%--------------------------------------------
%
% 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/>.
%
%--------------------------------------------

\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
}

% 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{%
	\global\def\pgfplots@glob@TMPa{0}%
	\begingroup
	\ifcase\csname pgfplots@scaled@ticks@#1@choice\endcsname
	% CASE 0 : scaled #1 ticks=false: do nothing here.
	\or
		% CASE 1 : scaled #1 ticks=true:
		%--------------------------------
		% 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
			\edef\pgfplots@loc@TMPa{\csname pgfplots@#1min\endcsname}%
			\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@loc@TMPa}%
			\let\pgfplots@cur@min@unscaled=\pgfmathresult
			\edef\pgfplots@loc@TMPa{\csname pgfplots@#1max\endcsname}%
			\expandafter\pgfmathfloatparsenumber\expandafter{\pgfplots@loc@TMPa}%
			\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@glob@TMPa{\pgfplots@scale@ticks@above@exponent}%
		\expandafter\ifnum\pgfplots@glob@TMPa<\pgfmathfloat@b@E
			% ok, scale it:
			\multiply\pgfmathfloat@b@E by-1
			\xdef\pgfplots@glob@TMPa{\the\pgfmathfloat@b@E}%
		\else
			\xdef\pgfplots@glob@TMPa{\pgfplots@scale@ticks@below@exponent}%
			\expandafter\ifnum\pgfplots@glob@TMPa>\pgfmathfloat@b@E
				% ok, scale it:
				\multiply\pgfmathfloat@b@E by-1
				\xdef\pgfplots@glob@TMPa{\the\pgfmathfloat@b@E}%
			\else
				% no scaling necessary:
				\xdef\pgfplots@glob@TMPa{0}%
			\fi
		\fi
	\or
		% CASE 2 : scaled #1 ticks=base 10:
		%--------------------------------
		\c@pgf@counta=\csname pgfplots@scaled@ticks@#1@arg\endcsname\relax
		%\multiply\c@pgf@counta by-1
		\xdef\pgfplots@glob@TMPa{\the\c@pgf@counta}%
	\or
		% CASE 3 : scaled #1 ticks=real:
		%--------------------------------
		\pgfmathfloatparsenumber{\csname pgfplots@scaled@ticks@#1@arg\endcsname}%
		\global\let\pgfplots@glob@TMPa=\pgfmathresult
	\or
		% CASE 4 : scaled #1 ticks=manual:
		\expandafter\global\expandafter\let\expandafter\pgfplots@glob@TMPa\csname pgfplots@scaled@ticks@#1@arg\endcsname
	\fi
	\endgroup
	\expandafter\let\csname pgfplots@tick@scale@#1\endcsname=\pgfplots@glob@TMPa%
}

% x-axis tick labels for #1th tick
% #1: the axis (x,y or z)
% #2: the value
% #3,#4: coordinates for \pgfplotspointonorientedsurfaceab
% #5: ticknumber
\def\pgfplots@show@ticklabel#1#2(#3,#4)#5{%
	\begingroup%
	\csname ifpgfplots@#1ticklabel@interval\endcsname
		% Special case for the INTERVAL feature:
		% we have to do additional work here.
		\pgfmathparse{#3}%
		\edef\pgfplots@show@ticklabel@coord@x@new{\pgfmathresult}%
		\pgfmathparse{#4}%
		\edef\pgfplots@show@ticklabel@coord@y@new{\pgfmathresult}%
		%
		\pgfplots@show@ticklabel@{#1}{#2}%
		\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*(\pgfplots@show@ticklabel@coord@x + \pgfplots@show@ticklabel@coord@x@new)}%
			\let\pgfplots@show@ticklabel@coord@x=\pgfmathresult%
			\pgfmathparse{0.5*(\pgfplots@show@ticklabel@coord@y + \pgfplots@show@ticklabel@coord@y@new)}%
			\let\pgfplots@show@ticklabel@coord@y=\pgfmathresult%
			\let\ticknum=\pgfplots@show@ticklabel@num\relax%
			\let\tick=\pgfplots@show@ticklabel@tick%
			\pgfplots@show@ticklabel@@{#1}{\pgfplotspointonorientedsurfaceab{\pgfplots@show@ticklabel@coord@x}{\pgfplots@show@ticklabel@coord@y}}%
		\fi
		\xdef\pgfplots@show@ticklabel@LASTTICK{%
			\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\edef\noexpand\pgfplots@show@ticklabel@num{#5}%
		}%
	\else
		\let\ticknum=#5\relax%
		\pgfplots@show@ticklabel@{#1}{#2}%
		\pgfplots@show@ticklabel@@{#1}{\pgfplotspointonorientedsurfaceab{#3}{#4}}%
	\fi
	\endgroup
}

