK@b=\expandafter{\pgfplots@stored@current@postcmd}%
+		\edef\pgfplots@TMP{%
+			\the\pgfplots@toka
+			{\the\pgfplotslist@TOK@a}{\the\pgfplotslist@TOK@b}}%
+		% Reverse sequence:
+		\expandafter\pgfplotslistpushfront\pgfplots@TMP\to\pgfplots@stored@plotlist@reversed
+	}%
+	% Now, overwrite the original list:
+	\global\let\pgfplots@stored@plotlist=\pgfplots@stored@plotlist@reversed
+	\endgroup
+}%
+
+\def\pgfplots@stacked@path@closed@cycle{%
+	\pgfplots@stacked@closedcycle@impl
+}
+
+% Saves the finalized variables into macro #1 such that a call to #1
+% restores them.
+%
+% This affects pgf zero level handlers and whether this here is the
+% first plot or not..
+\def\pgfplots@stacked@savestateto#1{%
+	\pgfplotslist@TOK@a=\expandafter{\pgfplots@stacked@PGFzerolevels}%
+	\ifpgfplots@stacked@isfirstplot
+		\pgfplotslist@TOK@b={\pgfplots@stacked@isfirstplottrue}%
+	\else
+		\pgfplotslist@TOK@b={\pgfplots@stacked@isfirstplotfalse}%
+	\fi
+	\pgfplots@toka=\expandafter{\pgfplots@stacked@closedcycle@impl}%
+	\edef#1{%
+		\noexpand\gdef\noexpand\pgfplots@stacked@PGFzerolevels{\the\pgfplotslist@TOK@a}%
+		\the\pgfplotslist@TOK@b
+		\noexpand\def\noexpand\pgfplots@stacked@closedcycle@impl{\the\pgfplots@toka}%
+	}%
+}
+
+% PGF interfaces:
+\def\pgfplotxzerolevelstream@@list{%
+	\def\pgf@plotxzerolevelstreamstart{%
+		\global\let\pgfplotxzerolevelstream@@list@@backup=\pgfplots@stacked@PGFzerolevels
+		\gdef\pgf@plotxzerolevelstreamnext{%
+			\pgfplotslistcheckempty\pgfplots@stacked@PGFzerolevels
+			\ifpgfplotslistempty
+				\global\pgf@x=\pgfplots@ZERO@x\relax
+			\else
+				{\globaldefs=1\relax
+				\pgfplotslistpopfront\pgfplots@stacked@PGFzerolevels\to\pgfmathresult
+				}%
+				\global\pgf@x=\pgfmathresult\relax
+			\fi
+		}%
+	}%
+	\def\pgf@plotxzerolevelstreamend{%
+		\global\let\pgfplots@stacked@PGFzerolevels=\pgfplotxzerolevelstream@@list@@backup
+	}%
+}%
+
+\def\pgfplotyzerolevelstream@@list{%
+	\def\pgf@plotyzerolevelstreamstart{%
+		\global\let\pgfplotyzerolevelstream@@list@@backup=\pgfplots@stacked@PGFzerolevels
+		\gdef\pgf@plotyzerolevelstreamnext{%
+			\pgfplotslistcheckempty\pgfplots@stacked@PGFzerolevels
+			\ifpgfplotslistempty
+				\global\pgf@x=\pgfplots@ZERO@y\relax
+			\else
+				{\globaldefs=1\relax
+				\pgfplotslistpopfront\pgfplots@stacked@PGFzerolevels\to\pgfmathresult
+				}%
+				\global\pgf@x=\pgfmathresult\relax
+			\fi
+		}%
+	}%
+	\def\pgf@plotyzerolevelstreamend{%
+		\global\let\pgfplots@stacked@PGFzerolevels=\pgfplotyzerolevelstream@@list@@backup
+	}%
+}%
diff --git a/Master/texmf-dist/tex/latex/pgfplots/liststructure.sty b/Master/texmf-dist/tex/latex/pgfplots/liststructure.sty
deleted file mode 100644
index c5930374f7d..00000000000
--- a/Master/texmf-dist/tex/latex/pgfplots/liststructure.sty
+++ /dev/null
@@ -1,196 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is a helper package with an elementary list datastructure.
-%
-% Its implementation is based on Knuth's list macros in "The TeXbook".
-%
-% The following macros are supplied:
-%
-% \listnewempty
-% \listnew
-% \listcopy
-% \listpopfront
-% \listpushback
-% \listpushfront
-% \listsize
-% \listselect
-% \listcheckempty
-% \listforeach
-%
-% Copyright 2007/2008 by Christian Feuersänger.
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-% 
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-% GNU General Public License for more details.
-% 
-% You should have received a copy of the GNU General Public License
-% along with this program.  If not, see <http://www.gnu.org/licenses/>.
-%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\ProvidesPackage{liststructure}[2008/02/17 Version 0.9.4]
-
-\newtoks\TOKL@ta
-\newtoks\TOKL@tb
-\newif\iflistempty
-
-% Creates a new, empty list.
-\long\def\listnewempty#1{\let#1=\empty}
-
-% Creates a new list with an abirtrary number of elements.
-% Arguments:
-% #1: the list's name (a macro name)
-% #2: the elements in the form 
-%     first\\second\\third\\ ...\\
-%     like in tabular with one column.
-%
-% Example:
-% \listnew\foolist{First Element\\Second Element\\Third Element\\}
-%
-% WARNING: do NOT forget the final '\\'!
-\long\def\listnew#1#2{%
-	\listnewempty{#1}%
-	\long\def\listnew@impl@rest{#2}%
-	\loop
-	\ifx\listnew@impl@rest\empty
-	\else
-		\expandafter\listnew@impl\listnew@impl@rest\tolist#1\relax
-	\repeat
-}
-
-% Copies list #1 to list #2.
-\def\listcopy#1\to#2{\let#2=#1}
-
-
-% helper macro for \listnew
-\long\def\listnew@impl#1\\#2\tolist#3{%
-	\listpushback#1\to#3\relax%
-	\def\listnew@impl@rest{#2}%
-}
-
-
-% #1: the item to prepend
-% #2: the list as macro name
-% Example:
-% \listpushfront Next first Element\to\foolist
-\long\def\listpushfront#1\to#2{%
-	\TOKL@ta={\list@sep{#1}}%
-	\TOKL@tb=\expandafter{#2}%
-  	\edef#2{\the\TOKL@ta\the\TOKL@tb}%
-}
-
-% #1: the item to append
-% #2: the list as macro name
-% Example:
-% \listpushback Next last element\to\foolist
-\long\def\listpushback#1\to#2{%
-	\TOKL@ta={\list@sep{#1}}%
-	\TOKL@tb=\expandafter{#2}%
- 	\edef#2{\the\TOKL@tb\the\TOKL@ta}%
-}
-
-% Concatenates two lists #2 and #3 into #1
-% Example:
-% \listconcat\result=\foolist&\bar
-\long\def\listconcat#1=#2&#3{%
-	\TOKL@ta=\expandafter{#2}%
-	\TOKL@tb=\expandafter{#3}%
-	\edef#1{\the\TOKL@ta\the\TOKL@tb}%
-}
-
-% implements #2 := pop_front(#1)
-% Example:
-% \listpopfront\foolist\to\poppedfirstelem
-\long\def\listpopfront#1\to#2{%
-	\listcheckempty#1\relax
-	\iflistempty
-		\errmessage{ERROR: \string\listpopfront\ from \string#1\ although list is EMPTY}%
-	\else
-		\expandafter\listpopfront@impl#1\listpopfront@macronames#1#2%
-	\fi
-}
-
-% implementation helper for listpopfront
-\long\def\listpopfront@impl\list@sep#1#2\listpopfront@macronames#3#4{%
-	\def#4{#1}%
-	\def#3{#2}%
-}
-
-% Counts the number of elements in list #1, storing it into the count
-% register #2.
-% Example:
-% \listsize\foo\to{\count0}%
-% \the\count0
-\long\def\listsize#1\to#2{%
-	#2=0%
-	\long\def\list@sep##1{\advance#2 by 1 }%
-	#1%
-}
-
-% Returns the #1th element of list #2 into macro #3
-% Arguments:
-% #1: a count 0,...,N-1 where N is the list size.
-%     You may specify a number of a count.
-% #2: a list
-% #3: a macro name
-% Example:
-%   Element 0:
-%   \listselect0\of\foo\to\elem
-%   \elem
-%   Element \count1:
-%   \listselect\count1\of\foo\to\elem
-\long\def\listselect#1\of#2\to#3{%
-	\def#3{\errmessage{The requested item #1 of \string#2 is OUT OF RANGE.}}%
-	\begingroup
-	\count0=#1\relax
- 	\long\def\list@sep##1{%
-		\advance\count0-1
-		\ifnum\count0=-1
-			\global\def\listselect@tmp{\def#3{##1}}%
-			% the command \listselect@tmp will be expander AFTER
-			% '\endgroup'
-			\aftergroup\listselect@tmp%
-		\fi%
-	}%
-	#2%
-	\endgroup
-}
-
-% Sets the boolean \iflistempty depending on whether list #1 is empty
-% or not.
-% Example:
-%
-% \listcheckempty\foolist
-% \iflistempty
-%    List foolist is empty!
-% \else
-%    List is not empty.
-% \fi
-\def\listcheckempty#1{%
-	\ifx#1\empty
-		\listemptytrue
-	\else
-		\listemptyfalse
-	\fi
-}
-
-
-% Iterates through each list element, names it #2 and calls code #3.
-% Example:
-% \listnew\foolist{Eins\\Zwei\\Drei\\}%
-% \listforeach\foolist\as\foo{Element \foo\par}%
-% results in
-%  Element Eins
-%  Element Zwei
-%  Element Drei
-\long\def\listforeach#1\as#2#3{{%
-	\long\def\list@sep##1{\def#2{##1}#3}%
-	#1\relax
-}}
diff --git a/Master/texmf-dist/tex/latex/pgfplots/pgfmathlog.sty b/Master/texmf-dist/tex/latex/pgfplots/pgfmathlog.sty
deleted file mode 100644
index 9e9b57ea137..00000000000
--- a/Master/texmf-dist/tex/latex/pgfplots/pgfmathlog.sty
+++ /dev/null
@@ -1,215 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% Package pgfmathlog.sty. 
-%
-% This file provides the public functions
-% 
-%   \pgfmathnormalisedfloatingpoint#1\to#2\powten#3
-% like
-%   \pgfmathnormalisedfloatingpoint 412.02451e-5to\M\powten\E
-%
-% and
-%   \pgfmathlog
-%   \pgfmathlog@
-% which both assign \pgfmathresult to the natural number of a given
-% number (without units).
-%
-% It is based on Till Tantaus pgfmath package which comes as part of
-% the PGF bundle, but it provides its own number parsing routines to
-% circumvent TeXs limited real number representations.
-%
-% Copyright 2007/2008 by Christian Feuersänger.
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-% 
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-% GNU General Public License for more details.
-% 
-% You should have received a copy of the GNU General Public License
-% along with this program.  If not, see <http://www.gnu.org/licenses/>.
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\ProvidesPackage{pgfmathlog}[2008/02/17 Version 0.9.4]
-\RequirePackage{pgf}[2007/01/01]
-\RequirePackage{sciformat}[2008/02/17]
-\RequirePackage{pgfplotshelpers}[2008/02/17]
-
-% See \sciparse docs
-\def\pgfmathnormalisedfloatingpoint#1\to#2\powten#3{%
-	\sciparse#1\to#2\powten{#3}%
-}
-
-% Evaluates the natural logarithm, log(x) for 0.1<=x<=1.
-% @see \pgfmathlog@ for the general method.
-% NON ACCURATE ENOUGH!
-\def\pgfmathlogzeroone#1{%
-	\begingroup%
-		\message{EVAL log(#1) STARTS:}%
-		\pgfmath@x=#1pt\relax
-		\pgfmath@y=\pgfmath@x
-		\advance\pgfmath@x by-1pt
-		\advance\pgfmath@y by 1pt
-		\pgfmathdivide{\pgfmath@x}{\pgfmath@y}%
-		% pgfmath@ya = tmp := (#1 -1)/ (#1+1)
-		\expandafter\pgfmath@ya\pgfmathresult pt
-		% pgfmath@xa := [ (#1 -1)/ (#1+1) ]^2
-		\pgfmathmultiply{\pgfmathresult}{\pgfmathresult}%
-		\expandafter\pgfmath@xa\pgfmathresult pt
-		% returnvalue:
-		\pgfmath@y=0pt
-		% loop counter:
-		\c@pgfmath@counta=0
-		% j:
-		\c@pgfmath@countb=1
-		\loop
-		\ifnum\c@pgfmath@counta<6
-			\let\multmp=\pgfmath@ya
-			\divide\pgfmath@ya by\c@pgfmath@countb
-			\advance\pgfmath@y by\pgfmath@ya
-			\let\pgfmath@ya=\multmp
-			\advance\c@pgfmath@countb by2
-			\message{[tmp *= x*x  tmp =\the\pgfmath@ya, x*x=\the\pgfmath@xa]}%
-			\pgfmathmultiply{\pgfmath@ya}{\pgfmath@xa}%
-			\expandafter\pgfmath@ya\pgfmathresult pt
-			\advance\c@pgfmath@counta by1
-			\message{[cur/2 = \the\pgfmath@y]}%
-		\repeat
-		\multiply\pgfmath@y by2
-		\message{fertiges Resultat fuer log(#1): \the\pgfmath@y}%
-		\pgfmath@returnone\pgfmath@y%
-	\endgroup%
-}
-
-
-% Computes a good guess for log(X.XXXX) where the input number should
-% be between 0 < x < 10.
-%
-% If it is not in this range, the returned value will be bad.
-%
-% For use in the newton implementation of log(x). Please note that we
-% first compute a normalized floating point representation of x, and
-% the mantisse is always between 0 and 10.
-\def\pgfmathlog@smaller@ten@newton@startval#1#2#3\to#4{%
-	\ifnum0<#1\relax
-		\def\axis@TMP{#2}%
-		\def\axis@TMPB{.}%
-		\ifx\axis@TMP\axis@TMPB
-			\ifcase#1
-			\errmessage{pgfmathlog.sty: INTERNAL ERROR: should not happen! 
-				[\#1=0 should have been caught before!]}%
-			\or#4=0.53062825106217pt
-			\or#4=0.993pt
-			\or#4=1.308pt
-			\or#4=1.5pt
-			\or#4=1.71pt
-			\or#4=1.872pt
-			\or#4=2.01pt
-			\or#4=2.145pt
-			\or#4=2.24pt
-			\fi
-%			\message{Newton: Start value \the#4 assigned}%
-		\else
-%			\message{Kein Komma an zweiter stelle (statt dessen: #2); Nehme standardstartwert.}%
-			#4=0.1pt
-		\fi
-	\else
-%		\message{Argument #1 <= 0. Nehme standardstartwert.}%
-		#4=0.1pt
-	\fi
-}
-
-% Computes log(x) into \pgfmathresult.
-%
-% REMARK
-% This method does NOT use TeX Registers to represent the numbers! The
-% computation is COMPLETELY STRING BASED.
-% This allows numbers such at 10000000 or 5.23e-10 to be represented
-% properly, although TeX-registers would produce overflow/underflow
-% errors in these cases. 
-%
-% The natural logarithm is computed using log(X*10^Y) = log(X) + log(10)*Y
-\def\pgfmathlog@#1{%
-	\pgfmathlog@newton{#1}%
-}
-
-% Public interface method. This is expected to use \pgfmathparse but
-% it DOESN'T do that. \pgfmathparse naturally can't handle numbers
-% which exceed TeX's numerical capabilities. However, exponentials are
-% typically either too large or too small for TeX.
-%
-% @see \pgfmathnormalisedfloatingpoint for how we parse arguments.
-% @see \pgfmathlog@
-\def\pgfmathlog#1{%
-	\pgfmathlog@newton{#1}%
-}
-
-% This implementation of log(X) is done with a newton method applied to x-exp(y) = 0.
-% The implementation \pgfmathexp is used for exp(y).
-%
-% see \pgfmathlog@
-\def\pgfmathlog@newton#1{%
-	\begingroup%
-		% compute #1 = M*10^E with normalised mantisse M = [+-]*[1-9].XXXXX
-		\sciparse#1\to\newtoninput@mantisse\powten\newtoninput@exponent
-		%
-		% Now, compute log(#1) = log(M) + E*log(10)
-%		\message{EVAL log(#1) = log(\newtoninput@mantisse) + \newtoninput@exponent*log(10) mit newton STARTS:}%
-		% input argument into \pgfmath@x
-		\expandafter\pgfmath@x\newtoninput@mantisse pt
-		\ifdim\pgfmath@x>0pt
-			% return value:
-			\expandafter\pgfmathlog@smaller@ten@newton@startval\newtoninput@mantisse\to\pgfmath@y
-			% loop counter:
-			\c@pgfmath@counta=0
-			\loop
-	%\message{Newton iter \#\the\c@pgfmath@counta: log(\newtoninput@mantisse) = \the\pgfmath@y }%
-			\ifnum\c@pgfmath@counta<2
-	%			\pgfmathexp\pgfmath@y%
-				\pgfmathlog@invoke@expanded\pgfmathexp@{{\pgf@sys@tonumber{\pgfmath@y}}}%
-				\let\tmp=\pgfmathresult
-				%\pgfmathdivide\pgfmath@x\tmp%
-				\pgfmathlog@invoke@expanded\pgfmathdivide@{{\pgf@sys@tonumber{\pgfmath@x}}{\tmp}}%
-				\expandafter\pgfmath@ya\pgfmathresult pt
-				\advance\pgfmath@y by\pgfmath@ya
-				\advance\pgfmath@y by-1pt
-				\advance\c@pgfmath@counta by1
-			\repeat
-			\pgfmath@x=2.302585pt% = log(10)
-			\multiply\expandafter\pgfmath@x\newtoninput@exponent
-			\advance\pgfmath@y by\pgfmath@x
-%\message{Newton final result: log(\newtoninput@mantisse)+\newtoninput@exponent*log(10) = \the\pgfmath@y [ nur \newtoninput@exponent * log(10) = \the\pgfmath@x]}%
-			\pgfmath@returnone\pgfmath@y%
-		\else
-			\global\let\pgfmathresult=\empty%
-		\fi
-	\endgroup%
-}
-
-% Usage:
-% \pgfmathapproxequalto@macro\argone\argtwo\result
-%
-% -> will set \resulttrue or \resultfalse
-% -> check with \ifresult
-\def\pgfmathlog@approxequalto@macro#1#2#3{%
-	\begingroup%
-		\expandafter\pgfmath@x#1pt\relax%
-		\expandafter\pgfmath@y#2pt\relax%
-		\advance\pgfmath@x-\pgfmath@y%
-		\ifdim\pgfmath@x<0pt
-			\multiply\pgfmath@x by-1
-		\fi
-		\ifdim\pgfmath@x<0.0001pt\relax%
-			\expandafter\aftergroup\csname #3true\endcsname
-		\else%
-			\expandafter\aftergroup\csname #3false\endcsname
-		\fi%
-	\endgroup%
-}
-
diff --git a/Master/texmf-dist/tex/latex/pgfplots/pgfplots.sty b/Master/texmf-dist/tex/latex/pgfplots/pgfplots.sty
index 114db197b55..3e63fdfa8b7 100644
--- a/Master/texmf-dist/tex/latex/pgfplots/pgfplots.sty
+++ b/Master/texmf-dist/tex/latex/pgfplots/pgfplots.sty
@@ -23,8 +23,8 @@
 % along with this program.  If not, see <http://www.gnu.org/licenses/>.
 %
 %--------------------------------------------
-\def\pgfplotsversion{0.92.4}
-\ProvidesPackage{pgfplots}[2008/02/17 Version \pgfplotsversion]
+\def\pgfplotsversion{1.0}
+\ProvidesPackage{pgfplots}[2008/06/07 Version \pgfplotsversion]
 
 % ATTENTION:
 % you MAY need one of
@@ -39,2559 +39,12 @@
 %   'pdftex' for 'pdflatex'
 % -> dvipdfm needs special attention.
 
-\RequirePackage{xkeyval}[2006/11/18]
-\RequirePackage{ifthen}
-\RequirePackage{liststructure}
-\RequirePackage{tikz}[2007/06/07]
-\RequirePackage{sciformat}
-\RequirePackage{pgfmathlog}
-\usetikzlibrary{plotmarks}
-
-\def\prefix{pgfplots}
-
-% FIXME: reduce number of variables!
-\newcount\axisticknum
-\newcount\axis@tickposnum
-\newcount\axis@xmode
-\newcount\axis@ymode
-\newcount\axis@numplots
-\newdimen\axis@xcoordminTEX
-\newdimen\axis@xcoordmaxTEX
-\newdimen\axis@ycoordminTEX
-\newdimen\axis@ycoordmaxTEX
-\newdimen\axis@tmpa
-\newdimen\axis@tmpb
-\newif\ifaxis@isuniformtick
-\newif\ifaxis@enlargelimits
-\newif\ifaxis@enlargelimits@rel@thresh
-\newif\ifaxis@enlargelimits@auto
-\let\axis@TMP=\empty
-\let\axis@TMPB=\empty
-\let\axis@TMPC=\empty
-
-\def\axis@leftover{}
-\def\axis@rightover{}
-\def\axisdefaultwidth{240pt}
-\def\axisdefaultheight{207pt}
-\def\axisdefaulttickwidth{35}% the maximum space between adjacent ticks (in pt, but don't specify the unit 'pt')
-\def\axisdefaulttryminticks{4}
-
-\listnew{\blackwhiteplotspeclist}{%
-	mark options={fill=gray},mark=*\\%
-	mark options={fill=gray},mark=square*\\%
-	mark options={fill=gray},mark=otimes*\\%
-	mark=star\\%
-	mark options={fill=gray},mark=diamond*\\%
-	densely dashed,mark options={solid,fill=gray},mark=*\\%
-	densely dashed,mark options={solid,fill=gray},mark=square*\\%
-	densely dashed,mark options={solid,fill=gray},mark=otimes*\\%
-	densely dashed,mark options={solid},mark=star\\%
-	densely dashed,mark options={solid,fill=gray},mark=diamond*\\%
-}
-\listnew{\coloredplotspeclist}{%
-	blue,mark options={fill=blue!80!black},mark=*\\%
-	red,mark options={fill=red!80!black},mark=square*\\%
-	brown!60!black,mark options={fill=brown!80!black},mark=otimes*\\%
-	black,mark=star\\%
-	blue,mark options={fill=blue!80!black},mark=diamond*\\%
-	red,densely dashed,mark options={solid,fill=red!80!black},mark=*\\%
-	brown!60!black,densely dashed,mark options={solid,fill=brown!80!black},mark=square*\\%
-	black,densely dashed,mark options={solid,fill=gray},mark=otimes*\\%
-	blue,densely dashed,mark=star,mark options=solid\\%
-	red,densely dashed,mark options={solid,fill=red!80!black},mark=diamond*\\%
-}
-
-
-\listcopy\coloredplotspeclist\to\autoplotspeclist%
-%\listcopy\blackwhiteplotspeclist\to\autoplotspeclist%
-
-\tikzstyle{every axis}=[]
-\tikzstyle{every axis plot}=[]
-\tikzstyle{every axis label}=[]
-\tikzstyle{every axis x label}=[at={(0.5,0)},below,yshift=-15pt]
-\tikzstyle{every axis y label}=[at={(0,0.5)},xshift=-35pt,rotate=90]
-\tikzstyle{every axis title}=[at={(0.5,1)},above,yshift=6pt]
-\tikzstyle{every tick}=[very thin,gray]
-\tikzstyle{every minor tick}=[]
-\tikzstyle{every major tick}=[]
-\tikzstyle{every axis grid}=[style=help lines]
-\tikzstyle{every minor grid}=[]
-\tikzstyle{every major grid}=[]
-\tikzstyle{every tick label}=[]
-\tikzstyle{every x tick label}=[]
-\tikzstyle{every y tick label}=[]
-
-% specifies how and where to draw the axis.
-%   \tikzstyle{every axis legend}+=[at={(0,0)}]
-% will draw it at the lower left corner of the axis while
-%   \tikzstyle{every axis legend}+=[at={(1,1)}]
-% means the upper right corner.
-%
-% The legend is a 'node' so you can use any tikz option which affects
-% nodes. The option 'text width' is set automatically, depending on
-% the \legend[textwidth=...] option.
-%
-% Examples:
-% -  \tikzstyle{every axis legend}+=[at={(1.02,1)},anchor=north west]
-%   draws the legend OUTSIDE TOP RIGHT.
-%
-% - \tikzstyle{every axis legend}+=[at={(1,0.5)},anchor=east,outer sep=0.5cm]
-%   draws the legend INSIDE MIDDLE RIGHT, separated by 0.5cm from the axis.
-\tikzstyle{every axis legend}=[%
-		cells={anchor=center},
-		inner xsep=3pt,inner ysep=2pt,nodes={inner sep=2pt,text depth=0.15em},
-		anchor=north east,%
-		shape=rectangle,%
-		fill=white,%
-		draw=black,
-		at={(0.98,0.98)}
-		]
-%		at={(1,1)},
-%		outer sep=0.1cm]
-
-
-\define@cmdkeys[\prefix]{axis}[axis@]{%
-	xmin,xmax,xticklabel,xtick,xtickten,xlabel,%
-	ymin,ymax,yticklabel,ytick,ytickten,ylabel,%
-	subtickwidth,tickwidth,%
-	xfilter,yfilter,%
-	width,height,%
-	title,%
-	execute at begin plot,%
-	execute at end plot,%
-	enlargelimits,%
-	legend columns,%
-	x,y}%
-
-\long\def\axis@foreach@to@list#1\to#2{%
-	\listnewempty\axis@TMP
-	\begingroup
-	\foreach \i in {#1} {%
-		\globaldefs=1
-		\expandafter\listpushback\i\to\axis@TMP
-		\globaldefs=0
-	}%
-	\endgroup
-	\listcopy\axis@TMP\to#2\relax
-}
-
-\define@cmdkey[\prefix]{axis}[axis@]{xticklabels}{%
-	\expandafter\axis@foreach@to@list\axis@xticklabels\to\axis@xticklabels
-	%\expandafter\listnew\expandafter\axis@xticklabels\expandafter{\axis@xticklabels}%
-	\let\axis@xticklabel=\axis@user@ticklabel@list@x
-}
-\define@cmdkey[\prefix]{axis}[axis@]{yticklabels}{%
-	\expandafter\axis@foreach@to@list\axis@yticklabels\to\axis@yticklabels
-	%\expandafter\listnew\expandafter\axis@yticklabels\expandafter{\axis@yticklabels}%
-	\let\axis@yticklabel=\axis@user@ticklabel@list@y
-}
-
-\define@cmdkey[\prefix]{axis}[axis@]{minor tick length}{%
-	\expandafter\let\expandafter\axis@subtickwidth\csname axis@minor tick length\endcsname
-}
-\define@cmdkey[\prefix]{axis}[axis@]{major tick length}{%
-	\expandafter\let\expandafter\axis@tickwidth\csname axis@major tick length\endcsname
-}
-
-% sets \axis@tickposnum to
-% left=0
-% right=1
-% both=2
-\define@choicekey[\prefix]{axis}{tickpos}[\val\nr]{left,right,both}{%
-  \axis@tickposnum=\nr\relax
-}
-\define@choicekey[\prefix]{axis}{legend plot pos}[\val\nr]{left,right,none}{%
-	\edef\axis@legend@plot@pos{\nr}%
-}
-
-\define@choicekey[\prefix]{axis}{anchor}[\val\nr]{north,north west,west,south west,south,south east,east,north east,center}{%
-  	\edef\axis@anchorchoicenum{\nr}%
-}
-
-\define@choicekey[\prefix]{axis}{ticks}[\val\nr]{none,major,minor,both}{%
-	\expandafter\ifcase\nr\relax
-		\axis@xminorticksfalse
-		\axis@yminorticksfalse
-		\axis@xmajorticksfalse
-		\axis@ymajorticksfalse
-	\or
-		\axis@xminorticksfalse
-		\axis@yminorticksfalse
-		\axis@xmajortickstrue
-		\axis@ymajortickstrue
-	\or
-		\axis@xminortickstrue
-		\axis@yminortickstrue
-		\axis@xmajorticksfalse
-		\axis@ymajorticksfalse
-	\or
-		\axis@xminortickstrue
-		\axis@yminortickstrue
-		\axis@xmajortickstrue
-		\axis@ymajortickstrue
-	\fi
-}
-\define@choicekey[\prefix]{axis}{grid}[\val\nr]{none,major,minor,both}{%
-	\expandafter\ifcase\nr\relax
-		\axis@xminorgridsfalse
-		\axis@yminorgridsfalse
-		\axis@xmajorgridsfalse
-		\axis@ymajorgridsfalse
-	\or
-		\axis@xminorgridsfalse
-		\axis@yminorgridsfalse
-		\axis@xmajorgridstrue
-		\axis@ymajorgridstrue
-	\or
-		\axis@xminorgridstrue
-		\axis@yminorgridstrue
-		\axis@xmajorgridsfalse
-		\axis@ymajorgridsfalse
-	\or
-		\axis@xminorgridstrue
-		\axis@yminorgridstrue
-		\axis@xmajorgridstrue
-		\axis@ymajorgridstrue
-	\fi
-}
-
-
-\define@boolkeys[\prefix]{axis}[axis@]{%
-	xminorticks,%
-	xmajorticks,%
-	yminorticks,%
-	ymajorticks,%
-	xminorgrids,%
-	xmajorgrids,%
-	yminorgrids,%
-	ymajorgrids,%
-	disablelogfilter,%
-	disabledatascaling,%
-	hide axis,%
-	scale only axis}[true]
-
-% sets \axis@xmode to
-% normal=0
-% log=1
-\define@choicekey[\prefix]{axis}{xmode}[\val\nr]{normal,log}{%
-  \axis@xmode=\nr\relax
-}
-
-% sets \axis@ymode to
-% normal=0
-% log=1
-\define@choicekey[\prefix]{axis}{ymode}[\val\nr]{normal,log}{%
-  \axis@ymode=\nr\relax
-}
-
-\long\def\axispreset#1{%
-	\presetkeys[\prefix]{axis}{#1}{}%
-}
-\long\def\legendpreset#1{%
-	\errmessage{Sorry, legendpreset is now deprecated, along with the legend options text width and font. Legends are now TikZ-matrizes which provide better alignment and can be placed horizontally. See the manual for details.}%
-}
-
-\presetkeys[\prefix]{axis}{%
-	xmode=normal,
-	xmin=,
-	xmax=,
-	xlabel=,
-	xtick=,
-	xtickten=,
-	xticklabel=,
-	xminorticks=true,
-	xmajorticks=true,
-	xminorgrids=false,
-	xmajorgrids=false,
-	ymode=normal,
-	ymin=,
-	ymax=,
-	ylabel=,
-	ytick=,
-	ytickten=,
-	yticklabel=,
-	yminorticks=true,
-	ymajorticks=true,
-	yminorgrids=false,
-	ymajorgrids=false,
-	grid=none,%
-	tickpos=both,
-	xfilter=,
-	yfilter=,
-	title=,
-	width=,
-	height=,
-	anchor=south west,
-	subtickwidth=0.1cm,
-	tickwidth=0.15cm,
-	scale only axis=false,
-	hide axis=false,
-	legend columns=1,
-	legend plot pos=left,
-	x=,% is implicitly set by 'width' and/or '\axisdefaultwidth'
-	y=,% is implicitly set by 'height' and/or '\axisdefaultheight'
-	execute at begin plot=,%
-	execute at end plot=,%
-	enlargelimits=auto,
-	disablelogfilter=false}{}
-
-\def\logten{2.3025851}
-\def\reciproc@logten{0.434294481903252}
-
-\newcommand{\logi}[1]{%
-	\ifcase#1
-	\or0
-	\or0.693147
-	\or1.098612
-	\or1.386294
-	\or1.60943791
-	\or1.7917594
-	\or1.94591014
-	\or2.07944154
-	\or2.197224
-	\fi
-}
-
-\newcommand{\show@yticklabel}[2]{{%
-	\let\ticknum=#1%
-	\ifaxis@float@numerics@mode@y
-		% this here stores \\tick@S, \\tick@M, \\tick@E
-		\axis@inverse@datascaletrafo@y{#2}\to\tick
-		% .. and this here provides \tick as fixed point repr:
-		\scitofixedsingle\tick\tick
-	\else
-		\def\tick{#2}%
-	\fi
-	\axis@yticklabel
-}}
-
-% x-Achsenbeschriftung zum #1.ten Tick:
-% #1: die ticknum
-% #2: der x wert dafuer
-\newcommand{\show@xticklabel}[2]{{%
-	\let\ticknum=#1%
-	\ifaxis@float@numerics@mode@x
-		% this here stores \\tick@S, \\tick@M, \\tick@E
-		\axis@inverse@datascaletrafo@x{#2}\to\tick
-		% .. and this here provides \tick as fixed point repr:
-		\scitofixedsingle\tick\tick
-	\else
-		\def\tick{#2}%
-	\fi
-	\axis@xticklabel
-}}
-
-\def\axis@user@ticklabel@list@x{%
-	\listselect\ticknum\of\axis@xticklabels\to\tick
-	\tick
-}
-\def\axis@user@ticklabel@list@y{%
-	\listselect\ticknum\of\axis@yticklabels\to\tick
-	\tick
-}
-
-\newcommand{\axisdefaultticklabel}[0]{%
-	$\prettyprintnumber{\tick}$%
-}
-
-\newcommand{\axisdefaultticklabellog}[0]{%
-	\logtologtentomacro{\tick}{\roundedtick}%
-	$10^{\prettyprintnumber{\roundedtick}}$%
-}
-	
-
-\newcommand{\axisshowxlabel}{%
-	\node 
-		[style=every axis label,%
-		style=every axis x label]
-	{\axis@xlabel};
-
-}
-\newcommand{\axisshowylabel}{%
-	\node 
-		[style=every axis label,
-		style=every axis y label] 
-	{\axis@ylabel};
-}
-\newcommand{\axisshowtitle}{%
-	\node%
-		[style=every axis title]
-		{\axis@title};
-}
-
-% Y-Achsen und Achsenbeschriftung LOG:
-% 1: Ticks
-\newcommand{\axis@drawyaxis}[1]{%
-	\begingroup
-	\newif\ifneedsminorloop
-	\axisticknum=0
-	\edef\axis@TMP{#1}%
-	\ifx\axis@TMP\empty
-	\else
-		\ifaxis@yminorticks
-			\needsminorlooptrue
-		\fi
-		\ifaxis@yminorgrids
-			\needsminorlooptrue
-		\fi
-		\def\axis@placecomputedtick##1[##2]{%
-			\draw[##2]
-			\ifcase\axis@tickposnum
-				(\axis@xcoordminTEX\axis@leftover,		\axis@tmpa)
-			--	(\axis@xcoordminTEX+##1,	\axis@tmpa)
-			\or
-				(\axis@xcoordmaxTEX\axis@rightover,		\axis@tmpa)
-			--	(\axis@xcoordmaxTEX-##1,	\axis@tmpa)
-			\or
-				(\axis@xcoordminTEX\axis@leftover,		\axis@tmpa)
-			--	(\axis@xcoordminTEX+##1,	\axis@tmpa)
-
-				(\axis@xcoordmaxTEX\axis@rightover,		\axis@tmpa)
-			--	(\axis@xcoordmaxTEX-##1,	\axis@tmpa)
-			\fi
-			;
-		}%
-		\def\placecomputedgridline[##1]{%
-			\draw[##1]
-				(\axis@xcoordminTEX\axis@leftover,	\axis@tmpa)
-			--	(\axis@xcoordmaxTEX\axis@rightover,	\axis@tmpa)
-			;
-		}%
-		\foreach \y in {#1} {	
-			\pgfextracty{\axis@tmpa}{\pgfpointxy{0}{\y}}%
-			%
-			\ifdim\axis@tmpa<\axis@ycoordminTEX
-			\else
-				\ifdim\axis@tmpa>\axis@ycoordmaxTEX
-				\else
-					% Achsenbeschriftung:
-					\ifnum\axis@tickposnum=1
-						\node at 
-							(\axis@xcoordmaxTEX\axis@leftover,\axis@tmpa)
-							[right,style=every tick label,style=every y tick label]
-							{\show@yticklabel\axisticknum\y};
-					\else
-						\node at 
-							(\axis@xcoordminTEX\axis@leftover,\axis@tmpa)
-							[left,style=every tick label,style=every y tick label]
-							{\show@yticklabel\axisticknum\y};
-					\fi
-				\fi
-			\fi
-			\global\advance\axisticknum by1
-			\begin{scope}
-			\clip 			(\axis@xcoordminTEX\axis@leftover,	\axis@ycoordminTEX\axis@leftover) 
-				rectangle	(\axis@xcoordmaxTEX\axis@rightover,	\axis@ycoordmaxTEX\axis@rightover);
-			% Y-ticks left and/or right
-			% in log:
-			%  log( i*10^k ) = log\i + k\log10 -> draw ticks for i=1..9
-			\ifneedsminorloop
-				\foreach \i in {1,...,9} {
-					% this code here is scoped inside of \foreach.
-					\pgfextracty{\axis@tmpb}{\pgfpointxy{0}{\logi\i}}%
-					\advance\axis@tmpa by\axis@tmpb
-					\ifaxis@yminorgrids
-						\placecomputedgridline[style=every axis grid,style=every minor grid]%
-					\fi
-					\ifaxis@yminorticks
-						\axis@placecomputedtick\axis@subtickwidth[style=every tick,style=every minor tick]%
-					\fi
-				}%
-			\fi
-			\ifaxis@ymajorgrids
-				\placecomputedgridline[style=every axis grid,style=every major grid]%
-			\fi
-			\ifaxis@ymajorticks
-				\axis@placecomputedtick\axis@tickwidth[style=every tick,style=every major tick]%
-			\fi
-			\end{scope}
-		}%
-	\fi
-	\endgroup
-}
-
-% X-Achsen und Achsenbeschriftung 
-% 1: Ticks
-\newcommand{\axis@drawxaxis}[1]{%
-	\begingroup
-	\axisticknum=0
-	\newif\ifneedsminorloop
-	\edef\axis@TMP{#1}%
-	\ifx\axis@TMP\empty
-	\else
-		\ifaxis@xminorticks
-			\needsminorlooptrue
-		\fi
-		\ifaxis@xminorgrids
-			\needsminorlooptrue
-		\fi
-		\def\axis@placecomputedtick##1[##2]{%
-			\draw[##2]
-			\ifcase\axis@tickposnum
-				(\axis@tmpa,	\axis@ycoordminTEX\axis@leftover)
-			--	(\axis@tmpa,	\axis@ycoordminTEX+##1)
-			\or
-				(\axis@tmpa,	\axis@ycoordmaxTEX\axis@rightover)
-			--	(\axis@tmpa,	\axis@ycoordmaxTEX-##1)
-			\or
-				(\axis@tmpa,	\axis@ycoordminTEX\axis@leftover)
-			--	(\axis@tmpa,	\axis@ycoordminTEX+##1)
-
-				(\axis@tmpa,	\axis@ycoordmaxTEX\axis@rightover)
-			--	(\axis@tmpa,	\axis@ycoordmaxTEX-##1)
-			\fi
-			;
-		}%
-		\def\placecomputedgridline[##1]{%
-			\draw[##1]
-				(\axis@tmpa,	\axis@ycoordminTEX\axis@leftover)
-			--	(\axis@tmpa,	\axis@ycoordmaxTEX\axis@rightover)
-			;
-		}%
-		\foreach \x in {#1} {	
-			\pgfextractx{\axis@tmpa}{\pgfpointxy{\x}{0}}%
-			%
-			\ifdim\axis@tmpa<\axis@xcoordminTEX
-			\else
-				\ifdim\axis@tmpa>\axis@xcoordmaxTEX
-				\else
-					% Achsenbeschriftung:
-					\ifnum\axis@tickposnum=1
-						\node at 
-							(\axis@tmpa,\axis@ycoordmaxTEX\axis@leftover)
-							[above,style=every tick label,style=every x tick label]
-							{\show@xticklabel\axisticknum\x};
-					\else
-						\node at 
-							(\axis@tmpa,\axis@ycoordminTEX\axis@leftover)
-							[below,style=every tick label,style=every x tick label]
-							{\show@xticklabel\axisticknum\x};
-					\fi
-				\fi
-			\fi
-			\global\advance\axisticknum by1
-			%
-			\begin{scope}
-			\clip 			(\axis@xcoordminTEX\axis@leftover,	\axis@ycoordminTEX\axis@leftover) 
-				rectangle	(\axis@xcoordmaxTEX\axis@rightover,	\axis@ycoordmaxTEX\axis@rightover);
-			% X-Axis ticks bottom and top
-			% in log:
-			%  log( i*10^k ) = log\i + k\log10 -> draw ticks for i=1..9
-			\ifneedsminorloop
-				\foreach \i in {1,...,9} {
-					\pgfextractx{\axis@tmpb}{\pgfpointxy{\logi\i}{0}}%
-					\advance\axis@tmpa by\axis@tmpb
-					\ifaxis@xminorgrids
-						\placecomputedgridline[style=every axis grid,style=every minor grid]%
-					\fi
-					\ifaxis@xminorticks
-						\axis@placecomputedtick\axis@subtickwidth[style=every tick,style=every minor tick]%
-					\fi
-				}%
-			\fi
-			\ifaxis@xmajorgrids
-				\placecomputedgridline[style=every axis grid,style=every major grid]%
-			\fi
-			\ifaxis@xmajorticks
-				\axis@placecomputedtick\axis@tickwidth[style=every tick,style=every major tick]%
-			\fi
-			\end{scope}
-		}%
-	\fi
-	\endgroup
-}
-
-\def\axis@rememberplotspec#1{{%
-	\globaldefs=1
-	\listpushback#1\to\axis@plotspeclist
-	\advance\axis@numplots by1%
-}}
-
-\def\axis@getautoplotspec into#1{%
-	\listsize\autoplotspeclist\to\c@pgf@counta
-	\ifnum\c@pgf@counta=0
-		\let#1=\empty
-	\else
-		\c@pgf@countb=\axis@numplots
-		\loop
-		\ifnum\c@pgf@countb<\c@pgf@counta
-		\else
-			\advance\c@pgf@countb by-\c@pgf@counta
-		\repeat
-		\listselect\c@pgf@countb\of\autoplotspeclist\to#1
-%\message{pgfplots.sty: using \string\autoplotspeclist\ specification no\#\the\c@pgf@countb (of \the\c@pgf@counta): #1}%
-	\fi
-}
-
-% The main interface to draw a plot into an axis.