% #1: the axis (x,y or z)
% #2: the location where to place it.
\def\pgfplots@show@ticklabel@@#1#2{%
	% Typeset the label!
	\pgfinterruptboundingbox
		% What makes this complicated is the 'ticklabel cs' feature.
		% What we need is to compute the MAXIMUM LENGTH over each tick
		% label IN DIRECTION OF THE OUTER NORMAL.
		%
		% This needs to
		% 1. enable bounding box computation even in case of
		% 'overlay',
		% 2. projection of the bounding box in direction of the outer
		% normal,
		% 3. update of the bounding box if 'overlay' is not active.
		\begingroup
		%
		% prepare step (1.):
		\pgfkeysalso{%
			/tikz/every node/.append code={%
				\ifpgf@relevantforpicturesize
					\gdef\pgfplots@show@ticklabel@@update@BB{1}%
				\else
					\gdef\pgfplots@show@ticklabel@@update@BB{0}%
				\fi
				\pgf@relevantforpicturesizetrue
			}%
		}%
		%
		% Compute and remember the position '#2':
		\pgf@process{#2}%
		\edef\pgfplots@ticklabel@at@x{\the\pgf@x}%
		\edef\pgfplots@ticklabel@at@y{\the\pgf@y}%
		%
		% ok, generate the label!
		\node at (\pgfplots@ticklabel@at@x,\pgfplots@ticklabel@at@y) {\csname pgfplots@#1ticklabel\endcsname};%
		%
		% compute the label's dimensions, step (2.):
		\pgfplots@ticklabel@maxtickdimen@updateforcurrentpath
			{#1}
			{\pgf@x=\pgfplots@ticklabel@at@x\space\pgf@y=\pgfplots@ticklabel@at@y\space}%%
		%
		% prepare step (3.): update of bounding box:
		\if\pgfplots@show@ticklabel@@update@BB1%
			\xdef\pgfplots@glob@TMPa{%
				\pgf@xa=\the\pgf@picminx\space
				\pgf@xb=\the\pgf@picminy\space
				\pgf@ya=\the\pgf@picmaxx\space
				\pgf@yb=\the\pgf@picmaxy\space
				\noexpand\pgf@protocolsizes{\pgf@xa}{\pgf@xb}%
				\noexpand\pgf@protocolsizes{\pgf@ya}{\pgf@yb}%
				\noexpand\pgf@resetpathsizes
			}%
		\else
			\global\let\pgfplots@glob@TMPa=\relax
		\fi
		\endgroup
	\endpgfinterruptboundingbox
	\begingroup
		\pgfplots@glob@TMPa
	\endgroup
}%

% TICK LABEL DIMENSION CONTROL
%
% The following framework is supposed to accumulate the value for
% \pgfplotsvalueoflargesttickdimen.
%
% It works like this:
%
% \pgfplots@ticklabel@maxtickdimen@reset{#1}
% \pgfplots@ticklabel@maxtickdimen@prepare@for@normalvec{#1}{<normal vector>}
% ...
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% ...
% \pgfplots@ticklabel@maxtickdimen@finish{#1}
%
% -> then, \pgfplotsvalueoflargesttickdimen expands to the largest
%  distance from a tick's coordinate to its tick label bounding box in
%  direction of the outer normal vector.
\def\pgfplots@ticklabel@maxtickdimen@reset#1{%
	\expandafter\gdef\csname pgfplots@maxtickdimen@#1\endcsname{0pt}%
	\expandafter\gdef\csname pgfplots@maxtickdimen@extrashift@#1\endcsname{0pt}%
}%