-%
-% Usage:
-% \addplot 
-% 	plot coordinates {
-% 		(0,0)
-% 		(1,1)
-% 	};
-% 
-% or
-%
-% \addplot[color=blue,mark=*]
-% 	plot coordinates {
-% 		(0,0)
-% 		(1,1)
-% 	};
-% 
-% The first syntax will use the next plot specification in the list
-% \autoplotspeclist
-% and the first will use blue color and * markers. 
-%
-% The linespec. will be used in the legend.
-\long\def\addplot{%
-	\@ifnextchar+{%
-		\axis@getautoplotspec into\nextplotspec
-		\axis@addplotimplAPPEND
-	}{%
-		\@ifnextchar[{%
-			\axis@addplotimpl%
-		}{%
-			\axis@getautoplotspec into\nextplotspec
-			% the space after ']' is required here:
-			% FIXME: 
-			% - \addplot[]plot coordinates is NOT allowed!?
-			\expandafter\axis@addplotimpl\expandafter[\nextplotspec]
-		}%
-	}%
-}
-
-\long\def\axis@addplotimplAPPEND+[{%
-	\expandafter\axis@addplotimpl\expandafter[\nextplotspec,
-}
-
-\long\def\axis@addplotimpl[#1] #2;{%
-%\tracingmacros=2\tracingcommands=2
-	% #2 = plot coordinates {...}
-	\ifx\csname axis@execute at begin plot\endcsname\empty
-	\else
-		\csname axis@execute at begin plot\endcsname
-	\fi
-	\axis@rememberplotspec{[#1]}%
-	\ifaxis@filtercoords
-		% FIXME : FREE THIS VARIABLE:
-		\axis@filtercoords@and@up@limits#2;\newplotcmdto\axis@filteredcoordinateplotcmd
-		\def\axis@TMP{\axispath@impl{\draw[style=every axis plot,#1]}}%
-		\expandafter\axis@TMP\axis@filteredcoordinateplotcmd%
-	\else
-		\ifaxis@draw@at@end
-			\axis@update@limits{#2;}%
-		\fi
-		\axispath@impl{\draw[style=every axis plot,#1]}#2;%
-	\fi
-	\ifx\csname axis@execute at end plot\endcsname\empty
-	\else
-		\csname axis@execute at end plot\endcsname
-	\fi
-%\tracingmacros=0\tracingcommands=0
-}%
-
-\long\def\axis@update@limits#1{%
-	\axis@foreach@plot@coord@do%
-		\axis@update@limits@for@one@point
-	\for
-	#1%
-	\EOI
-}
-
-% PRECONDITIONS:
-%   - 'floating point numerics active' 
-%   		=> coordinate filtering is active
-%   		=> #1 and #2 are MACRO names
-%   		=> these macros are encoded with \scisetcomponents
-%   - no coordinate filters active 
-%   		=> #1 and #2 MAY be macros, but they must be valid TeX
-%   		length (without unit).
-\long\def\axis@update@limits@for@one@point#1#2{%
-%\tracingmacros=2\tracingcommands=2
-%\message{Updating limits for (#1,#2) ...}%
-	\ifaxis@autocompute@xlim
-		\ifaxis@float@numerics@mode@x
-%\scitofixedsingle\axis@xmin\axis@TMP
-%\scitofixedsingle\axis@xmax\axis@TMPB
-%\message{current limits: xmin=\axis@TMP, xmax=\axis@TMPB}%
-			\scigetcomponents#1\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\scigetcomponents\axis@xmin\axis@lim@S\axis@lim@M\axis@lim@E
-			\scimathmin%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\and%
-				\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\to%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\scisetcomponents\axis@xmin\axis@lim@S\axis@lim@M\axis@lim@E
-			%
-			\scigetcomponents\axis@xmax\axis@lim@S\axis@lim@M\axis@lim@E
-			\scimathmax%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\and%
-				\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\to%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\scisetcomponents\axis@xmax\axis@lim@S\axis@lim@M\axis@lim@E
-%\scitofixedsingle\axis@xmin\axis@TMP
-%\scitofixedsingle\axis@xmax\axis@TMPB
-%\message{updated limits: xmin=\axis@TMP, xmax=\axis@TMPB}%
-		\else
-			\pgfmathmin{\axis@xmin}{#1}%
-			\let\axis@xmin=\pgfmathresult
-			\pgfmathmax{\axis@xmax}{#1}%
-			\let\axis@xmax=\pgfmathresult
-		\fi
-	\fi
-	\ifaxis@autocompute@ylim
-		\ifaxis@float@numerics@mode@y
-%\scitofixedsingle\axis@ymin\axis@TMP
-%\scitofixedsingle\axis@ymax\axis@TMPB
-%\message{current limits: ymin=\axis@TMP, ymax=\axis@TMPB}%
-			\scigetcomponents#2\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\scigetcomponents\axis@ymin\axis@lim@S\axis@lim@M\axis@lim@E
-			\scimathmin%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\and%
-				\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\to%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\scisetcomponents\axis@ymin\axis@lim@S\axis@lim@M\axis@lim@E
-			%
-			\scigetcomponents\axis@ymax\axis@lim@S\axis@lim@M\axis@lim@E
-			\scimathmax%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\and%
-				\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\to%
-				\axis@lim@S\axis@lim@M\axis@lim@E
-			\scisetcomponents\axis@ymax\axis@lim@S\axis@lim@M\axis@lim@E
-%\scitofixedsingle\axis@ymin\axis@TMP
-%\scitofixedsingle\axis@ymax\axis@TMPB
-%\message{updated limits: ymin=\axis@TMP, ymax=\axis@TMPB}%
-		\else
-			\pgfmathmin{\axis@ymin}{#2}%
-			\let\axis@ymin=\pgfmathresult
-			\pgfmathmax{\axis@ymax}{#2}%
-			\let\axis@ymax=\pgfmathresult
-		\fi
-	\fi
-	\axis@limits@are@computedtrue
-%\tracingmacros=0\tracingcommands=0
-}
-
-% Filters coordinates and writes a new, modified 'plot coordinates'
-% command to macro #2.
-\long\def\axis@filtercoords@and@up@limits#1\newplotcmdto#2{%
-	\let#2=\empty
-	\let\axis@filter@output=#2
-	\axis@foreach@plot@coord@do%
-		\axis@filter@one@coord@pair
-	\for
-	#1%
-	\EOI
-	\edef#2{plot coordinates {\axis@filter@output};}%
-}%
-
-\def\axis@filter@one@coord@pair#1#2{%
-	\ifx\axis@xfilter\empty
-		\def\axis@filter@tmp@x{#1}%
-	\else
-		\let\axis@filter@tmp@x=\empty
-		\axis@xfilter#1\to\axis@filter@tmp@x
-	\fi
-	\ifx\axis@yfilter\empty
-		\def\axis@filter@tmp@y{#2}%
-	\else
-		\let\axis@filter@tmp@y=\empty
-		\axis@yfilter#2\to\axis@filter@tmp@y
-	\fi
-	\ifx\axis@filter@tmp@x\empty
-		\message{NOTE: coordinate (#1,#2) has been dropped because of the x-coordinate filter.}%
-	\else
-		\ifx\axis@filter@tmp@y\empty
-			\message{NOTE: coordinate (#1,#2) has been dropped because of the y-coordinate filter.}%
-		\else
-			\ifaxis@draw@at@end
-				% update also axis limits:
-				\axis@update@limits@for@one@point{\axis@filter@tmp@x}{\axis@filter@tmp@y}%
-			\else
-				% apply data transformation directly.
-				\ifaxis@float@numerics@mode@x
-					\axis@datascaletrafo@x\axis@filter@tmp@x\to\axis@filter@tmp@x
-				\fi
-				\ifaxis@float@numerics@mode@y
-					\axis@datascaletrafo@y\axis@filter@tmp@y\to\axis@filter@tmp@y
-				\fi
-			\fi
-			% remind:
-			%  \the\tokenregister
-			% will yield the contents of the token register, it will
-			% NOT expand recursively (like \expandafter)!
-			%
-			% Employ that here to maintain macros inside of
-			%   \axis@filter@tmp[xy]
-			% (macros inside of those things are used by the floating
-			% point numerics to scale input data to TeX-lengths)
-			\pgfplots@toka=\expandafter{\axis@filter@output}%
-			\TOKL@ta=\expandafter{\axis@filter@tmp@x}%
-			\TOKL@tb=\expandafter{\axis@filter@tmp@y}%
-			\edef\axis@filter@output{\the\pgfplots@toka (\the\TOKL@ta,\the\TOKL@tb)}%
-%\message{FILTERING: appended \axis@filter@tmp@x,\axis@filter@tmp@y}%  -> results in \axis@filter@output}%
-		\fi
-	\fi
-}
-
-
-% A looping command to loop through plot coordinates.
-% For every point, #3{X}{Y} will be invoked.
-%
-% No scoping is used during this operation, so you can access outer
-% variables.
-\long\def\axis@foreach@plot@coord@do#1\for plot coordinates #2;\EOI{%
-	\axis@foreach@plot@coord@ITERATE#1\n#2\EOI%
-}
-
-\def\axis@foreach@plot@coord@ITERATE#1\n{%
-	\@ifnextchar;{%
-		\axis@foreach@plot@coord@FINISH@SEMICOLON%
-	}{%
-		\@ifnextchar\EOI{%
-			\axis@foreach@plot@coord@FINISH%
-		}{%
-			\axis@foreach@plot@coord@NEXT#1\n%
-		}%
-	}%
-}
-
-\def\axis@foreach@plot@coord@NEXT#1\n(#2,#3){%
-	#1{#2}{#3}%
-	\axis@foreach@plot@coord@ITERATE#1\n
-}
-
-\def\axis@foreach@plot@coord@FINISH\EOI{}
-\def\axis@foreach@plot@coord@FINISH@SEMICOLON;\EOI{}
-
-% INPUT: 
-%   a sequence of points (SMeE,SMeE) (terminated with ';') 
-%   where S=sign, M=mantisse, E = exponent.
-%   Such input is generated in the case axis@float@numerics@modetrue
-%   by the coordinate filters.
-% OUTPUT: 
-%   proper sequence of fixed point coordinates which are the result of the
-%   data scaling transformation (\axis@datascaletrafo@x).
-%
-% The output will be written into the macro #1.
-\long\def\axis@apply@data@scaletrafo@to@plot@data#1\to#2{%
-	\let#2=\empty
-	\let\axis@data@scaletrafo@result=\empty
-	\axis@foreach@plot@coord@do
-		\axis@apply@data@scaletrafo@to@one@point
-	\for
-	#1%
-	\EOI
-	\edef#2{plot coordinates {\axis@data@scaletrafo@result};}%
-	%\axis@apply@data@scaletrafo@to@plot@data@ITERATE\to#2 #1;%
-}
-	
-\def\axis@apply@data@scaletrafo@to@one@point#1#2{%
-	\ifaxis@float@numerics@mode@x
-		\axis@decode@filtered@float@numerics#1\to\axis@filter@tmp@x
-		\axis@datascaletrafo@x\axis@filter@tmp@x\to\axis@filter@tmp@x
-	\else
-		\def\axis@filter@tmp@x{#1}%
-	\fi
-	\ifaxis@float@numerics@mode@y
-		\axis@decode@filtered@float@numerics#2\to\axis@filter@tmp@y
-		\axis@datascaletrafo@y\axis@filter@tmp@y\to\axis@filter@tmp@y
-	\else
-		\def\axis@filter@tmp@y{#2}%
-	\fi
-	\edef\axis@data@scaletrafo@result{\axis@data@scaletrafo@result (\axis@filter@tmp@x,\axis@filter@tmp@y)}%
-}
-
-
-\def\axis@decode@filtered@float@numerics#1#2e#3\to#4{%
-	\scisetcomponents#4{#1}{#2}{#3}%
-}
-
-
-\long\def\axispath#1;{%
-	\axispath@impl{}#1;
-}
-
-% low-level \axispath implementation.
-% #1:
-%    the command which is responsable for drawing.
-%    - If #1 is NOT '\empty', we expect #2 to contain only
-%      EXPANDABLE DATA.
-%      That's important for postponed floating point arithmetics in #2.
-%    - If #1='\empty', we don't make any assumption about #2
-%      and process it as-is.
-%
-% #2: see above.
-\long\def\axispath@impl#1#2;{%
-	\ifaxis@draw@at@end
-		\listpushback{#1}\to\axis@stored@plot@cmds
-		\listpushback{#2;}\to\axis@stored@plot@data
-	\else
-		#1#2;%
-	\fi
-}
-
-
-% Assigns a legend.
-% Syntax:
-% \legend{entry 1\\entry2\\entry3}
-\newcommand{\legend}[2][]{
-	{%
-		\globaldefs=1% this will ONLY store the options and the legend into global variables
-		\def\axis@TMP{#1}%
-		\ifx\axis@TMP\empty
-		\else
-			\errmessage{Sorry, legend are now deprecated. Legends are now TikZ-matrizes which provide better alignment and can be placed horizontally. See the manual for details.}%
-		\fi
-		\def\axis@TMP{#2}%
-		\ifx\axis@TMP\empty
-		\else
-			\listnew\axis@legend{#2}%
-		\fi
-	}
-}
-
-\newcommand{\addlegendentry}[1]{%
-	{%
-	\globaldefs=1% this will ONLY store the options and the legend into global variables
-	\listpushback#1\to\axis@legend
-	}%
-}
-
-\def\axis@pop@next@legend{{%
-	\globaldefs=1
-	\listcheckempty\axis@plotspeclist
-	\iflistempty
-		\let\axis@curplotlist=\empty
-	\else
-		\listpopfront\axis@plotspeclist\to\axis@curplotlist
-	\fi
-	%
-	\listcheckempty\axis@legend
-	\iflistempty
-		\let\axis@curlegend=\empty
-	\else
-		\listpopfront\axis@legend\to\axis@curlegend
-	\fi
-	\advance\axis@numplots by-1
-}}
+\RequirePackage{tikz}
 
-\long\def\axis@show@small@legendplots#1{
-	\draw#1
-			[mark repeat=2,mark phase=2] 
-			plot coordinates {
-				(0cm,0cm) 
-				(0.3cm,0cm)
-				(0.6cm,0cm)%
-			};%
-}
 
-% Typesets a legend node.
-%
-% It will either typeset a previously computed legend (which needs to be
-% stored in the macro \axis@already@computed@legend@node)
-%
-% or it creates a legend, stores the commands into the macro named
-% above and typesets it.
-\newcommand\axis@createlegend{%
-	\ifx\axis@already@computed@legend@node\empty
-		\listcheckempty\axis@legend
-		\iflistempty
-		\else
-		%
-		% 
-		\begingroup
-			% assemble a 
-			% \matrix {
-			% 	small plot  & legend1\\
-			% 	small plot  & legend2\\
-			% 	...
-			% };
-			% command [and using the 'legend columns' option]
-			%
-			% \TOKL@ta={
-			% 	small plot  & legend1\\
-			% 	small plot  & legend2\\
-			% 	...
-			% }
-			% ( I have allocated the token register in my simplelist.sty)
-			% 
-			% \global\def\axis@TMP{
-			% 	\matrix {
-			% 		\TOKL@TA
-			% 	};
-			% }
-			% -> finally, \axis@TMP will contain the complete command.
-			\TOKL@ta={}%
-			\let\curcolumnNum=\c@pgf@counta
-			\let\maxcolumnCount=\c@pgf@countb
-			\let\legendplotpos=\c@pgf@countc
-			\legendplotpos\expandafter=\axis@legend@plot@pos
-			\curcolumnNum=0
-			\maxcolumnCount\expandafter=\csname axis@legend columns\endcsname\relax
-			%
-			\loop
-			\ifnum0<\axis@numplots\relax
-				\axis@pop@next@legend
-				\ifx\axis@curlegend\empty
-				\else
-					\advance\curcolumnNum by1
-					\edef\axis@TMP{%
-						\the\TOKL@ta
-						\ifcase\legendplotpos
-							% legend plot pos=left 
-							\noexpand\axis@show@small@legendplots{\axis@curplotlist}%
-							\noexpand\pgfmatrixnextcell
-							\noexpand\node {\axis@curlegend};
-						\or
-							% legend plot pos=right
-							\noexpand\node {\axis@curlegend};
-							\noexpand\pgfmatrixnextcell
-							\noexpand\axis@show@small@legendplots{\axis@curplotlist}%
-						\or
-							% legend plot pos=none
-							\noexpand\node {\axis@curlegend};
-						\fi
-						\ifnum\curcolumnNum=\maxcolumnCount
-							\noexpand\\
-						\else
-							\ifnum\axis@numplots=0
-								\noexpand\\
-							\else
-								\noexpand\pgfmatrixnextcell
-							\fi
-						\fi
-					}%
-					\ifnum\curcolumnNum=\maxcolumnCount
-						\curcolumnNum=0
-					\fi
-					\expandafter\TOKL@ta\expandafter{\axis@TMP}%
-				\fi
-			\repeat
-			\TOKL@tb={\matrix[style=every axis legend]}%
-			\xdef\axis@TMP{%
-				\the\TOKL@tb {%
-					\the\TOKL@ta
-				};%
-			}%
-		\endgroup
-		\let\axis@already@computed@legend@node=\axis@TMP
-		\fi
-	\fi
-	\axis@already@computed@legend@node
-}
-
-% Checks whether the argument to xtick or ytick is a UNIFORM tick
-% sequence.
-%
-% A uniform tick sequence is 0,...,10 and 3,4,5 and -5,-4,-2 but 
-% NOT 0,2,4 or 4,10.
-%
-% Furthermore, any NON-integer tick arguments are also assumed to be
-% NOT uniform.
-%
-% INPUT:
-% #1: a tick argument (i.e. something which can be put to 
-%     \foreach \x in {#1})
-%
-% OUTPUT:
-%    \axis@isuniformticktrue
-%    or
-%    \axis@isuniformtickfalse
-% depending on the check.
-% This variable will be set globally.
-\def\axis@checkisuniformLOGtick#1{%
-	\begingroup
-	\global\axis@isuniformticktrue
-	\newif\ifisfirst
-	\newif\iftwo@are@equal
-	\isfirsttrue
-	\foreach \x in {#1}{%
-		\pgfmathmultiply@\x\reciproc@logten
-		\let\cur=\pgfmathresult
-		% check whether
-		%  \cur - last == 1 (last = \axis@TMPB)
-		\ifisfirst
-			\global\isfirstfalse
-		\else
-			\pgfmathsubtract@\cur\axis@TMPB%
-			\pgfmathlog@approxequalto@macro\pgfmathresult{1.0}{two@are@equal}%
-			\iftwo@are@equal
-			\else
-				\global\axis@isuniformtickfalse
-				\breakforeach
-			\fi
-		\fi
-		\global\let\axis@TMPB=\cur
-	}%
-	\endgroup
-}
-
-\def\skipsuffixzero#1.#2|{
-	{%
-	\def\axis@TMP{#2}%
-	\def\axis@TMPB{0}%
-	\ifx\axis@TMP\axis@TMPB
-		\global\def\pgfmathresult{#1}%
-	\else
-		\global\def\pgfmathresult{#1.#2}%
-	\fi
-	}%
-}
-
-\def\logtologtentomacro#1#2{%
-	\pgfmathmultiply@{#1}\reciproc@logten%
-	\expandafter\skipsuffixzero\pgfmathresult|%
-	\let#2=\pgfmathresult
-}
-
-% Expands to #1/log(10). It will also skip a suffix '.0'
-\def\logtologten#1{%
-	\pgfmathmultiply@{#1}\reciproc@logten%
-	\expandafter\skipsuffixzero\pgfmathresult|%
-	\pgfmathresult
-}
-
-% helper method which computes log10*\x foreach \x in {#1}.
-% The result will be \xdef'ed into #2.
-\def\axis@compute@tick@times@logten#1\to#2{%
-	\global\let#2=\empty
-	\foreach \axis@TMPB in {#1} {%
-		\pgfmathmultiply@\axis@TMPB\logten%
-		\ifx#2\empty
-			\xdef#2{\pgfmathresult}%
-		\else
-			\xdef#2{#2,\pgfmathresult}%
-		\fi
-	}%
-}
-
-\def\axis@init@enlarge@limit@booleans{%
-	\axis@enlargelimits@autofalse
-	\axis@enlargelimitsfalse
-	\axis@enlargelimits@rel@threshfalse
-	\edef\axis@TMP{\axis@enlargelimits}%
-	%
-	\def\axis@TMPB{true}%
-	\ifx\axis@TMP\axis@TMPB
-		\axis@enlargelimitstrue
-	\else
-		\def\axis@TMPB{false}%
-		\ifx\axis@TMP\axis@TMPB
-		\else
-			\def\axis@TMPB{auto}%
-			\ifx\axis@TMP\axis@TMPB
-				\axis@enlargelimits@autotrue
-			\else
-				\begingroup
-				% try to read it as number:
-				\expandafter\pgf@xa\axis@enlargelimits pt\relax
-				\endgroup
-				\axis@enlargelimitstrue
-				\axis@enlargelimits@rel@threshtrue
-			\fi
-		\fi
-	\fi
-}
-
-\def\axis@enlarge@limit@for#1{%
-	\begingroup
-	\expandafter\let\expandafter\min\expandafter=\csname axis@#1min\endcsname
-	\expandafter\let\expandafter\max\expandafter=\csname axis@#1max\endcsname
-	\ifcase\csname axis@#1mode\endcsname
-		\ifaxis@enlargelimits@rel@thresh
-			\edef\enlargepercent{\axis@enlargelimits}%
-		\else
-			\def\enlargepercent{0.1}% FIXME : pack 10% as default into option 'enlargelimits' or so
-		\fi
-		\pgfmathsubtract@\max\min%
-		\expandafter\pgf@xa\pgfmathresult pt
-		\expandafter\pgf@xb\enlargepercent\pgf@xa
-		\ifdim\pgf@xb>0.001pt
-			% the case with 
-			%   enlargeabsolute ~= 0
-			% means that \min ~= \max.
-			% It is handled in another method.
-			\edef\enlargeabsolute{\pgf@sys@tonumber{\pgf@xb}}%
-			%
-			% compute xmin := xmin - enlargeabsolute
-			\pgfmathsubtract@\min\enlargeabsolute%
-			\let\min=\pgfmathresult
-			\pgfmathadd@\max\enlargeabsolute%
-			\let\max=\pgfmathresult
-		\fi
-	\or
-		% compute
-		%   \pgfmathsetmacro{\min}{\min - 0.5*\logten}%
-		%   \pgfmathsetmacro{\max}{\max + 0.5*\logten}%
-		% just a more efficiently (I hope so):
-		\expandafter\pgfmath@x\logten pt
-		\divide\pgfmath@x by2
-		\pgfmathlog@invoke@expanded\pgfmathsubtract@{{\min}{\pgf@sys@tonumber{\pgfmath@x}}}%
-		\let\min=\pgfmathresult
-		\pgfmathlog@invoke@expanded\pgfmathadd@{{\max}{\pgf@sys@tonumber{\pgfmath@x}}}%
-		\let\max=\pgfmathresult
-	\fi
-	\xdef\axis@TMP{\min}%
-	\xdef\axis@TMPB{\max}%
-	\endgroup
-	\expandafter\let\csname axis@#1min\endcsname=\axis@TMP
-	\expandafter\let\csname axis@#1max\endcsname=\axis@TMPB
-}
-
-% Computes tick positions using the current axis limits.
-%
-% Parameters:
-% \axisdefaulttickwidth
-%    Determines the maximum space which is not filled by at least one
-%    tick label (approximate, there is some rounding internally)
-% \axisdefaulttryminticks
-%    see manual
-%
-% Idea:
-% We want ticks at each 
-%    { i*H, i in \Z }.
-% Of course, there shouldn't be TOO MUCH ticks. 
-%
-% Our heuristics is to set
-%    desirednumticks = round(ACTUAL WIDTH / axisdefaulttickwidth)
-% and generate H = (axis range) / desirednumticks.
-%
-% Since not all step sizes H look well, restrict H to a set of allowed 
-% step sizes such as 
-%   { 1, 1/2, 1/5, 1/10 },
-% or, to be more precise:
-%   { 1*10^e, 2*10^e, 5*10^e }
-% -> round to the nearest matching number!
-%
-% Then, the resulting tick is
-% TICK={MIN,MIN+H,...,MAX}
-% where
-%    MIN = I*H
-% is chosen such that 
-%    axis minimum limit = I*H + rest; |rest| < H.
-%
-%
-% PRECONDITION:
-% - limits are correct
-% - axis width/height is set correctly
-%
-% POSTCONDITION:
-% - Tick for axis #1 is assigned
-% - \ifaxis@needs@check@uniformtick is set
-\def\axis@assign@default@tick@foraxis#1{%
-	\begingroup
-	% Shortcut-names:
-	\expandafter\let\expandafter\ifaxis@is@datascaled\csname ifaxis@float@numerics@mode@#1\endcsname
-	\expandafter\let\expandafter\axis@data@scale@trafo\csname axis@datascaletrafo@#1\endcsname
-	\expandafter\let\expandafter\axis@data@scale@inverse@trafo\csname axis@inverse@datascaletrafo@#1\endcsname
-	%
-	\let\desirednumticks=\c@pgf@countd
-	\let\Wr=\pgf@xc
-	\Wr=\csname axis@#1coordmaxTEX\endcsname
-	\advance\Wr by-\csname axis@#1coordminTEX\endcsname
-	% r = max place without ticks in pt -> choose desirednumticks >= W/r
-	\expandafter\expandafter\divide\Wr\axisdefaulttickwidth
-	\pgfmathsetcount{\desirednumticks}{\Wr}%
-	\advance\desirednumticks by1
-	\expandafter\ifnum\axisdefaulttryminticks>\desirednumticks
-		\expandafter\desirednumticks\axisdefaulttryminticks
-	\fi
-	\ifcase\csname axis@#1mode\endcsname
-		% compute tick := MIN,MIN+H,....,MAX
-		\let\MINH=\pgf@xa
-		\let\H=\pgf@xb
-		\let\MAX=\axis@tmpa
-		\let\MIN=\axis@tmpb
-			% compute step size 'H':
-			\expandafter\MAX\csname axis@#1max\endcsname pt
-			\advance\MAX by0.001pt% avoid round errors
-			%\expandafter\MIN\the\c@pgf@counta pt
-			\expandafter\MIN\csname axis@#1min\endcsname pt
-			\H=\MAX
-			\advance\H by-\MIN
-			\c@pgf@counta=\desirednumticks
-			\advance\c@pgf@counta by-1
-			\divide\H by\c@pgf@counta
-%\message{determining ticks for #1-axis: Wr := (width/max space between ticks) = \the\Wr, desirednumticks=max(\axisdefaulttryminticks, trunc(Wr)) = \the\desirednumticks, H=(axis range/(desirednumticks-1)) = \the\H}%
-			%
-			% SEARCH for the NEXT FEASABLE H.
-			% 
-			\edef\Hmacro{\pgf@sys@tonumber\H}%
-			\ifaxis@is@datascaled
-				\expandafter\axis@data@scale@inverse@trafo\Hmacro\to\Hmacro
-			\else
-				\expandafter\sciparsesignsingle\expandafter{\Hmacro}\Hmacro
-			\fi
-			\scigetcomponents\Hmacro\H@S\H@M\H@E
-%\message{Got T^{-1}(H) = [\H@S] \H@M * 10^\H@E}%
-			% modify the mantisse:
-			\expandafter\H\H@M pt
-			\ifdim\H<2pt
-				\ifdim\H<1.5pt
-					\def\H@M{1.0}%
-				\else
-					\def\H@M{2.0}%
-				\fi
-			\else
-				\ifdim\H<4.9999pt
-					\ifdim\H<3.5pt
-						\def\H@M{2.0}%
-					\else
-						\def\H@M{5.0}%
-					\fi
-				\else
-					\ifdim\H<7.5pt
-						\def\H@M{5.0}%
-					\else
-						\def\H@M{1.0}%
-						\expandafter\c@pgf@counta\H@E
-						\advance\c@pgf@counta by1
-						\edef\H@E{\the\c@pgf@counta}%
-					\fi
-				\fi
-			\fi
-			\scisetcomponents\Hmacro\H@S\H@M\H@E
-			\ifaxis@is@datascaled
-				\axis@data@scale@trafo\Hmacro\to\Hmacro
-			\else
-				\scitofixedsingle\Hmacro\Hmacro
-			\fi
-%\message{I have computed H=\Hmacro}%
-			\expandafter\H\Hmacro pt
-%\message{final H=\the\H}%
-			%
-			% Now, we want to activate the Tick set {i*H, i in \Z}
-			% compute I such that
-			%   xmin = I * H + rest;  |rest| < H
-			% -> I = round(xmin/H)
-			% -> MIN = I * H
-			\pgfmathlog@invoke@expanded\pgfmathdivide@{%
-				{\pgf@sys@tonumber\MIN}%
-				{\pgf@sys@tonumber\H}%
-			}%
-			\pgfmathsetcount{\c@pgf@counta}{\pgfmathresult}%
-			\ifdim\MIN<0pt
-				% the truncation rounds TOWARDS 0 which is not what I want.
-				\advance\c@pgf@counta by-1
-			\fi
-			\MIN=\H
-			\multiply\MIN by\c@pgf@counta
-			\MINH=\MIN
-			\advance\MINH by\H
-		\xdef\axis@TMP{\pgf@sys@tonumber{\MIN},\pgf@sys@tonumber{\MINH},...,\pgf@sys@tonumber{\MAX}}%
-		\aftergroup\axis@needs@check@uniformtickfalse
-	\or
-		\expandafter\ifx\csname axis@#1tickten\endcsname\empty
-			% I want ticks at 10^k. So determine k_min and k_max.
-			%
-			% FIXME: optimize!
-			\pgfmathsetcount{\c@pgf@counta}{\csname axis@#1min\endcsname*\reciproc@logten-1}%
-			\pgfmathsetmacro{\tmp@min}{\c@pgf@counta*\logten}%
-			\pgfmathsetcount{\c@pgf@counta}{\csname axis@#1max\endcsname*\reciproc@logten}%
-			\pgfmathsetmacro{\tmp@max}{\c@pgf@counta*\logten}%
-			\pgfmathadd\tmp@min\logten%
-			\xdef\axis@TMP{\tmp@min,\pgfmathresult,...,\tmp@max}%
-			\aftergroup\axis@needs@check@uniformtickfalse
-		\else
-			\edef\axis@TMP{\csname axis@#1tickten\endcsname}%
-			\expandafter\axis@compute@tick@times@logten\axis@TMP\to\axis@TMP
-			\aftergroup\axis@needs@check@uniformticktrue
-		\fi
-	\fi
-	\endgroup
-	\expandafter\let\csname axis@#1tick\endcsname=\axis@TMP
-%\message{pgfplots.sty: #1tick set to \csname axis@#1tick\endcsname [#1mode=\the\csname axis@#1mode\endcsname,  #1min=\csname axis@#1min\endcsname, #1max=\csname axis@#1max\endcsname].}%
-}
-
-% Helper method for 
-%  \axis@apply@data@scale@trafo@to@options@for
-% #1: the ticks
-% #2: the trafo macro name (the form taking three args)
-% #3: the output macro name
-\long\def\axis@apply@data@scale@trafo@to@user@ticks#1#2\to#3{%
-	\let#3=\empty
-	\foreach \axis@TMPB in {#1} {%
-		\expandafter\sciparsesign\expandafter{\axis@TMPB}\sci@S\sci@M\sci@E
-		#2\sci@S\sci@M\sci@E\to\axis@TMPB
-		\ifx#3\empty
-			\xdef#3{\axis@TMPB}%
-		\else
-			\xdef#3{#3,\axis@TMPB}%
-		\fi
-	}%
-	%
-}%
-
-% helper for \axis@apply@data@scale@trafo@to@options@for.
-\def\axis@compute@number@order@for@trafo@isdimen#1\tocount#2{%
-	\edef\axis@TMP{\pgf@sys@tonumber{#1}}%
-	\expandafter\sciparsesign\expandafter{\axis@TMP}\S\M\E
-	\expandafter#2\E\relax
-	\advance#2 by1
-}
-
-% helper for \axis@apply@data@scale@trafo@to@options@for.
-% 
-\def\axis@compute@number@order@for@trafo@isfloat#1\tocount#2{%
-	\scigetcomponents#1\S\M\E
-	\expandafter#2\E\relax
-	\advance#2 by1
-}
-
-% Initialises the data scale transformation and applies it to any
-% user specified options.
-%
-% PRECONDITION:
-%   - all axis limits are available in float representation
-%     (i.e. with \scisetcomponents)
-%   - \axis@set@default@size@options has been called before
-% POSTCONDITION:
-%   - the scaling transformation is set up,
-%   - all axis limits are transformed,
-%   - any user input (like ticks and tick labels)
-%     will reflect the changes.
-\def\axis@apply@data@scale@trafo@to@options@for#1{%
-	% initialise data scale transformation 
-	%   T(x) = 10^{q-m} * x
-	%
-	\begingroup
-	\let\data@max@order=\c@pgf@counta
-	\let\data@cur@order=\c@pgf@countb
-	\let\data@dimen=\pgf@xa
-	\let\data@dimen@order=\c@pgf@countc
-	%
-	% Step 1: compute 'm', the data order
-	\expandafter\axis@compute@number@order@for@trafo@isfloat
-		\csname axis@#1min\endcsname
-		\tocount\data@cur@order
-	%
-	\data@max@order=\data@cur@order
-	%
-	\expandafter\axis@compute@number@order@for@trafo@isfloat
-		\csname axis@#1max\endcsname
-		\tocount\data@cur@order
-	%
-	\ifnum\data@cur@order>\data@max@order
-		\data@max@order=\data@cur@order
-	\fi
-	%
-	% Step 2: compute 'q', the #1-size of the axis.
-	\expandafter\ifx\csname axis@#1\endcsname\empty
-		% We have 'width' or 'height'.
-		%
-		% Use the order of these parameters.
-		\def\axis@TMP{#1}%
-		\def\axis@TMPB{x}%
-		\ifx\axis@TMP\axis@TMPB
-			\expandafter\data@dimen\axis@width\relax
-		\else
-			\def\axis@TMPB{y}%
-			\ifx\axis@TMP\axis@TMPB
-				\expandafter\data@dimen\axis@height\relax
-			\fi
-		\fi
-		\axis@compute@number@order@for@trafo@isdimen
-			\data@dimen
-			\tocount\data@dimen@order
-		% This here is to avoid inaccuracies in the final
-		% axis rectangle size, see \axis@initsizes:
-		\advance\data@dimen@order by-1
-	\else
-		% FIXME:
-		% we have either the 'x=1cm' or 'y=1cm' option!
-		% How should I initialise the trafo!?
-		\data@dimen@order=3
-	\fi
-	%
-%\message{Direction #1: data max order=\the\data@max@order;  data dimen order=\the\data@dimen@order. }%
-	\advance\data@dimen@order by-\data@max@order
-	\xdef\axis@TMP{\the\data@dimen@order}%
-	\endgroup
-%\message{Initialising the data scale transformation in direction #1 to \axis@TMP...}%
-	% COMPLETE INITIALISATION:
-	\ifaxis@EMERGENCY@FORCE@DATA@TRAFO@TO@IDENTITY
-		\message{WARNING: the automatic scaling of input data has been DISABLED to allow axispath commands [otherwise, axispath commands would not know of the pgfplots scalings - leading to wrong images). DISABLING THE DATA SCALING LIMITS THE DATA RANGE! I hope I can fix this issue as soon as possible. Please take a look at the manual for more information. If you get 'OVERFLOW' or 'UNDERFLOW' errors, you may need to disable the axispath.}%
-		\def\axis@TMP{0}%
-		\expandafter\let\csname axis@data@scale@trafo@SHIFT@#1\endcsname\axis@TMP
-	\else
-		\expandafter\let\csname axis@data@scale@trafo@SHIFT@#1\endcsname\axis@TMP
-	\fi
-	%
-	% ... and apply transformation to any user input
-	%
-	% Transform axis limits:
-	\expandafter\expandafter\csname axis@datascaletrafo@#1\endcsname\csname axis@#1min\endcsname\to\axis@TMP
-	\expandafter\let\csname axis@#1min\endcsname=\axis@TMP
-	%
-	\expandafter\expandafter\csname axis@datascaletrafo@#1\endcsname\csname axis@#1max\endcsname\to\axis@TMP
-	\expandafter\let\csname axis@#1max\endcsname=\axis@TMP
-	%
-	% Convert any user-specified ticks:
-	\edef\axis@TMP{\csname axis@#1tick\endcsname}%
-	% this here should also work with 'xtick=\empty', the "No tick" command.
-	\ifx\axis@TMP\empty
-	\else
-%\message{Converting #1tick='\csname axis@#1tick\endcsname'}%
-		\pgfplots@toka=\expandafter{\csname axis@datascaletrafo@#1@three\endcsname}%
-		\edef\axis@TMP{{\csname axis@#1tick\endcsname}\the\pgfplots@toka}%
-		\expandafter\axis@apply@data@scale@trafo@to@user@ticks\axis@TMP\to\axis@TMPC
-		\expandafter\let\csname axis@#1tick\endcsname=\axis@TMPC
-	\fi
-	%
-	% Transform any explicit axis unit scalings:
-	\expandafter\ifx\csname axis@#1\endcsname\empty
-	\else
-%\message{Converting #1 unit scale='\csname axis@#1\endcsname' ... }%
-		\expandafter\pgfmathparse\expandafter{\csname axis@#1\endcsname}%
-		\expandafter\expandafter\csname axis@inverse@datascaletrafo@tofixed@#1\endcsname\pgfmathresult\to\axis@TMP
-		\edef\axis@TMP{\axis@TMP pt}%
-		\expandafter\edef\csname axis@#1\endcsname{\axis@TMP}%
-%\message{to #1='\csname axis@#1\endcsname'.}%
-	\fi
-}
-
-\def\axis@determinedefaultvalues{%
-	\ifx\axis@xmin\empty
-		\errmessage{Sorry, the argument 'xmin=NUM' is mandatory to draw axes }%
-		\def\axis@xmin{0}%
-	\fi
-	\ifx\axis@xmax\empty
-		\errmessage{Sorry, the argument 'xmax=NUM' is mandatory to draw axes }%
-		\def\axis@xmax{1}%
-	\fi
-	\ifx\axis@ymin\empty
-		\errmessage{Sorry, the argument 'ymin=NUM' is mandatory to draw axes }%
-		\def\axis@ymin{0}%
-	\fi
-	\ifx\axis@ymax\empty
-		\errmessage{Sorry, the argument 'ymax=NUM' is mandatory to draw axes }%
-		\def\axis@ymax{1}%
-	\fi
-	%
-	\axis@set@default@size@options
-	%
-	\ifaxis@float@numerics@mode@x
-		\axis@apply@data@scale@trafo@to@options@for x%
-	\fi
-	\ifaxis@float@numerics@mode@y
-		\axis@apply@data@scale@trafo@to@options@for y%
-	\fi
-	%
-	\ifnum\axis@xmode=0
-		\axis@xminorticksfalse
-	\fi
-	\ifnum\axis@ymode=0
-		\axis@yminorticksfalse
-	\fi
-	%
-	\axis@init@enlarge@limit@booleans
-	\ifaxis@enlargelimits
-		% relax the sizes.
-		%
-		% Idea: if the user chose his xmin,xmax tight to his data,
-		% this here will look better.
-		\axis@enlarge@limit@for x
-		\axis@enlarge@limit@for y
-	\else
-		\ifaxis@enlargelimits@auto
-			\ifaxis@hide
-				% there is no axis, so skip this enlargement (unless
-				% the user explizitly requests it)
-			\else
-				% FIXME : this here should be user-configurable!