% Adds the extra shift '#2' along the normal vector for axis '#1'.
\def\pgfplots@ticklabel@maxtickdimen@extrashift#1#2{%
	\begingroup
	\afterassignment\pgfplots@gobble@until@relax
	\pgf@xa=#2pt\relax
	\advance\pgf@xa by\csname pgfplots@maxtickdimen@extrashift@#1\endcsname\relax
	\expandafter\xdef\csname pgfplots@maxtickdimen@extrashift@#1\endcsname{\the\pgf@xa}%
	\endgroup
}

% Finalizes the maxtickdimen computation.
%
% This applies any extra shifts (including '#1ticklabel shift').
\def\pgfplots@ticklabel@maxtickdimen@finish#1{%
	\pgfkeysgetvalue{/pgfplots/#1ticklabel shift}\pgfmathresult
	\ifx\pgfmathresult\pgfutil@empty
	\else
		\pgfplots@ticklabel@maxtickdimen@extrashift{#1}{\pgfkeysvalueof{/pgfplots/#1ticklabel shift}}%
	\fi
	\begingroup
	\pgf@xa=\csname pgfplots@maxtickdimen@extrashift@#1\endcsname\relax
	\advance\pgf@xa by \csname pgfplots@maxtickdimen@#1\endcsname\relax
	\expandafter\xdef\csname pgfplots@maxtickdimen@#1\endcsname{\the\pgf@xa}%
	\endgroup
}%
% 
% #1: the axis (x,y or z)
% #2: the normal vector
\def\pgfplots@ticklabel@maxtickdimen@prepare@for@normalvec#1#2{%
	\pgf@process{#2}%
	\edef\pgfplots@loc@vector@to@outside{\pgf@x=\the\pgf@x\space\pgf@y=\the\pgf@y\space}%
	% Identify the corner point of the ticklabel bounding box which
	% shall be used: 
	\ifdim\pgf@x>0sp
		\ifdim\pgf@y>0sp
			% NORTH EAST
			\def\pgfplots@loc@ticklabel@bb@corner{\pgf@x=\pgf@picmaxx\pgf@y=\pgf@picmaxy}%
		\else
			% SOUTH EAST
			\def\pgfplots@loc@ticklabel@bb@corner{\pgf@x=\pgf@picmaxx\pgf@y=\pgf@picminy}%
		\fi
	\else
		\ifdim\pgf@y>0sp
			% NORTH WEST
			\def\pgfplots@loc@ticklabel@bb@corner{\pgf@x=\pgf@picminx\pgf@y=\pgf@picmaxy}%
		\else
			% SOUTH WEST
			\def\pgfplots@loc@ticklabel@bb@corner{\pgf@x=\pgf@picminx\pgf@y=\pgf@picminy}%
		\fi
	\fi
}%

% #1: the axis (x,y or z)
% #2: the point from where dimension shall be computed (the 'at'
% argument of the tick label)
\def\pgfplots@ticklabel@maxtickdimen@updateforcurrentpath#1#2{%
	\pgfplotsscalarproductofvectors
		{\pgfplots@loc@vector@to@outside}%
		{\pgfpointdiff
			{#2}%
			{\pgfplots@loc@ticklabel@bb@corner}}%
	\ifdim\pgf@x>\csname pgfplots@maxtickdimen@#1\endcsname\relax
		\expandafter\xdef\csname pgfplots@maxtickdimen@#1\endcsname{\the\pgf@x}%
	\fi
}%

% Expands to the largest distance of a tick position to its tick label
% bounding box in direction of the outer unit normal vector.
%
% It does also include the value of the 'ticklabel shift' key.
%
% This function assumes that
% \pgfplots@ticklabel@maxtickdimen@reset{#1}
% \pgfplots@ticklabel@maxtickdimen@prepare@for@normalvec{#1}{<normal vector>}
% ...
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% \pgfplots@ticklabel@maxtickdimen@updateforcurrentpath{#1}
% ...
% \pgfplots@ticklabel@maxtickdimen@finish{#1}
% has been invoked completely.
%
% #1: either x,y or z. It denotes the axis for which the ticks are
% requested.
\def\pgfplotsvalueoflargesttickdimen#1{%
	\csname pgfplots@maxtickdimen@#1\endcsname
}%