-				\ifaxis@autocompute@xlim
-					\axis@enlarge@limit@for x
-				\fi
-				\ifaxis@autocompute@ylim
-					\axis@enlarge@limit@for y
-				\fi
-			\fi
-		\fi
-	\fi
-	%
-	\axis@avoid@empty@axis@range@for x%
-	\axis@avoid@empty@axis@range@for y%
-	%
-	\axis@initsizes
-	%
-	\newif\ifaxis@xisuniform
-	\newif\ifaxis@yisuniform
-	\axis@xisuniformtrue
-	\axis@yisuniformtrue
-	\newif\ifaxis@needs@check@uniformtick
-	\axis@needs@check@uniformticktrue
-	\ifx\axis@xtick\empty
-		\axis@assign@default@tick@foraxis{x}%
-	\fi
-	\ifaxis@needs@check@uniformtick
-		\ifnum\axis@xmode=1
-			\expandafter\axis@checkisuniformLOGtick\expandafter{\axis@xtick}%
-		\fi
-		\ifaxis@isuniformtick
-			\axis@xisuniformtrue
-		\else
-			\axis@xminorticksfalse
-			\axis@xisuniformfalse
-		\fi
-	\fi
-	%
-	%
-	%
-	\axis@needs@check@uniformticktrue
-	\ifx\axis@ytick\empty
-		\axis@assign@default@tick@foraxis{y}%
-	\fi
-	\ifaxis@needs@check@uniformtick
-		\ifnum\axis@ymode=1
-			\expandafter\axis@checkisuniformLOGtick\expandafter{\axis@ytick}%
-		\fi
-		\ifaxis@isuniformtick
-			\axis@yisuniformtrue
-		\else
-			\axis@yminorticksfalse
-			\axis@yisuniformfalse
-		\fi
-	\fi
-	\ifx\axis@xticklabel\empty
-		\ifcase\axis@xmode
-			\def\axis@xticklabel{\axisdefaultticklabel}%
-		\or
-			\def\axis@xticklabel{\axisdefaultticklabellog}%
-		\fi
-	\fi
-	\ifx\axis@yticklabel\empty
-		\ifcase\axis@ymode
-			\def\axis@yticklabel{\axisdefaultticklabel}%
-		\or
-			\def\axis@yticklabel{\axisdefaultticklabellog}%
-				%--------------------------------------------------
-				% \def\axis@yticklabel{%
-				% 	\pgfmathexp\tick
-				% 	\expandafter\skipsuffixzero\pgfmathresult|%
-				% 	$\pgfmathresult$}%
-				%-------------------------------------------------- 
-		\fi
-	\fi
-}
-
-
-% Helper method for initsizes.
-%
-% It computes a scaling such that \axis@width = SCALE * ACTUAL WIDTH.
-% 
-% The actual width is 
-% 	c + x*(xmax-xmin)
-% based on
-% - x*xmax = \axis@xcoordmaxTEX
-% - x*xmin = \axis@xcoordminTEX
-% - c = estimated, a constant for the axis label/tick labels
-%
-% Arguments: 
-% #1: the output argument for the SCALE.
-\def\axis@initsizes@getXscale\into#1{%
-	\expandafter\axis@tmpa\axis@width\relax
-	% EXPECTED WIDTH = X = \axis@width
-	% ACTUAL WIDTH = c + x * (xmax-xmin)
-	% where c is a CONSTANT (for the axis labels/tick labels).
-	% -> \axis@tmpXscale = (X - c) / (x *(xmax-xmin))
-	%
-	% \axis@tmpa := X-c:
-	\ifaxis@scale@only@axis
-	\else
-		\advance\axis@tmpa by-45pt% FIXME determine 'c' correctly!
-	\fi
-	\ifdim\axis@tmpa<0pt
-		\errmessage{Error: Plot width `\axis@width' is too small. This can't be realised while maintaining constant width for y-labels. Sorry, label width are only approximate. You will need to adjust your width.}%
-		\axis@tmpa=0pt
-	\fi
-	% \axis@tmpb := x*(xmax-xmin):
-	\axis@tmpb=\axis@xcoordmaxTEX
-	\advance\axis@tmpb by-\axis@xcoordminTEX
-	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
-		{\pgf@sys@tonumber\axis@tmpa}%
-		{\pgf@sys@tonumber\axis@tmpb}%
-	}%
-	\let#1=\pgfmathresult
-%\message{pgfplots.sty: Computing 'x' such that 'width = c + x*(xmax-xmin)';
-%	c=estimated, 
-%	width-c =\the\axis@tmpa,  
-%	x*(xmax[=\the\axis@xcoordmaxTEX] - xmin[=\the\axis@xcoordminTEX)]) = \the\axis@tmpb  
-%	-> x-scale =#1 }%
-}
-
-% The same as \axis@initsizes@getXscale, just for the height.
-\def\axis@initsizes@getYscale\into#1{%
-	\expandafter\axis@tmpa\axis@height\relax
-	% EXPECTED WIDTH = X = \axis@width
-	% ACTUAL WIDTH = c + x * (xmax-xmin)
-	% where c is a CONSTANT (for the axis labels/tick labels).
-	% -> \axis@tmpXscale = (X - c) / (x *(xmax-xmin))
-	%
-	% \axis@tmpa := X-c:
-	\ifaxis@scale@only@axis
-	\else
-		\advance\axis@tmpa by-45pt\relax% FIXME determine 'c' correctly!
-	\fi
-	\ifdim\axis@tmpa<0pt
-		\errmessage{Error: Plot height `\axis@height' is too small. This can't be realised while maintaining constant height for x-labels. Sorry, label heights are only approximate. You will need to adjust your height.}%
-		\axis@tmpa=0pt
-	\fi
-	% \axis@tmpb := x*(xmax-xmin):
-	\axis@tmpb=\axis@ycoordmaxTEX
-	\advance\axis@tmpb by-\axis@ycoordminTEX
-	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
-		{\pgf@sys@tonumber\axis@tmpa}%
-		{\pgf@sys@tonumber\axis@tmpb}%
-	}%
-	\let#1=\pgfmathresult
-%\message{pgfplots.sty: Computing 'y' such that 'height = c + y*(ymax-ymin)';
-%	height=\axis@height,
-%	c=estimated,
-%	height-c =\the\axis@tmpa,  
-%	y*(ymax[=\the\axis@ycoordmaxTEX] - ymin[=\the\axis@ycoordminTEX)]) = \the\axis@tmpb  
-%	-> y-scale =#1 }%
-}
-
-
-% Checks whether axis limits in coordinate #1 are approximately equal.
-%
-% If that is the case, force a non-zero width of the range.
-%
-\def\axis@avoid@empty@axis@range@for#1{%
-	% Check if axis limits are empty:
-	\begingroup
-	\expandafter\let\expandafter\if@cur@is@scaled\csname ifaxis@float@numerics@mode@#1\endcsname
-	\expandafter\let\expandafter\min\csname axis@#1min\endcsname
-	\expandafter\let\expandafter\max\csname axis@#1max\endcsname
-	\let\min@d=\pgf@xa
-	\let\max@d=\pgf@xb
-	\let\diff=\pgf@xc
-	\newif\ifrange@is@approx@equal
-	\expandafter\min@d\min pt
-	\expandafter\max@d\max pt
-	\diff=\max@d
-	\advance\diff by-\min@d
-	% FIXME : I need a RELATIVE check here!
-	% but: real number point division is expensive
-	\if@cur@is@scaled
-		% this here should be sufficient because the axis
-		% has absolute values of order O( 10^3 ) or so.
-		\ifdim\diff<1pt
-			\range@is@approx@equaltrue
-		\fi
-	\else
-		% there is no data scaling, so I should be much more defensive
-		% with absolute thresholds...
-		\ifdim\diff<0.05pt
-			\range@is@approx@equaltrue
-		\fi
-	\fi
-	\ifrange@is@approx@equal
-%\message{avoid range is approx equal for coord #1: MODIFYING (\min,\max)...}%
-		% the case \min ~= \max
-		%
-		% enlarge \max and shrink \min:
-		\ifdim\max@d<0pt
-			\ifdim\max@d<-1pt
-				\max@d=0.8\max@d
-				\min@d=1.2\min@d
-			\else
-				\advance\max@d by-1pt
-				\advance\min@d by1pt
-			\fi
-		\else
-			\ifdim\max@d>1pt
-				\max@d=1.2\max@d
-				\min@d=0.8\min@d
-			\else
-				\ifdim\max@d=0pt
-					\if@cur@is@scaled
-						% we can't simply add a constant in the
-						% transformed range.
-						%
-						% So: set limits to [-1,1] = [-1.0e0,+1.0e0]
-						\def\sci@S{2}%
-						\def\sci@M{1.0}%
-						\def\sci@E{0}%
-						\csname axis@datascaletrafo@#1@three\endcsname\sci@S\sci@M\sci@E\to\min
-						\def\sci@S{1}%
-						\def\sci@M{1.0}%
-						\def\sci@E{0}%
-						\csname axis@datascaletrafo@#1@three\endcsname\sci@S\sci@M\sci@E\to\max
-%\message{[trafo shift = \csname axis@data@scale@trafo@SHIFT@#1\endcsname; setting limits -1:1]}%
-						\expandafter\min@d\min pt
-						\expandafter\max@d\max pt
-					\else
-						\advance\max@d by1pt
-						\advance\min@d by-1pt
-					\fi
-				\else
-					\advance\max@d by1pt
-					\advance\min@d by-1pt
-				\fi
-			\fi
-		\fi
-		\xdef\axis@TMP{\pgf@sys@tonumber{\min@d}}%
-		\xdef\axis@TMPB{\pgf@sys@tonumber{\max@d}}%
-%\message{ -> #1 = \axis@TMP : \axis@TMPB;}%
-	\else
-		\global\let\axis@TMP=\min%
-		\global\let\axis@TMPB=\max%
-	\fi
-	\endgroup
-	\expandafter\let\csname axis@#1min\endcsname=\axis@TMP
-	\expandafter\let\csname axis@#1max\endcsname=\axis@TMPB
-}
-
-% PRECONDITION:
-% 	none
-% POSTCONDITION:
-% 	\axis@default@aspect@ratio is set.
-\def\axis@compute@default@aspect@ratio{%
-	\expandafter\pgfmath@x\axisdefaultwidth
-	\expandafter\pgfmath@y\axisdefaultheight
-	\pgfmathlog@invoke@expanded\pgfmathdivide@{%
-		{\pgf@sys@tonumber{\pgfmath@x}}%
-		{\pgf@sys@tonumber{\pgfmath@y}}%
-	}%
-	\let\axis@default@aspect@ratio=\pgfmathresult
-}
-
-\def\axis@set@default@size@options{%
-	% The axes 'x' and 'y' vectors will be scaled such that the total
-	% size is (\axisdefaultwidth, \axisdefaultheight).
-	%
-	% If the user specifies ONE of width OR height, 
-	% the plot will be resized; keeping the aspect ratio.
-	%
-	\let\axis@default@aspect@ratio=\empty
-	% CASES:
-	% hasx := 'x' option non-empty
-	% hasy := 'y' option non-empty
-	% W := 'width' option non-empty
-	% H := 'height' option non-empty
-	%
-	% hasx = 1 -> width is not interesting; we use 'x' option.
-	% hasx = 0 -> determine final width:
-	% 		W H
-	% 		0 0 -> \axisdefaultwidth 
-	% 		0 1 -> determine width out of H and the default aspect ratio
-	% 		1 X -> ok, use the user parameter.
-	%
-	% hasy = 1 -> height is not interesting, we use 'y' option.
-	% hasy = 0 -> determine final height:
-	% 		W H
-	% 		0 0 -> \axisdefaultheight
-	% 		X 1 -> ok, use the user parameter
-	% 		1 0 -> determine height out of W and the default aspect ratio
-	%
-	\ifx\axis@x\empty
-		\ifx\axis@y\empty
-			% hasx=0, hasy=0 
-			%
-			% -> KEEP ASPECT RATIO if just one W, or H is given!
-			\ifx\axis@width\empty
-				\ifx\axis@height\empty
-					% The case hasx=0, hasy=0,  W=0 H=0:
-					\let\axis@width=\axisdefaultwidth
-					\let\axis@height=\axisdefaultheight
-				\else
-					% The case hasx=0, hasy=0,  W=0 H=1:
-					\axis@compute@default@aspect@ratio
-					\expandafter\pgfmath@y\axis@height
-					\pgfmathlog@invoke@expanded\pgfmathmultiply@{%
-						{\pgf@sys@tonumber{\pgfmath@y}}%
-						{\axis@default@aspect@ratio}%
-					}%
-					\edef\axis@width{\pgfmathresult pt}%
-				\fi
-			\else
-				\ifx\axis@height\empty
-					% The case hasx=0, hasy=0,  W=1 H=0:
-					\axis@compute@default@aspect@ratio
-					\expandafter\pgfmath@x\axis@width
-					\pgfmathlog@invoke@expanded\pgfmathdivide@{%
-						{\pgf@sys@tonumber{\pgfmath@x}}%
-						{\axis@default@aspect@ratio}%
-					}%
-					\edef\axis@height{\pgfmathresult pt}%
-				\else
-					% The case hasx=0, hasy=0,  W=1 H=1:
-				\fi
-			\fi
-		\else
-			% hasx=0, hasy=1, W=0:
-			\ifx\axis@width\empty
-				\let\axis@width=\axisdefaultwidth
-			\fi
-		\fi
-	\else
-		\ifx\axis@y\empty
-			% hasx=1, hasy=0, H=0
-			\ifx\axis@height\empty
-				\let\axis@height=\axisdefaultheight
-			\fi
-		\fi
-	\fi
-}
-
-% PRECONDITION: 
-% 	- final axis limits are given in transformed range
-% 	-  \axis@set@default@size@options has been invoked before
-% POSTCONDITION: 
-% 	- the current x- and y unit vectors are changed;
-% 	- \axis@[xy]coord{min,max}TEX  are set
-%
-\def\axis@initsizes{%
-	% INIT.
-	%
-	%
-	\pgfpointxy{\axis@xmin}{\axis@ymin}%
-	\axis@xcoordminTEX=\pgf@x
-	\axis@ycoordminTEX=\pgf@y
-	\pgfpointxy{\axis@xmax}{\axis@ymax}%
-	\axis@xcoordmaxTEX=\pgf@x
-	\axis@ycoordmaxTEX=\pgf@y
-	%
-	%
-	%-----------------------------------------
-	% PROCESS THE 'width' and 'height' options
-	%-----------------------------------------
-	%
-	% FIXME: make these variables LOCAL:
-	%
-	\let\axis@rectangle@width=\empty
-	\let\axis@rectangle@height=\empty
-	%
-	\ifx\axis@x\empty
-		\ifx\axis@width\empty
-			\errmessage{INTERNAL LOGIC ERROR! WIDTH NOT SET}%
-		\fi
-		\axis@initsizes@getXscale\into\axis@tmpXscale
-		\ifaxis@scale@only@axis
-			\let\axis@rectangle@width=\axis@width
-		\fi
-	\else
-		\def\axis@tmpXscale{1}%
-	\fi
-	%
-	\ifx\axis@y\empty
-		\ifx\axis@height\empty
-			\errmessage{INTERNAL LOGIC ERROR! HEIGHT NOT SET}%
-		\fi
-		\axis@initsizes@getYscale\into\axis@tmpYscale
-		\ifaxis@scale@only@axis
-			\let\axis@rectangle@height=\axis@height
-		\fi
-	\else
-		\def\axis@tmpYscale{1}%
-	\fi
-	%
-	% 
-	% assert( \axis@tmpXscale != \empty && \axis@tmpYscale != \empty )
-	%
-	% Apply scaling:
-	\pgfpointxy{\axis@tmpXscale}{\axis@tmpYscale}%
-	\axis@tmpa=\pgf@x
-	\axis@tmpb=\pgf@y
-	\ifx\axis@x\empty
-		\pgfsetxvec{\pgfpoint{\axis@tmpa}{0pt}}%
-	\else
-		\pgfsetxvec{\pgfpoint{\axis@x}{0pt}}%
-	\fi
-	\ifx\axis@y\empty
-		\pgfsetyvec{\pgfpoint{0pt}{\axis@tmpb}}%
-	\else
-		\pgfsetyvec{\pgfpoint{0pt}{\axis@y}}%
-	\fi
-	%
-	% Determine final rectangle dimensions.
-	% There are the following cases: 
-	% 1. the user really wants a fixed dimension,
-	%    i.e. he used 'scale only axis'.
-	%    Then, we have to work to get the correct dimension!
-	%
-	%    Up to now, the scaling mechanism looses to many significant
-	%    digits such that the final width/height differs by 1-2 pt.
-	%
-	%    If I am not mistaken, this does ONLY affect the final size,
-	%    not the relative plot precision.
-	%    
-	%    FIXME : really compute the plot precision!
-	% 
-	% 2. The use specified width and/or height, but not 'scale only
-	%    axis'. Accept inaccurate final widths/heights (see above).
-	%
-	% 3. The user supplied 'x' and or 'y'. Simply use them, its
-	% accurate.
-	%
-	\pgfpointxy{\axis@xmin}{\axis@ymin}%
-	\axis@xcoordminTEX=\pgf@x
-	\axis@ycoordminTEX=\pgf@y
-	\pgfpointxy{\axis@xmax}{\axis@ymax}%
-	\ifx\axis@rectangle@width\empty
-		\axis@xcoordmaxTEX=\pgf@x
-	\else
-		% this 'if' here should only make a difference of about
-		% 1-2pt, not more.
-		%
-		% and I am quite sure that this inaccuracy (and this
-		% work-around) only affects the
-		% final size, not the relative plot accuracy.
-		\axis@xcoordmaxTEX=\axis@xcoordminTEX
-		\expandafter\advance\expandafter\axis@xcoordmaxTEX\axis@width
-	\fi
-	\ifx\axis@rectangle@height\empty
-		\axis@ycoordmaxTEX=\pgf@y
-	\else
-		\axis@ycoordmaxTEX=\axis@ycoordminTEX
-		\expandafter\advance\expandafter\axis@ycoordmaxTEX\axis@height
-	\fi
-%--------------------------------------------------
-% \begingroup
-% \pgf@x=\axis@xcoordmaxTEX\advance\pgf@x by-\axis@xcoordminTEX
-% \pgf@y=\axis@ycoordmaxTEX\advance\pgf@y by-\axis@ycoordminTEX
-% \message{Axis scaling x=\axis@tmpXscale, y=\axis@tmpYscale\ yields lower-left-corner (\axis@xmin,\axis@ymin) = (\the\axis@xcoordminTEX,\the\axis@ycoordminTEX) and upper right (\axis@xmax,\axis@ymax) = (\the\axis@xcoordmaxTEX,\the\axis@ycoordmaxTEX).   Axis dimensions are width=\the\pgf@x, height=\the\pgf@y.}%
-% \endgroup
-%-------------------------------------------------- 
-}
-
-\def\axis@BEGIN@init@and@draw@axis{%
-	\axis@determinedefaultvalues
-	
-	% move the anchor to (0,0):
-	\expandafter\ifcase\axis@anchorchoicenum
-	% north:
-		\begin{scope}[
-			yshift=-\axis@ycoordmaxTEX,
-			xshift=-0.5\axis@xcoordminTEX-0.5\axis@xcoordmaxTEX
-		]
-	\or% north west:
-		\begin{scope}[
-			yshift=-\axis@ycoordmaxTEX,
-			xshift=-\axis@xcoordminTEX
-		]
-	\or% west:
-		\begin{scope}[
-			yshift=-0.5\axis@ycoordminTEX-0.5\axis@ycoordmaxTEX,
-			xshift=-\axis@xcoordminTEX
-		]
-	\or% south west:
-		\begin{scope}[
-			yshift=-\axis@ycoordminTEX,
-			xshift=-\axis@xcoordminTEX
-		]
-	\or% south:
-		\begin{scope}[
-			yshift=-\axis@ycoordminTEX,
-			xshift=-0.5\axis@xcoordminTEX-0.5\axis@xcoordmaxTEX
-		]
-	\or% south east:
-		\begin{scope}[
-			yshift=-\axis@ycoordminTEX,
-			xshift=-\axis@xcoordmaxTEX
-		]
-	\or% east:
-		\begin{scope}[
-			yshift=-0.5\axis@ycoordminTEX-0.5\axis@ycoordmaxTEX,
-			xshift=-\axis@xcoordmaxTEX
-		]
-	\or% north east:
-		\begin{scope}[
-			yshift=-\axis@ycoordmaxTEX,
-			xshift=-\axis@xcoordmaxTEX
-		]
-	\or% center
-		\begin{scope}[
-			yshift=-0.5\axis@ycoordminTEX-0.5\axis@ycoordmaxTEX,
-			xshift=-0.5\axis@xcoordminTEX-0.5\axis@xcoordmaxTEX
-		]
-	\fi
-
-	\begin{scope}
-	\ifaxis@hide
-		\clip
-						(\axis@xcoordminTEX,	\axis@ycoordminTEX) 
-			rectangle	(\axis@xcoordmaxTEX,	\axis@ycoordmaxTEX);
-	\else
-
-		% X-Achsenbeschriftung:
-		% LADE DIE \axis@xtick -variable REIN
-		\expandafter\axis@drawxaxis\expandafter{\axis@xtick}
-		%
-		% Y-Achsen und Achsenbeschriftung:
-		\expandafter\axis@drawyaxis\expandafter{\axis@ytick}%
-		\draw[clip]
-						(\axis@xcoordminTEX,	\axis@ycoordminTEX) 
-			rectangle	(\axis@xcoordmaxTEX,	\axis@ycoordmaxTEX);
-
-	\fi
-}
-
-\def\axis@END@init@and@draw@axis{%
-	\end{scope}%
-}
-
-% Writes output to \axis@TMP
-\def\axis@filter@input@ticks@with@log#1{%
-	\let\axis@TMP=\empty
-	\foreach \axis@TMPB in {#1} {%
-		\expandafter\pgfmathlog@\expandafter{\axis@TMPB}%
-		\ifx\axis@TMP\empty
-			\xdef\axis@TMP{\pgfmathresult}%
-		\else
-			\xdef\axis@TMP{\axis@TMP,\pgfmathresult}%
-		\fi
-	}%
-}
-
-\tikzdeclarecoordinatesystem{axis}{\axis@evalute@tikz@coord@system@interface#1\axis@coord@end}
-
-
-% Assigns \pgfmathresult := canvas coordinate (#2) for axis #1.
-\long\def\axis@evalute@tikz@coord@system@interface@for#1#2{%
-	\expandafter\let\expandafter\if@datascaled@cur\csname ifaxis@float@numerics@mode@#1\endcsname
-	\expandafter\ifcase\csname axis@#1mode\endcsname
-		\if@datascaled@cur
-			\csname axis@datascaletrafo@fromfixed@#1\endcsname#2\to\pgfmathresult
-		\else
-			\def\pgfmathresult{#2}%
-		\fi
-	\or
-		\pgfmathlog@{#2}%
-	\fi
-}
-
-\long\def\axis@evalute@tikz@coord@system@interface#1,#2\axis@coord@end{%
-	\begingroup
-	\axis@evalute@tikz@coord@system@interface@for{x}{#1}%
-	\let\axis@evaluate@tikz@coord@x=\pgfmathresult
-	\axis@evalute@tikz@coord@system@interface@for{y}{#2}%
-	\xdef\axis@TMP{\axis@evaluate@tikz@coord@x pt}%
-	\xdef\axis@TMPB{\pgfmathresult pt}%
-	\endgroup
-	\pgfpointxy{\axis@TMP}{\axis@TMPB}%
-}
-
-% In case of (semi-) logplots, this command will 
-% - assign a filter which invokes \pgfmathlog@{} for each coordinate
-% - replace any user-specified coordinate by its log.
-%
-% All subsequent commands will then work with logarithmic coordinates.
-%
-% @see pgfmathlog.sty for details about the implementation of log().
-%
-% PRECONDITION: 
-% - The user input options have been set correctly, 
-% - the option processing has not yet begun
-%
-% POSTCONDITION: 
-% - any user input for log-axis has been replaced by its log
-% - coordinate filters to compute logs are installed
-%
-% See also:
-%     \axis@apply@data@scale@trafo@to@options@for
-\def\axis@prepare@coord@filtering@for#1{%
-	\expandafter\ifcase\csname axis@#1mode\endcsname
-		\ifaxis@disabledatascaling
-			\csname axis@float@numerics@mode@#1false\endcsname
-			\axis@float@numerics@modefalse
-		\else
-			\csname axis@float@numerics@mode@#1true\endcsname
-			\axis@float@numerics@modetrue
-		\fi
-		\ifaxis@float@numerics@mode
-			% Install coordinate filters that
-			% - read input as normalised floating point numbers,
-			% - return [SIGN][MANTISSE]eEXPONENT
-			% Motivation: 
-			% 1. we can compute axis limits using such data
-			% 2. we can remember the floating point representation for 
-			%    the data scaling transformation.
-			% ATTENTION:
-			% this here is a preprocessing step! You will need to
-			% apply the data scaling later!
-			% see 
-			% \axis@apply@data@scaletrafo@to@plot@data
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1filter\endcsname
-			\ifx\axis@TMP\empty
-				\expandafter\def\csname addplot@float@numerics@#1filter\endcsname##1\to##2{%
-					\sciparsesign{##1}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-					\scisetcomponents{##2}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-					\edef##2{\axis@tmp@S\axis@tmp@M e\axis@tmp@E}%
-				}%
-			\else
-				\expandafter\let\csname axis@#1filter@orig\endcsname=\axis@TMP
-				\expandafter\def\csname addplot@float@numerics@#1filter\endcsname##1\to##2{%
-					\csname axis@#1filter@orig\endcsname##1\to##2\relax
-					\ifx##2\empty
-					\else
-						\expandafter\sciparsesign\expandafter{##2}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-						\scisetcomponents{##2}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-						\edef##2{\axis@tmp@S\axis@tmp@M e\axis@tmp@E}%
-					\fi
-				}%
-			\fi
-			\expandafter\let\expandafter\axis@TMP\csname addplot@float@numerics@#1filter\endcsname
-			\expandafter\let\csname axis@#1filter\endcsname\axis@TMP
-			%
-			% Check for any existing axis limits:
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1min\endcsname
-			\ifx\axis@TMP\empty
-			\else
-				\expandafter\sciparsesign\expandafter{\axis@TMP}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-				\expandafter\scisetcomponents\csname axis@#1min\endcsname\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\fi
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1max\endcsname
-			\ifx\axis@TMP\empty
-			\else
-				\expandafter\sciparsesign\expandafter{\axis@TMP}\axis@tmp@S\axis@tmp@M\axis@tmp@E
-				\expandafter\scisetcomponents\csname axis@#1max\endcsname\axis@tmp@S\axis@tmp@M\axis@tmp@E
-			\fi
-		\fi
-	\or
-		\ifaxis@disablelogfilter
-		\else
-			% any user-specified axis limits:
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1min\endcsname
-			\ifx\axis@TMP\empty
-			\else
-				\expandafter\pgfmathlog@\expandafter{\axis@TMP}%
-				\expandafter\let\csname axis@#1min\endcsname=\pgfmathresult
-			\fi
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1max\endcsname
-			\ifx\axis@TMP\empty
-			\else
-				\expandafter\pgfmathlog@\expandafter{\axis@TMP}%
-				\expandafter\let\csname axis@#1max\endcsname=\pgfmathresult
-			\fi
-			%
-			% any user specified axis ticks:
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1tick\endcsname
-			\ifx\axis@TMP\empty
-			\else
-				\expandafter\axis@filter@input@ticks@with@log\expandafter{\axis@TMP}%
-				\expandafter\edef\csname axis@#1tick\endcsname{\axis@TMP}%
-			\fi
-			%
-			\expandafter\let\expandafter\axis@TMP\csname axis@#1filter\endcsname
-			\ifx\axis@TMP\empty
-				\expandafter\def\csname addplot@log@compute@#1filter\endcsname##1\to##2{%
-					\pgfmathlog@{##1}%
-					\let##2=\pgfmathresult
-				}%
-			\else
-				\expandafter\let\csname axis@#1filter@orig\endcsname=\axis@TMP
-				\expandafter\def\csname addplot@log@compute@#1filter\endcsname##1\to##2{%
-					\pgfmathlog@{##1}%
-					\ifx\pgfmathresult\empty
-						\let##2=\empty
-					\else
-						\expandafter\expandafter\csname axis@#1filter@orig\endcsname\pgfmathresult\to##2\relax
-					\fi
-				}%
-			\fi
-			\expandafter\let\expandafter\axis@TMP\csname addplot@log@compute@#1filter\endcsname
-			\expandafter\let\csname axis@#1filter\endcsname\axis@TMP
-		\fi
-	\fi
-}
-
-\def\axis@create@axis@descriptions{%
-	\ifaxis@hide
-	\else
-		\ifx\axis@xlabel\empty
-		\else
-			\axisshowxlabel
-		\fi
-		\ifx\axis@ylabel\empty
-		\else
-			\axisshowylabel
-		\fi
-	\fi
-	\ifx\axis@title\empty
-	\else
-		\axisshowtitle
-	\fi
-	\axis@createlegend
-}
-
-% DATA TRANSFORMATION T(x) = X
-%
-% Input: 
-%    a number in the original data range, given in **floating** point representation
-% Output: 
-%    a fixed point number in transformed range
-% @see
-% \axis@datascaletrafo@x@three
-% \axis@datascaletrafo@fromfixed@x
-\def\axis@datascaletrafo@x#1\to#2{%
-	\scigetcomponents#1\axis@tmp@S\axis@tmp@M\axis@tmp@E
-	\axis@datascaletrafo@x@three\axis@tmp@S\axis@tmp@M\axis@tmp@E\to#2
-}
-
-% Overloaded function.
-% Input: 
-%     The same as above, but with Sign, Mantisse, Exponent.
-%     #1,#2 and #3 are expected to be MACRO NAMES.
-\def\axis@datascaletrafo@x@three#1#2#3\to#4{%
-	\def\axis@TMP{\scimathshift{#1}{#2}{#3}}%
-	\expandafter\axis@TMP\expandafter{\axis@data@scale@trafo@SHIFT@x}%
-	\scitofixed{#1}{#2}{#3}{#4}%
-}
-
-% Overloaded function.
-% Input:
-%     a FIXED point number instead of a floating point one.
-% @see \axis@datascaletrafo@x
-\def\axis@datascaletrafo@fromfixed@x#1\to#2{%
-	\begingroup
-	\sciparsesign{#1}\axis@S\axis@M\axis@E
-	\axis@datascaletrafo@x@three\axis@S\axis@M\axis@E\to{#2}%
-	\global\let\axis@TMP=#2\relax
-	\endgroup
-	\let#2=\axis@TMP
-}
-
-\def\axis@datascaletrafo@y#1\to#2{%
-	\scigetcomponents#1\axis@tmp@S\axis@tmp@M\axis@tmp@E
-	\axis@datascaletrafo@y@three\axis@tmp@S\axis@tmp@M\axis@tmp@E\to#2
-}
-\def\axis@datascaletrafo@y@three#1#2#3\to#4{%
-	\def\axis@TMP{\scimathshift{#1}{#2}{#3}}%
-	\expandafter\axis@TMP\expandafter{\axis@data@scale@trafo@SHIFT@y}%
-	\scitofixed{#1}{#2}{#3}{#4}%
-}
-\def\axis@datascaletrafo@fromfixed@y#1\to#2{%
-	\begingroup
-	\sciparsesign{#1}\axis@S\axis@M\axis@E
-	\axis@datascaletrafo@y@three\axis@S\axis@M\axis@E\to{#2}%
-	\global\let\axis@TMP=#2\relax
-	\endgroup
-	\let#2=\axis@TMP
-}
-
-% INVERSE transformation x = T^{-1}( X )
-% Input: 
-%    a fixed point number in transformed domain
-% Output:
-%    a number in the data domain, given in floating point
-%    representation
-\def\axis@inverse@datascaletrafo@x#1\to#2{%
-	\expandafter\sciparsesignsingle\expandafter{#1}#2
-	\edef\axis@TMP{\noexpand#2{-\axis@data@scale@trafo@SHIFT@x}}%
-	\expandafter\scimathshiftsingle\axis@TMP
-}
-
-\def\axis@inverse@datascaletrafo@y#1\to#2{%
-	\expandafter\sciparsesignsingle\expandafter{#1}#2
-	\edef\axis@TMP{\noexpand#2{-\axis@data@scale@trafo@SHIFT@y}}%
-	\expandafter\scimathshiftsingle\axis@TMP
-}
-
-% Overloaded function.
-%
-% In contrast to \axis@inverse@datascaletrafo@x, this method
-% returns a number in FIXED point representation.
-% @see \axis@inverse@datascaletrafo@x
-\def\axis@inverse@datascaletrafo@tofixed@x#1\to#2{%
-	\axis@inverse@datascaletrafo@x#1\to{#2}%
-	\scitofixedsingle{#2}{#2}%
-}
-\def\axis@inverse@datascaletrafo@tofixed@y#1\to#2{%
-	\axis@inverse@datascaletrafo@y#1\to{#2}%
-	\scitofixedsingle{#2}{#2}%
-}
-
-\newenvironment{axis}[1][]{%
-	\begingroup
-%	\def\axis@setkeys{\setkeys*[\prefix]{axis}}%
-%\tracingmacros=2\tracingcommands=2
-%	\message{Der every-axis-style ist gerade \csname tikz@st@every axis\endcsname}%
-%\tracingmacros=0\tracingcommands=0
-%    \expandafter\expandafter\expandafter\axis@setkeys
- %   \expandafter\expandafter\expandafter{\csname tikz@st@every axis\endcsname}%
-	\begin{scope}[style=every axis,%
-		x=1pt,y=1pt% see below
-	]
-	% The explicit specification of 'x' and 'y' as 1pt is to avoid
-	% numeric overflow/underflow during scale computations:
-	%
-	% The scaling (i.e. proper values for 'x' and 'y') will be
-	% determined later-on, dependend on the axis limits.  Since axis
-	% limits are implicitly in units of 1pt, it is reasonable to use
-	% '1pt' here as well.
-	%
-	%
-%--------------------------------------------------
-% \draw[very thin,color=gray,xstep=1,ystep=\logten] 
-% 		  		(\xcoordmin\axis@leftover,\ycoordmin) 
-% 		grid	(\xcoordmax\axis@rightover,\ycoordmax);
-%-------------------------------------------------- 
-	\setkeys[\prefix]{axis}{#1}%
-	%
-	% --------------------
-	% Allocations:
-	% --------------------
-	\listnewempty\axis@plotspeclist
-	\listnewempty\axis@legend
-	\listnewempty\axis@stored@plot@cmds
-	\listnewempty\axis@stored@plot@data
-	\newif\ifaxis@autocompute@xlim
-	\newif\ifaxis@autocompute@ylim
-	\newif\ifaxis@filtercoords
-	\newif\ifaxis@float@numerics@mode@x
-	\newif\ifaxis@float@numerics@mode@y
-	\newif\ifaxis@float@numerics@mode
-	% rename '\ifaxis@hide axis'  to mask the white space:
-	\expandafter\let\expandafter\ifaxis@hide\csname ifaxis@hide axis\endcsname
-	% the same for other options with white spaces:
-	\expandafter\let\expandafter\ifaxis@scale@only@axis\csname ifaxis@scale only axis\endcsname
-	\newif\ifaxis@draw@at@end
-	\newif\ifaxis@limits@are@computed
-	\newif\ifaxis@EMERGENCY@FORCE@DATA@TRAFO@TO@IDENTITY
-	\axis@numplots=0
-	\let\axis@already@computed@legend@node=\empty
-	%
-	% --------------------
-	% Option preprocessing
-	% --------------------
-	\axis@prepare@coord@filtering@for x
-	\axis@prepare@coord@filtering@for y
-	%
-	\ifx\axis@xfilter\empty
-	\else
-		\axis@filtercoordstrue
-	\fi
-	\ifx\axis@yfilter\empty
-	\else
-		\axis@filtercoordstrue
-	\fi
-	% 
-	\ifx\axis@xmin\empty
-		\axis@autocompute@xlimtrue
-		\def\axis@xmin{16300}%
-		\ifaxis@float@numerics@mode@x
-			\scisetcomponents\axis@xmin{1}{1.0}{324}%
-		\fi
-	\fi
-	\ifx\axis@xmax\empty
-		\axis@autocompute@xlimtrue
-		\def\axis@xmax{-16300}%
-		\ifaxis@float@numerics@mode@x
-			\scisetcomponents\axis@xmax{2}{1.0}{324}%
-		\fi
-	\fi
-	\ifx\axis@ymin\empty
-		\axis@autocompute@ylimtrue
-		\def\axis@ymin{16300}%
-		\ifaxis@float@numerics@mode@y
-			\scisetcomponents\axis@ymin{1}{1.0}{324}%
-		\fi
-	\fi
-	\ifx\axis@ymax\empty
-		\axis@autocompute@ylimtrue
-		\def\axis@ymax{-16300}%
-		\ifaxis@float@numerics@mode@y
-			\scisetcomponents\axis@ymax{2}{1.0}{324}%
-		\fi
-	\fi
-	%
-	\ifaxis@autocompute@xlim
-		\axis@draw@at@endtrue
-		\axis@limits@are@computedfalse
-	\else
-		\axis@limits@are@computedtrue
-	\fi
-	\ifaxis@autocompute@ylim
-		\axis@draw@at@endtrue
-		\axis@limits@are@computedfalse
-	\else
-		\axis@limits@are@computedtrue
-	\fi
-	%
-	%
-	% --------------------
-	% Start axis:
-	% either postponed to \end or directly.
-	% --------------------
-	%
-	\ifaxis@draw@at@end
-	\else
-		\axis@BEGIN@init@and@draw@axis
-	\fi
-}{%
-	%\end{axis}:
-	% --------------------
-	%  All plotting commands
-	%  have been done.
-	%  -> apply postponed drawing commands!
-	% --------------------
-	\ifaxis@draw@at@end
-		\ifaxis@limits@are@computed
-		\else
-			% EMPTY AXIS:
-			\def\axis@xmin{0}%
-			\def\axis@xmax{1}%
-			\def\axis@ymin{0}%
-			\def\axis@ymax{1}%
-		\fi
-		\axis@BEGIN@init@and@draw@axis
-		\listforeach\axis@stored@plot@cmds\as\plotcmd{%
-			\listpopfront\axis@stored@plot@data\to\plotdata
-			\ifaxis@float@numerics@mode
-				\ifx\plotcmd\empty
-					\plotdata
-				\else
-					% Apply the data scaling transformation
-					\expandafter\axis@apply@data@scaletrafo@to@plot@data\plotdata\to\plotdata
-					\expandafter\plotcmd\plotdata
-				\fi
-			\else
-				\expandafter\plotcmd\plotdata
-			\fi
-		}%
-	\fi
-	\axis@END@init@and@draw@axis
-	%
-	\begin{scope}[%
-		xshift=+\axis@xcoordminTEX,
-		yshift=\axis@ycoordminTEX,
-		x={\axis@xcoordmaxTEX-\axis@xcoordminTEX},
-		y={\axis@ycoordmaxTEX-\axis@ycoordminTEX}
-	]%
-		\axis@create@axis@descriptions
-	\end{scope}%
-	\end{scope}% this scope starts inside of \axis@BEGIN@init@and@draw@axis
-	%
-	\end{scope}%
-	\endgroup
-}
+\input pgfplots.code.tex
+\usetikzlibrary{plotmarks}
 
-\newenvironment{semilogxaxis}[1][]{%
-	\begin{axis}[xmode=log,ymode=normal,#1]
-}{%
-	\end{axis}%
-}
 
-\newenvironment{semilogyaxis}[1][]{%
-	\begin{axis}[xmode=normal,ymode=log,#1]
-}{%
-	\end{axis}%
-}
 
-\newenvironment{loglogaxis}[1][]{%
-	\begin{axis}[xmode=log,ymode=log,#1]
-}{%
-	\end{axis}%
-}
+\endinput
diff --git a/Master/texmf-dist/tex/latex/pgfplots/pgfplotshelpers.sty b/Master/texmf-dist/tex/latex/pgfplots/pgfplotshelpers.sty
deleted file mode 100644
index 304448fbef4..00000000000
--- a/Master/texmf-dist/tex/latex/pgfplots/pgfplotshelpers.sty
+++ /dev/null
@@ -1,208 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% Low-level helper methods for string parsing and number conversion.
-%
-% This file comes as part of the pgfplots-package.
-%
-% Copyright 2007/2008 by Christian Feuersänger.
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-% 
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-% GNU General Public License for more details.
-% 
-% You should have received a copy of the GNU General Public License
-% along with this program.  If not, see <http://www.gnu.org/licenses/>.
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\ProvidesPackage{pgfplotshelpers}[2008/02/17 Version 0.9.4]
-
-\newtoks\pgfplots@toka
-
-\def\prettyprintnumberprecision{2}
-
-\def\pgfmathlog@tonumber#1pt{#1}
-
-% Invokes command #1 with #2 without the 'pt' suffix.