% Just like \pgfplotsqpointoutsideofaxis, but this one here uses the
% axis on which tick labels will be drawn.
%
% #1: one of x, y or z.
% #2: the coordinate on the tick axis designated by '#1'.
% #3: a scale (a dimen) in which the point is moved in direction of
% the outward normal vector of the axis.
%
% @see \pgfplotsqpointoutsideofaxis
\def\pgfplotsqpointoutsideofticklabelaxis#1#2#3{%
	\pgfplotsqpointoutsideofaxis{\csname pgfplots@#1ticklabelaxisspec\endcsname}{#2}{#3}%
}%
\def\pgfplotsqpointoutsideofticklabelaxisrel#1#2#3{%
	\pgfplotsqpointoutsideofaxisrel{\csname pgfplots@#1ticklabelaxisspec\endcsname}{#2}{#3}%
}%
\def\pgfplotsqpointoutsideofticklabelaxistransformed#1#2#3{%
	\pgfplotsqpointoutsideofaxistransformed{\csname pgfplots@#1ticklabelaxisspec\endcsname}{#2}{#3}%
}%

% Expands to the three-character-identification for the axis
% containing tick labels for axis #1.
%
% #1: either x, y or z.
\def\pgfplotsticklabelaxisspec#1{\csname pgfplots@#1ticklabelaxisspec\endcsname}%

% The unit outer normal vector for axis #1.
% #1: one of x, y or z.
\def\pgfplotspointouternormalvectorofticklabelaxis#1{%
	\pgfplotspointouternormalvectorofaxis{\csname pgfplots@#1ticklabelaxisspec\endcsname}%
}

% 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}%
		\ifcase\csname pgfplots@scaled@ticks@#1@choice\endcsname
		\or
			\expandafter\pgfmathfloatshift@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
		\or
			\expandafter\pgfmathfloatshift@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
		\or
			\expandafter\pgfmathfloatdivide@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
		\or
			% scaled #1 ticks=manual. Invoke manual tick scaling code:
			\expandafter\let\expandafter\pgfplots@loc@TMPa\csname pgfplots@tick@scale@#1\endcsname
			\expandafter\pgfplots@loc@TMPa\expandafter{\pgfmathresult}%
		\fi
		% .. and this here provides \tick as fixed point repr:
		\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
		\let\tick=\pgfmathresult
	\else
		\edef\tick{#2}%
		\pgfplots@if{pgfplots@#1islinear}{%
			\ifnum\csname pgfplots@scaled@ticks@#1@choice\endcsname=0
			\else
				\pgfmathfloatparsenumber{#2}%
				\ifnum\csname pgfplots@scaled@ticks@#1@choice\endcsname=3
					\expandafter\pgfmathfloatdivide@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
				\else
					\expandafter\pgfmathfloatshift@\expandafter{\pgfmathresult}{\csname pgfplots@tick@scale@#1\endcsname}%
				\fi
				\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
				\let\tick=\pgfmathresult
			\fi
		}{}%
	\fi
	\pgfkeysgetvalue{/pgfplots/#1 coord inv trafo/.@cmd}\pgfplots@loc@TMPa
	\ifx\pgfplots@loc@TMPa\pgfplots@empty@command@key
	\else
		\let\pgfmathresult=\tick%
		\expandafter\pgfplots@loc@TMPa\expandafter{\tick}\pgfeov
		\let\tick=\pgfmathresult
	\fi
}%

\def\pgfplots@user@ticklabel@list@x{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@xticklabels\to\tick
	\tick
}
\def\pgfplots@user@ticklabel@list@y{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@yticklabels\to\tick
	\tick
}
\def\pgfplots@user@ticklabel@list@z{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@zticklabels\to\tick
	\tick
}
\def\pgfplots@user@extra@ticklabel@list@x{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@extra@xticklabels\to\tick
	\tick
}
\def\pgfplots@user@extra@ticklabel@list@y{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@extra@yticklabels\to\tick
	\tick
}
\def\pgfplots@user@extra@ticklabel@list@z{%
	\pgfplotslistselectorempty\ticknum\of\pgfplots@extra@zticklabels\to\tick
	\tick
}