-\def\invokepgf@math@one#1#2{%
-	%\edef\pgfmath@resulttemp{\pgf@sys@tonumber{#2}}%
-	%\expandafter#1\expandafter{\pgfmath@resulttemp}%
-	\edef\pgfmath@resulttemp{{\pgf@sys@tonumber{#2}}}%
-	\expandafter#1\pgfmath@resulttemp%
-}
-
-% Expands #2 using \edef and invokes #1 with the resulting string.
-%
-% Example:
-%   \pgfmath@y=7.9pt
-%   \pgfmathlog@invoke@expanded\pgfmathexp@{{\pgf@sys@tonumber{\pgfmath@y}}}%
-% will invoke
-%   \pgfmathexp@{7.9}
-\def\pgfmathlog@invoke@expanded#1#2{%
-	\edef\pgfmath@resulttemp{#2}%
-	\expandafter#1\pgfmath@resulttemp
-}
-
-% Expands the NUMBER (without units) to a pretty printed string argument: rounded to
-% several digits, discard any suffix zeros etc.
-%
-% It uses \prettyprintnumberprecision digits after the comma.
-\def\prettyprintnumber#1{%
-	\begingroup
-%	\edef\argument{#1}%
-%	\expandafter\prettyprintnumber@impl\argument.\END
-	\edef\argument{#1\noexpand\prec\prettyprintnumberprecision}%
-	\expandafter\fixedpointround\argument\to\result
-	\result
-	\endgroup
-}
-
-\def\prettyprintnumber@impl#1.#2\END{%
-	% This implementation is really bad.
-	% I hope I find time to get something better...
-	\def\tmp{#2}%
-	\ifx\tmp\empty
-		% there was no '.' in the original arg
-		#1
-	\else
-		% ok, there is a dot in the arg.
-		% 1. ROUND
-		% 2. DISCARD ZEROS
-		\toksdef\tokens=2
-		\let\i=\c@pgf@counta
-		\let\lastdigit=\c@pgf@countb
-		\let\numberAsDIM=\pgfmath@x
-		\let\zeroFilledNum=\pgfmath@y
-		\i=0
-		\tokens={}%
-		\def\D{#2}%
-		\def\DOT{.}%
-		\ifx\D\DOT
-			% the number '#1.'
-			\let\D=\empty
-		\else
-			\expandafter\prettyprintnumber@impl@getfirst
-				\prettyprintnumberprecision
-				\of#2%
-				\to\tokens%
-				\nextto\D
-				\count\i
-		\fi
-		%\message{Pretty print: first <= \prettyprintnumberprecision\ digits after period: \the\tokens, (strlen=\the\i), next rounding-relevant-digit: '\D'}%
-		\ifx\D\empty
-			\numberAsDIM=#1\expandafter.\the\tokens pt
-			% Nothing to do - we have our desired precision.
-		\else
-			\lastdigit\expandafter=\D\relax
-%		\message{D=\D!}%
-			\ifnum\lastdigit>4
-				\numberAsDIM=#1\expandafter.\expandafter\the\tokens\D pt
-				% round up:
-				% compute numberAsDIM += 0.0000[10-digit]
-				\advance\lastdigit by-10
-				\multiply\lastdigit by-1
-				\tokens={0.}%
-				\loop
-				\ifnum\i>0
-					\tokens=\expandafter{\the\tokens0}%
-					\advance\i by-1
-				\repeat
-				\edef\D{\the\tokens\the\lastdigit pt}%
-				\expandafter\zeroFilledNum\D
-				\ifdim\numberAsDIM<0pt
-					\advance\numberAsDIM by-\zeroFilledNum
-				\else
-					\advance\numberAsDIM by\zeroFilledNum
-				\fi
-			\else
-				\numberAsDIM=#1\expandafter.\the\tokens pt
-			\fi
-		\fi
-		%\message{Pretty print: Result after rounding = \the\numberAsDIM / zeroFilledNum = \the\zeroFilledNum [only defined on up-rounding}%
-		\edef\D{\pgf@sys@tonumber{\numberAsDIM}}%
-		\expandafter\prettyprintnumber@onlyrelevant@digits\D\to\D
-		% FIXME : I could return '\D' as macro!? May thats a better
-		% way...
-		\D
-	\fi
-}
-
-% This macro takes the first \prettyprintnumberprecision digits after
-% the period and squeezes away any trailing zeros.
-%
-% If no digits after the period remain, the period will be discarded
-% as well.
-\def\prettyprintnumber@onlyrelevant@digits#1.#2\to#3{%
-	\begingroup
-	\toksdef\tokens=2
-	\let\i=\c@pgf@counta
-	\let\maxDigits=\c@pgf@countc
-	\let\numsuffixZeros=\c@pgf@countb
-	\tokens={#1.}%
-	\i=0
-	\expandafter\maxDigits\prettyprintnumberprecision
-	\numsuffixZeros=0
-	\prettyprintnumber@onlyrelevant@digits@leftshift#2\to#3
-	\ifnum\numsuffixZeros>0
-		\ifnum\numsuffixZeros=\i
-			\tokens={#1}%
-		\else
-			\maxDigits=\i
-			\advance\maxDigits by-\numsuffixZeros
-			\tokens={#1.}%
-			\i=0
-			\prettyprintnumber@onlyrelevant@digits@leftshift#2\to#3
-		\fi
-	\fi
-	\xdef\pgfplotshelpersTMP{\the\tokens}%
-	\endgroup
-	\let#3=\pgfplotshelpersTMP
-}
-
-
-% shifts the input argument until either no more input is left or
-% \maxDigits entries have been acquired.
-%
-% It also updates \i (will contain the number of acquired elements)
-% and \numsuffixZeros (the number of zeros at the tail of #3 on
-% output).
-\def\prettyprintnumber@onlyrelevant@digits@leftshift#1#2\to#3{%
-	\ifnum\i<\maxDigits
-		\tokens=\expandafter{\the\tokens#1}%
-		\advance\i by1
-		\ifnum#1=0
-			\advance\numsuffixZeros by1
-		\else
-			\numsuffixZeros=0
-		\fi
-		\def\tmp{#2}%
-		\ifx\tmp\empty
-		\else
-			\prettyprintnumber@onlyrelevant@digits@leftshift#2\to#3
-		\fi
-	\fi
-}
-
-\def\prettyprintnumber@impl@getfirst#1\of#2#3.\to#4\nextto#5\count#6{%
-	\edef#5{#3}%
-	#4=\expandafter{\the#4#2}%
-	\advance#6 by1
-	\ifx#5\empty
-	\else
-		\ifnum#6<#1
-			\prettyprintnumber@impl@getfirst #1\of#3.\to#4\nextto#5\count{#6}%
-		\else
-			\prettyprintnumber@impl@firstof#3\to#5
-		\fi
-	\fi
-}
-
-\def\prettyprintnumber@impl@firstof#1#2\to#3{\def#3{#1}}%
-
diff --git a/Master/texmf-dist/tex/latex/pgfplots/sciformat.sty b/Master/texmf-dist/tex/latex/pgfplots/sciformat.sty
deleted file mode 100644
index 493aca948d1..00000000000
--- a/Master/texmf-dist/tex/latex/pgfplots/sciformat.sty
+++ /dev/null
@@ -1,861 +0,0 @@
-%--------------------------------------------
-%
-% Package sciformat.sty
-%
-% Provides support for floating point number representations of the
-% form
-%
-% S * M * 10^e
-%
-% with S in [-,+,0], 0<M<10, e in Z.
-%
-% Example:
-%
-% +1.62452*10^-8
-%
-% The conversion routines are complete text-based.
-%
-% Copyright 2007/2008 by Christian Feuersänger.
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-% 
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-% GNU General Public License for more details.
-% 
-% You should have received a copy of the GNU General Public License
-% along with this program.  If not, see <http://www.gnu.org/licenses/>.
-%
-%--------------------------------------------
-\ProvidesPackage{sciformat}[2008/02/17 v.0.9.4]
-\RequirePackage{pgf}[2007/01/01]
-\RequirePackage{pgfplotshelpers}[2008/02/17]
-
-% Computes a normalised floating point representation for #1 of the
-% form
-%   [+-]X.XXXXXXX*10^C
-% where 
-%   X.XXXXXX is a mantisse with first number != 0
-% and C is a count.
-%
-% This method does NOT use TeX Registers to represent the numbers! The
-% computation is COMPLETELY STRING BASED.
-% This allows numbers such at 10000000 or 5.23e-10 to be represented
-% properly, although TeX-registers would produce overflow/underflow
-% errors in these cases. 
-%
-% It is to be used to compute logs, because log(X*10^Y) = log(X) + log(10)*Y
-%
-% Arguments:
-% #1 a -possibly non-normalized- number representation. Accepted input
-%    format is
-%     [+-]XXXXX.XXXXXX
-%     [+-]XXXXX.XXXXXXeXXXX
-%     [+-]0.0000XXXXXX
-%     [+-]0.0000XXXXXXeXXXX
-%    NOT accepted input format is
-%     [+-]0000.XXXXXX	[leading zeros not supported]
-%     [+-]XXXXX.XXXXXXEXXXXX	[E notation not yet implemented]
-% #2 a macro name. \def#2{.....} will be used to assign the mantisse.
-% #3 a macro name. \def#3{.....} will be used to assign the exponent (base 10).
-%
-% Example:
-%	\def\normalize#1{%
-%		\sciparse#1\to\M\powten\E
-%		\[ #1 \mapsto \M\cdot 10^{\E} \]
-%	}
-%	\normalize{123.41251}%
-%	\normalize{3.26101452e-06}%
-%
-% REMARKS:
-%  - the mantisse will ALWAYS have a period and one following number.
-%  - Special case: the number +- 0 will always have the mantisse 0.0. The sign and
-%     the exponent is undefined.
-\def\sciparse#1\to#2\powten#3{%
-	\begingroup
-	\sciparse@impl@possibly@signed#1\to#2\powten{#3}%
-	\xdef\sciparseTMP{%
-		\noexpand\def\noexpand#2{#2}%
-		\noexpand\def\noexpand#3{#3}%
-	}%
-	\endgroup
-	\sciparseTMP
-}
-
-% Overloaded scientific parser.
-%
-% In addition to '\sciparse', this method checks for '+- 0' cases 
-% and sets #2 accordingly.
-%
-% \S #2:  will be \def'ed to one of [0,1,2] with
-% 		0 == '0',   (  \def#2{0}  )
-% 		1 == '+', 
-% 		2 == '-',
-%   -> can be used with \ifcase
-% \M #3:  will be filled with a positive mantisse (undefined in case \S=0).
-% \E #4:  the exponent basis 10 (an integer). Undefined in case \S = 0.
-%
-% Example:
-% \sciparsesign141.212\S\M\E
-% -> \S = 1, \M = 1.41212, \E =2
-%
-\def\sciparsesign#1#2#3#4{%
-	\begingroup
-	\sciparsesign@impl@possibly@signed#1\S#2\M#3\E{#4}%
-	\def\sciparseTMP{0}%
-	\ifx\sciparseTMP#2\relax
-		\def#4{0}%
-	\fi
-	\xdef\sciparseTMP{%
-		\noexpand\def\noexpand#2{#2}%
-		\noexpand\def\noexpand#3{#3}%
-		\noexpand\def\noexpand#4{#4}%
-	}%
-	\endgroup
-	\sciparseTMP
-}
-
-\def\sciparsesignsingle#1#2{%
-	\begingroup
-	\sciparsesign{#1}\sci@S\sci@M\sci@E
-	\xdef\sciparseTMP{\noexpand\scisetcomponents{\noexpand#2}{\sci@S}{\sci@M}{\sci@E}}%
-	\endgroup
-	\sciparseTMP
-}
-
-% Compares
-% x = Sign(#1) #2 * 10^#3
-% with
-% y = Sign(#4) #5 * 10^#6
-%
-% example:
-% \scimathlessthan\S\M\E\and\SS\MM\EE
-% \ifscimathlessthan
-% 	is smaller!
-% \else
-% 	is not smaller.
-% \fi
-%
-% and sets the boolean 
-%   \ifscimathlessthan :=  (x<y).
-\def\scimathlessthan#1#2#3\and#4#5#6{%
-	\scimathlessthanfalse
-	\begingroup
-	\let\S@first=\c@pgf@counta
-	\let\S@second=\c@pgf@countb
-	\S@first\expandafter=#1\relax
-	\S@second\expandafter=#4\relax
-	\ifcase\S@first
-		% x = 0 -> (x<y <=> y >0)
-		\ifnum1=\S@second
-			\aftergroup\scimathlessthantrue
-		\fi
-	\or
-		% x > 0 -> (x<y <=> ( y > 0 && |x| < |y|) )
-		\ifnum1=\S@second
-			% y>0:
-			\scimathlessthan@positive\M#2\E#3\MM#5\EE{#6}%
-		\fi
-	\or
-		% x < 0 -> (x<y <=> (y >= 0 ||   |x| > |y|) )
-		\ifnum2=\S@second
-			% 'y<0':
-			\scimathlessthan@positive\M#5\E#6\MM#2\EE{#3}%
-		\else
-			\aftergroup\scimathlessthantrue
-		\fi
-	\fi
-	\endgroup
-}
-
-\def\scimathmax#1#2#3\and#4#5#6\to#7#8#9{%
-	\scimathlessthan#1#2#3\and#4#5#6\relax
-	\ifscimathlessthan
-		\let#7=#4
-		\let#8=#5
-		\let#9=#6
-	\else
-		\let#7=#1
-		\let#8=#2
-		\let#9=#3
-	\fi
-}
-
-\def\scimathmin#1#2#3\and#4#5#6\to#7#8#9{%
-	\scimathlessthan#1#2#3\and#4#5#6\relax
-	\ifscimathlessthan
-		\let#7=#1
-		\let#8=#2
-		\let#9=#3
-	\else
-		\let#7=#4
-		\let#8=#5
-		\let#9=#6
-	\fi
-}
-
-% Takes \S, \M and \E as sign, mantisse and exponent and computes a 
-% fixed point representation for that number.
-%
-% example:
-% \S=1
-% \M=4.2
-% \E=1
-% \scitofixed\S\M\E\result
-% -> 42.0
-\def\scitofixed#1#2#3#4{%
-	\begingroup
-	\let\sci@sign=\c@pgf@counta
-	\sci@sign\expandafter=#1\relax
-	\ifnum0=\sci@sign
-		\xdef\sciparseTMP{0.0}%
-	\else
-		\expandafter\scitofixed@impl#2\E#3\END
-		\ifnum2=\sci@sign
-			\xdef\sciparseTMP{-\sciparseTMP}%
-		\fi
-	\fi
-	\endgroup
-	\let#4=\sciparseTMP
-}
-
-% Single macro SCI-representation to #2.
-\def\scitofixedsingle#1#2{%
-	\begingroup
-	\scigetcomponents{#1}\sci@S\sci@M\sci@E
-	\scitofixed\sci@S\sci@M\sci@E{#2}%
-	\global\let\sciparseTMP=#2%
-	\endgroup
-	\let#2=\sciparseTMP
-}
-
-% Takes a SINGLE macro representing a floating point and extracts
-% sign, mantisse and exponent.
-% #1: the name of the single macro.
-%     The expansion of #1 is COMPLETELY independend of associated
-%     floating point number. You can even use \def#1{foo bar}
-%     so change the meaning of #1 without affecting the number.
-% #2: will be set to #1's sign
-% #3: will be set to #1's mantisse
-% #4: will be set to #1's exponent
-%
-% @see scisetcomponents
-\def\scigetcomponents#1#2#3#4{%
-	\expandafter\let\expandafter#2\csname\string#1@S\endcsname
-	\expandafter\let\expandafter#3\csname\string#1@M\endcsname
-	\expandafter\let\expandafter#4\csname\string#1@E\endcsname
-}
-
-% Assigns sign #2, mantisse #3 and exponent #4 to a single macro
-% representing the floating point.
-%
-% #1: the target name. Will create macros #1@S, #1@M and #1@E 
-%     which will be filled with #2, #3 and #4.
-%
-% Remark:
-% It is perfectly save to use the macro name #1 for other uses since
-% only the '@{S,M,E}' - macros are used to maintain the numerical
-% information.
-%
-% @see scigetcomponents
-\def\scisetcomponents#1#2#3#4{%
-	\expandafter\edef\csname\string#1@S\endcsname{#2}%
-	\expandafter\edef\csname\string#1@M\endcsname{#3}%
-	\expandafter\edef\csname\string#1@E\endcsname{#4}%
-}
-
-% Divides or multiplies the input number by 10^#4 using an arithmetic
-% left/right shift.
-%
-% Input:
-% #1 Sign macro
-% #2 Mantisse macro
-% #3 exponent macro
-% #4 a positive or negative integer number denoting the shift.
-%
-% Example:
-% \scimathshift\S\M\E4
-\def\scimathshift#1#2#3#4{%
-	\begingroup
-	\c@pgf@counta\expandafter=#3\relax
-	\advance\c@pgf@counta by#4\relax
-	\xdef\sciparseTMP{\the\c@pgf@counta}%
-	\endgroup
-	\let#3=\sciparseTMP
-}
-
-\def\scimathshiftsingle#1#2{%
-	\begingroup
-	\expandafter\let\expandafter\E\csname\string#1@E\endcsname
-	\c@pgf@counta\expandafter=\E\relax
-	\advance\c@pgf@counta by#2\relax
-	\xdef\sciparseTMP{\the\c@pgf@counta}%
-	\endgroup
-	\expandafter\let\csname\string#1@E\endcsname\sciparseTMP%
-}
-
-
-% Rounds a fixed point number #1 to #2 digits precision and returns
-% the result into macro #3.
-%
-% This method is PURELY text based and can work with arbirtrary
-% precision (well, limited to TeX's stack size and integer size).
-\def\fixedpointround#1\prec#2\to#3{%
-	\begingroup
-	\pgfplots@toka={}%
-	\let\fp@round@next=\empty
-	\let\fp@round@prec=\c@pgf@countb
-	\let\fp@offsetbehindperiod=\c@pgf@counta
-	\let\fp@round@lastzeros=\c@pgf@countc
-	\let\fp@round@trg=#3\relax
-	\def\fp@round@input{#1}%
-	\fp@round@prec=#2\relax
-	\fp@round@lastzeros=0
-	\fp@offsetbehindperiod=-1 % means: no period found so far
-	\fixedpointround@impl@ITERATE@NODOT #1\fp@round@EOI
-	\xdef\sciparseTMP{\fp@round@trg}%
-	\endgroup
-	\let#3=\sciparseTMP
-}
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%
-% 
-% IMPL
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% \fixedpointround implementation in WORDS:
-%
-% coarse idea: 
-%    1. collect all digits/sign BEFORE the first period in REVERSE order
-%    2. then, collect UP TO \prec digits after the period in REVERSE order
-% Steps 1. and 2. lead to the digit [sign] sequence
-%    "x_{-p} x_{-p+1} ... x_{-2} x_{-1} '.' x_0 ... x_r"
-% where 'r' is the total number of digits. The integer 'p' denotes the
-% ACTUALLY collected number of digits behind the period.
-%
-% Let 'k' be the desired precision.
-%
-% There are exactly TWO cases:
-% 1. The case with p<=k and x_{-p-1} = end of input.
-% 2. The case with p=k and x_{-p-1} is a further, next character.
-%
-% Then, we do in case 1.)
-% 	discard any unused zeros at the tail of our number (possibly
-% 	including the period)
-%
-% and in case 2.)
-%   if NEXT DIGIT < 5:
-%       do exactly the same as in case 1.) above and discard any
-%       following digits.
-%   else
-%   	let q := -p
-%   	while(x_q = 9 and q<=r )
-%   		if q>=0
-%   			set x_q = '0'
-%   		else
-%   			discard digit x_q='9'
-%   		fi
-%   		++q
-%   		if q=0
-%   			discard the period 
-%   		fi
-%   	end while
-%   	if q = r+1
-%   		insert a '1'
-%   	else
-%   		set x_q = x_q + 1
-%   	fi
-%   fi
-%
-% All these loops have been implemented in spaghetti-code below.
-% Sorry, I fear its hard to understand. In principle, everything is
-% realised using more or less finite state machines (with some number
-% counting logic).
-%
-% Some comments:
-%   - The token register \pgfplots@toka is used to accumulate the REVERSED input number.
-%	- \fp@round@EOI always denotes 'END OF INPUT'.
-%	- in the second stage, we need to reverse \pgfplots@toka.
-%	  This is -again- done with \pgfplots@toka.
-
-\def\fixedpointround@impl@discard@period#1.#2\fp@round@EOI{%
-	\def\fp@round@trg{#1}%
-}
-
-\def\fixedpointround@impl@gobble@rest@and@start#1\fp@round@EOI{%
-	\fixedpointround@impl@start
-}
-\def\fixedpointround@impl@gobble@and@start\fp@round@EOI{%
-	\fixedpointround@impl@start
-}
-\def\fixedpointround@impl@gobble\fp@round@EOI{}%
-
-\def\fixedpointround@impl@start{%
-	\ifx\fp@round@next\empty
-		\ifnum\fp@offsetbehindperiod<0
-			\edef\fp@round@trg{\fp@round@input}%
-		\else
-			\ifnum\fp@offsetbehindperiod>\fp@round@prec
-				\errmessage{Internal logic error in fixedpointround at [I] - should not have happened!?}%
-			\fi
-			\fixedpointround@impl@discard@suffix@zeros
-		\fi
-	\else
-		\ifnum\fp@offsetbehindperiod=\fp@round@prec
-		\else
-			\errmessage{Internal logic error in fixedpointround at [II] - should not have happened!? I have offsetbehindperiod=\the\fp@offsetbehindperiod and prec = \the\fp@round@prec}%
-		\fi
-		\expandafter\ifnum\fp@round@next<5
-			\fixedpointround@impl@discard@suffix@zeros
-		\else
-			\multiply\fp@offsetbehindperiod by-1
-			%\edef\fp@round@trg{B\the\pgfplots@toka B}%
-			\expandafter\fixedpointround@impl@ADD@ONE\the\pgfplots@toka\fp@round@EOI
-		\fi
-	\fi
-}
-
-\def\fixedpointround@impl@ADD@ONE{%
-	\pgfplots@toka={}%
-	\fixedpointround@impl@ADD@ONE@ITERATE
-}
-\def\fixedpointround@impl@ADD@ONE@ITERATE{%
-	\@ifnextchar\fp@round@EOI{%
-		\edef\fp@round@trg{1\the\pgfplots@toka}%
-		\fixedpointround@impl@gobble
-	}{%
-		\@ifnextchar.{%
-			\fixedpointround@impl@ADD@ONE@NEXT@COLLECT
-		}{%
-			\@ifnextchar+{%
-				\fixedpointround@impl@ADD@ONE@NEXT@COLLECT
-			}{%
-				\@ifnextchar-{%
-					\fixedpointround@impl@ADD@ONE@NEXT@COLLECT
-				}{%
-					\fixedpointround@impl@ADD@ONE@NEXT
-				}%
-			}%
-		}%
-	}%
-}
-
-\def\fixedpointround@impl@ADD@ONE@ITERATE@gobble@dot.{%
-	\fixedpointround@impl@ADD@ONE@ITERATE
-}
-
-\def\fixedpointround@impl@ADD@ONE@NEXT@COLLECT#1{%
-	\pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
-	\fixedpointround@impl@ADD@ONE@ITERATE
-}
-\def\fixedpointround@impl@ADD@ONE@NEXT#1{%
-	\ifnum#1=9
-		\ifnum\fp@offsetbehindperiod<0
-			% silently DROP digit
-		\else
-			\pgfplots@toka=\expandafter{\expandafter0\the\pgfplots@toka}%
-		\fi
-		\advance\fp@offsetbehindperiod by1
-		\ifnum\fp@offsetbehindperiod=0
-			\def\fp@round@nextcmd{\fixedpointround@impl@ADD@ONE@ITERATE@gobble@dot}%
-		\else
-			\def\fp@round@nextcmd{\fixedpointround@impl@ADD@ONE@ITERATE}%
-		\fi
-	\else
-		% re-use this counter:
-		\fp@round@lastzeros=#1
-		\advance\fp@round@lastzeros by1
-		\edef\fp@round@trg{\the\fp@round@lastzeros\the\pgfplots@toka}%
-		\pgfplots@toka=\expandafter{\fp@round@trg}%
-		\def\fp@round@nextcmd{\fixedpointround@impl@REVERSE@ITERATE}%
-	\fi
-	\fp@round@nextcmd
-}
-
-
-\def\fixedpointround@impl@discard@suffix@zeros{%
-	\ifnum\fp@round@lastzeros=\fp@offsetbehindperiod
-		\expandafter\fixedpointround@impl@discard@period\fp@round@input\fp@round@EOI
-	\else
-		\ifnum\fp@round@lastzeros=0
-			\expandafter\fixedpointround@impl@REVERSE\the\pgfplots@toka\fp@round@EOI
-		\else
-			\expandafter\fixedpointround@impl@discard@suffix@zeros@ITERATE\the\pgfplots@toka\fp@round@EOI
-		\fi
-	\fi
-}
-
-% PRECONDITION: 
-%    \fp@round@lastzeros > 0
-\def\fixedpointround@impl@discard@suffix@zeros@ITERATE#1{%
-	\advance\fp@round@lastzeros by-1
-	\ifnum\fp@round@lastzeros=0
-		\def\fp@round@nextcmd{\fixedpointround@impl@REVERSE}%
-	\else
-		\def\fp@round@nextcmd{\fixedpointround@impl@discard@suffix@zeros@ITERATE}%
-	\fi
-	\fp@round@nextcmd
-}
-
-\def\fixedpointround@impl@REVERSE{%
-	\pgfplots@toka={}%
-	\fixedpointround@impl@REVERSE@ITERATE
-}
-
-\def\fixedpointround@impl@REVERSE@ITERATE{%
-	\@ifnextchar\fp@round@EOI{%
-		\edef\fp@round@trg{\the\pgfplots@toka}%
-		\fixedpointround@impl@gobble
-	}{%
-		\fixedpointround@impl@REVERSE@NEXT
-	}%
-}
-
-\def\fixedpointround@impl@REVERSE@NEXT#1{%
-	\pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
-	\fixedpointround@impl@REVERSE@ITERATE
-}
-
-\def\fixedpointround@impl@BEGIN@DOT.{%
-	\pgfplots@toka=\expandafter{\expandafter.\the\pgfplots@toka}%
-	\fp@offsetbehindperiod=0
-	\fixedpointround@impl@ITERATE@DOT
-}
-\def\fixedpointround@impl@ITERATE@DOT{%
-	\@ifnextchar\fp@round@EOI{%
-		% finished.
-		\fixedpointround@impl@gobble@and@start
-	}{%
-		\fixedpointround@impl@NEXT@DOT
-	}%
-}
-\def\fixedpointround@impl@NEXT@DOT#1{%
-	\ifnum\fp@offsetbehindperiod=\fp@round@prec
-		\def\fp@round@next{#1}%
-		\def\fp@round@nextcmd{\fixedpointround@impl@gobble@rest@and@start}%
-	\else
-		\advance\fp@offsetbehindperiod by1
-		\ifnum#1=0
-			\advance\fp@round@lastzeros by1
-		\else
-			\fp@round@lastzeros=0
-		\fi
-		\pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
-		\def\fp@round@nextcmd{\fixedpointround@impl@ITERATE@DOT}%
-	\fi
-	\fp@round@nextcmd
-}%
-
-\def\fixedpointround@impl@ITERATE@NODOT{%
-	\@ifnextchar\fp@round@EOI{%
-		\fixedpointround@impl@gobble@and@start
-	}{%
-		\@ifnextchar.{%
-			\fixedpointround@impl@BEGIN@DOT
-		}{%
-			\fixedpointround@impl@NEXT@NODOT
-		}%
-	}%
-}
-\def\fixedpointround@impl@NEXT@NODOT#1{%
-	\pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
-	\fixedpointround@impl@ITERATE@NODOT
-}%
-
-%--------------------------------------------
-% END of fixedpointround implementation.
-%--------------------------------------------
-
-\newif\ifscimathlessthan
-
-% first character MAY be + or -. This is checked, then
-% \sciparse@impl@positive will be called for the
-% absolute value. The sign is inserted afterwards.
-\def\sciparse@impl@possibly@signed#1#2\to#3\powten#4{%
-	\def\sciparseTMP{#1}%
-	\def\sciparseTMPB{-}%
-	\if\sciparseTMP\sciparseTMPB
-		\sciparse@impl@positive@possibly@noperiod#2.\to#3\powten#4\S\sciparseTMPB%
-		\edef#3{-#3}%
-	\else
-		\def\sciparseTMPB{+}%
-		\if\sciparseTMP\sciparseTMPB
-			\sciparse@impl@positive@possibly@noperiod#2.\to#3\powten#4\S\sciparseTMPB%
-		\else
-			\sciparse@impl@positive@possibly@noperiod#1#2.\to#3\powten#4\S\sciparseTMPB%
-		\fi
-	\fi
-}
-
-% the same as above, only the return value is different.
-\def\sciparsesign@impl@possibly@signed#1#2\S#3\M#4\E#5{%
-	\def\sciparseTMP{#1}%
-	\def\sciparseTMPB{-}%
-	\if\sciparseTMP\sciparseTMPB
-		\def#3{2}%
-		\sciparse@impl@positive@possibly@noperiod#2.\to#4\powten#5\S#3%
-	\else
-		\def#3{1}%
-		\def\sciparseTMPB{+}%
-		\if\sciparseTMP\sciparseTMPB
-			\sciparse@impl@positive@possibly@noperiod#2.\to#4\powten#5\S#3%
-		\else
-			\sciparse@impl@positive@possibly@noperiod#1#2.\to#4\powten#5\S#3%
-		\fi
-	\fi
-}
-
-% XXXX -> XXXX.0
-% XXXX.YYY -> XXXX.YYYY
-\def\sciparse@impl@positive@possibly@noperiod#1.#2\to#3\powten#4\S#5{%
-%\tracingmacros=2\tracingcommands=2
-	\def\sciparseTMP{#2}%
-	\ifx\sciparseTMP\empty
-		\sciparse@impl@positive@noperiod@possibly@SCI#1e\to#3\powten#4\S{#5}%
-	\else
-		\expandafter\sciparse@impl@positive\sciformat@pop@last@of@two@dots#1.#2\to#3\powten#4\S{#5}%
-	\fi
-}
-\def\sciformat@pop@last@of@two@dots#1.#2.{#1.#2}%
-
-\def\sciparse@impl@positive@noperiod@possibly@SCI#1e#2\to#3\powten#4\S#5{%
-	\def\sciparseTMP{#2}%
-	\ifx\sciparseTMP\empty
-		% this case applies to
-		% 1234  -> 1234.0
-		\sciparse@impl@positive#1.0\to#3\powten#4\S{#5}%
-	\else
-		% this case applies to
-		% 1e1  -> 1.0e1
-		% in this case, #1e#2 = 1e1e, so we have to discard a suffix 'e'.
-		\edef\sciparseTMP{#1.0e\sciformat@popsuffix@e@expansion#2}%
-		\expandafter\sciparse@impl@positive\sciparseTMP\to#3\powten#4\S{#5}%
-	\fi
-}
-
-% XXXXX.XXXXX -> X.XXXXXXX * 10^4
-% 0.0000XXXXX -> X.XXXX * 10^{-5}
-%
-% or
-% XXXX.XXXXXeYYY -> X.XXXXXX* 10^{3+YYY}
-% 0.0000XXXXeYYY -> X.XXX* 10^{-5+YYY}
-%
-% this version does not accept a sign. A period is required.
-%
-% The return value #6 will be \def'ed to '0' if the resulting mantisse is '0'.
-% Won't be touched otherwise.
-\def\sciparse@impl@positive#1#2.#3\to#4\powten#5\S#6{%
-%	\begingroup
-%	FIXME! restore variables!!
-%\tracingmacros=2\tracingcommands=2
-%\tracingmacros=0\tracingcommands=0
-	\sciparse@positive@getexisting@exponent@e#3e\preexponentto\preexponentstring\exponenttocount\c@pgf@counta
-	% will \c@pgf@counta will be initialised in the line above
-	% \c@pgf@counta=0
-	\ifnum#1=0
-		% the case 0.0000XXXX 
-		% does also handle 0.0000XXXXeXXX
-		\def\sciparseTMP{#2}%
-		\ifx\sciparseTMP\empty
-			\c@pgf@countb=0
-			\expandafter\sciformat@count@leading@zeros\preexponentstring\to\c@pgf@countb
-			\advance\c@pgf@countb by1
-			\advance\c@pgf@counta by-\c@pgf@countb
-			\edef#5{\the\c@pgf@counta}%
-			\expandafter\sciformat@assignmantisse\preexponentstring\to#4\countdownzerosfrom\c@pgf@countb\S{#6}%
-		\else
-			% the case 000.0000XXXXX
-			% is not allowed and does not make sense.
-			\errmessage{INVALID NUMBER FORMAT: leading zeros 00*.* not supported yet}%
-		\fi
-	\else
-		% the case NXXXXX.XXXXXXX
-		% or NXXXXXX.XXXXXXeXXXX
-		% where N in [1-9]
-		\sciformat@strlen#1#2\to\c@pgf@counta
-		\advance\c@pgf@counta by-1
-		\edef#4{#1.#2\preexponentstring}%
-		\edef#5{\the\c@pgf@counta}%
-	\fi
-%\tracingmacros=0\tracingcommands=0
-%	\endgroup
-}
-
-% parses scientific notation and returns the exponent and everything
-% before the exponent like
-%
-% XXXXXXXeYYYY -> \def#2{XXXXXXX}  #3=YYYY
-% or
-% XXXXXXXXe -> \def#2{XXXXXXXX} #3=0
-%
-% Examples:
-% - \sciparse@exponent@e123456e\preexponentto\M\exponenttocount\acount
-%   \M->123456
-%   \acount=0
-%   Please note that the input was 123456e -> at least 'e' is expected!
-%
-% - \sciparse@exponent@e123456e-10e\preexponentto\M\exponenttocount\acount
-%   \M->123456
-%   \acount=-10
-%   Again, the suffix 'e' is REQUIRED. This allows to reduce \ifs.
-\def\sciparse@positive@getexisting@exponent@e#1e#2\preexponentto#3\exponenttocount#4{%
-	\def#3{#1}%
-	\def\sciparseTMP{#2}%
-	\ifx\sciparseTMP\empty
-		#4=0
-	\else
-		\sciformat@popsuffix@e#2\tocount{#4}%
-	\fi
-}
-
-% XXXXXe -> #2=XXXXX where X in [+-0-9].
-\def\sciformat@popsuffix@e#1e\tocount#2{%
-	#2=#1
-}
-
-\def\sciformat@popsuffix@e@expansion#1e{%
-	#1%
-}%
-
-% 00000XXXXXX -> X.XXXXX
-% Inputs:
-% #1 = 00000XXXXXX
-% #2 a macro name
-% #3 a count in which the number of zeros plus one is contained (i.e.
-% the number of shifts).
-% #4 a macro name which will be \def'ed to '0' if the resulting
-% mantisse is 0. Won't be touched otherwise.
-\def\sciformat@assignmantisse#1\to#2\countdownzerosfrom#3\S#4{%
-	\pgfplots@toka={#1}%
-	\loop
-	\ifnum#3=1
-	\else
-		\expandafter\sciformat@popfirst\the\pgfplots@toka\to{\pgfplots@toka}%
-		\advance#3 by-1
-	\repeat
-	\edef\sciformat@assignmantisseTMP{\the\pgfplots@toka}%
-	\ifx\sciformat@assignmantisseTMP\empty
-		% The case 0.0 * 10^0
-		\def#2{0.0}%
-		\def#4{0}%
-	\else
-		\expandafter\sciformat@insertperiod\the\pgfplots@toka\to{#2}%
-	\fi
-}
-
-% XXXXXX -> X.XXXXX into #3
-\def\sciformat@insertperiod#1#2\to#3{%
-	\def\sciparseTMP{#2}%
-	\ifx\sciparseTMP\empty
-		\def#3{#1.0}%
-	\else
-		\def#3{#1.#2}%
-	\fi
-}
-
-% discards the first token.
-\def\sciformat@popfirst#1#2\to#3{%
-	#3={#2}%
-}
-
-% adds the string length of #1#2 into the count register #3.
-%
-% The register won't be initialised to zero!
-\def\sciformat@strlen#1#2\to#3{%
-	\advance#3 by1
-	\def\sciparseTMP{#2}%
-	\ifx\sciparseTMP\empty
-	\else
-		\sciformat@strlen#2\to{#3}%
-	\fi
-}
-
-% Adds the number of leadings zeros of #1#2 into the count register
-% #3.
-%
-% The register won't be initialised to zero!
-\def\sciformat@count@leading@zeros#1#2\to#3{%
-	\ifnum#1=0
-		\advance#3 by1
-		\def\sciparseTMP{#2}%
-		\ifx\sciparseTMP\empty
-		\else
-			\sciformat@count@leading@zeros#2\to{#3}%
-		\fi
-	\fi
-}
-
-
-
-
-
-
-\def\scimathlessthan@positive\M#1\E#2\MM#3\EE#4{%
-	\c@pgf@counta\expandafter=#2\relax
-	\c@pgf@countb\expandafter=#4\relax
-	\ifnum\c@pgf@counta<\c@pgf@countb
-		\aftergroup\scimathlessthantrue
-	\else
-		\ifnum\c@pgf@counta=\c@pgf@countb\relax
-			\pgfmath@xa\expandafter=#1 pt\relax
-			\pgfmath@xb\expandafter=#3 pt\relax
-			\ifdim\pgfmath@xa<\pgfmath@xb
-				\aftergroup\scimathlessthantrue
-			\fi
-		\fi
-	\fi
-}
-
-\def\scitofixed@impl#1.#2\E#3\END{%
-	\let\scitofixed@exponent=\c@pgf@countb
-	\scitofixed@exponent\expandafter=#3\relax
-	\ifnum\scitofixed@exponent<0
-		\pgfplots@toka={0.}%
-		\loop
-		\ifnum\scitofixed@exponent<-1
-			\pgfplots@toka=\expandafter{\the\pgfplots@toka 0}%
-			\advance\scitofixed@exponent by1
-		\repeat
-		\def\sciparseTMPB{#2}%
-		\def\sciparseTMPC{0}%
-		\ifx\sciparseTMPB\sciparseTMPC
-			\xdef\sciparseTMP{\the\pgfplots@toka #1}%
-		\else
-			\xdef\sciparseTMP{\the\pgfplots@toka #1#2}%
-		\fi
-	\else
-		\ifnum\scitofixed@exponent=0
-			\xdef\sciparseTMP{#1.#2}%
-		\else
-			\pgfplots@toka={#1}%
-			\scitofixed@impl@collectmantisse#2\count\scitofixed@exponent
-			\xdef\sciparseTMP{\the\pgfplots@toka}%
-		\fi
-	\fi
-}
-
-\def\scitofixed@impl@collectmantisse#1#2\count#3{%
-	\pgfplots@toka=\expandafter{\the\pgfplots@toka #1}%
-	\advance\scitofixed@exponent by-1
-	\def\sciparseTMPB{#2}%
-	\ifx\sciparseTMPB\empty
-		\loop
-		\ifnum\scitofixed@exponent>0
-			\pgfplots@toka=\expandafter{\the\pgfplots@toka 0}%
-			\advance\scitofixed@exponent by-1
-		\repeat
-	\else
-		\ifnum\scitofixed@exponent=0
-			\pgfplots@toka=\expandafter{\the\pgfplots@toka .#2}%
-		\else
-			\scitofixed@impl@collectmantisse#2\count#3%
-		\fi
-	\fi
-}
diff --git a/Master/texmf-dist/tex/plain/pgfplots/pgfplots.tex b/Master/texmf-dist/tex/plain/pgfplots/pgfplots.tex
new file mode 100644
index 00000000000..22e526ef23e
--- /dev/null
+++ b/Master/texmf-dist/tex/plain/pgfplots/pgfplots.tex
@@ -0,0 +1,49 @@
+%--------------------------------------------
+%
+% Package pgfplots
+%
+% Provides a user-friendly interface to create function plots (normal
+% plots, semi-logplots and double-logplots).
+% 
+% It is based on Till Tantau's PGF package.
+%
+% Copyright 2007/2008 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%--------------------------------------------
+% ATTENTION:
+% you MAY need one of
+%   \def\pgfsysdriver{pgfsys-dvipdfm.def}
+%   \def\pgfsysdriver{pgfsys-pdftex.def}
+%   \def\pgfsysdriver{pgfsys-dvips.def}
+%
+% BEFORE the first \input pgf.tex, \input tikz.tex or
+% \input pgfplots.tex
+% Default is
+%   'dvips' for 'tex'
+%   'pdftex' for 'pdftex'
+% -> dvipdfm needs special attention.
+%
+\input tikz.tex%
+%
+\edef\pgfplotscatcode{\the\catcode`\@}%
+\catcode`\@=11
+%
+\input pgfplots.code.tex%
+\usetikzlibrary{plotmarks}%
+%
+\catcode`\@=\pgfplotscatcode
+%
+\endinput