% Check if a label does not cross the x-axis
\def\pgfplots@ytick@check@tickshow{%
	\pgfplots@tickshowtrue
	\if\pgfplots@yaxislinesnum2% center
		\ifcase\pgfplots@xaxislinesnum\relax
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@ymin@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@ymax@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@ymin@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{%
				}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@logical@ZERO@y pt}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@ymax@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\fi
	\fi
}
\def\pgfplots@ztick@check@tickshow{%
	\pgfplots@tickshowtrue
	\if\pgfplots@zaxislinesnum2% center
		\pgfplotsmath@ifapproxequal@dim
			{\pgfplots@tmpa}{\pgfplots@logical@ZERO@z pt}
			{\pgfplots@loc@tick@placement@tolerance}
			{%
				\pgfplots@tickshowfalse
			}{}%
	\fi
}%

% Fills the macros
%   \pgfplots@tick@beg@a \pgfplots@tick@end@a
%   \pgfplots@tick@beg@b \pgfplots@tick@end@b
% with coordinates such that 
%   (\pgfplots@tick@beg@a,\pgfplots@tmpa) -- (\pgfplots@tick@end@a,\pgfplots@tmpa)
% produces a correct tick line. 
%
% The '@b' variant is only used in case of \pgfplots@ytickposnum = 0
%
% #1 : the current axis (x or y).
% #2 : the current tick width
%
\def\pgfplots@prepare@tick@offsets@for@#1#2{%
	% FIXME : this stuff was ok for 2D.
	% For 3D, it works only for the cases of boxed axes or centered
	% axis lines.
	\ifcase\csname pgfplots@#1tickposnum\endcsname\relax
		% both
		%(\pgfplots@xcoordminTEX-\pgfplots@tick@offset, \pgfplots@tmpa) -- ++( #2, 0pt)
		\edef\pgfplots@tick@beg@a{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}%
		\pgfmathsubtract@{\pgfplots@tick@beg@a}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@a=\pgfmathresult
		\pgfmathadd@{\pgfplots@tick@beg@a}{#2}%
		\let\pgfplots@tick@end@a=\pgfmathresult
		%
		%(\pgfplots@xcoordmaxTEX+\pgfplots@tick@offset, \pgfplots@tmpa)	-- ++(-#2, 0pt)
		\edef\pgfplots@tick@beg@b{\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname}%
		\pgfmathadd@{\pgfplots@tick@beg@b}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@b=\pgfmathresult
		\pgfmathsubtract@{\pgfplots@tick@beg@b}{#2}%
		\let\pgfplots@tick@end@b=\pgfmathresult%
	\or
		% left
		% (\pgfplots@xcoordminTEX-\pgfplots@tick@offset, \pgfplots@tmpa) -- ++( #2, 0pt);
		\edef\pgfplots@tick@beg@a{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}%
		\pgfmathsubtract@{\pgfplots@tick@beg@a}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@a=\pgfmathresult
		\pgfmathadd@{\pgfplots@tick@beg@a}{#2}%
		\let\pgfplots@tick@end@a=\pgfmathresult
	\or
		% center
		% (\pgfplots@ZERO@x      -\pgfplots@tick@offset, \pgfplots@tmpa) -- ++( #2, 0pt);
		\pgfmathsubtract@{\csname pgfplots@logical@ZERO@\pgfplotspointonorientedsurfaceB \endcsname}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@a=\pgfmathresult
		\pgfmathadd@{\pgfplots@tick@beg@a}{#2}%
		\let\pgfplots@tick@end@a=\pgfmathresult%
	\or
		% right
		% (\pgfplots@xcoordmaxTEX+\pgfplots@tick@offset, \pgfplots@tmpa)	-- ++(-#2, 0pt);
		\edef\pgfplots@tick@beg@b{\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname}%
		\pgfmathadd@{\pgfplots@tick@beg@b}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@b=\pgfmathresult
		\pgfmathsubtract@{\pgfplots@tick@beg@b}{#2}%
		\let\pgfplots@tick@end@b=\pgfmathresult%
	\else
		% FALL BACK. never used, I guess?
		% (\pgfplots@xcoordminTEX-\pgfplots@tick@offset, \pgfplots@tmpa) -- ++( #2, 0pt);
		\edef\pgfplots@tick@beg@a{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}%
		\pgfmathsubtract@{\pgfplots@tick@beg@a}{\pgfplots@tick@offset}%
		\let\pgfplots@tick@beg@a=\pgfmathresult
		\pgfmathadd@{\pgfplots@tick@beg@a}{#2}%
		\let\pgfplots@tick@end@a=\pgfmathresult
	\fi
}%


\newif\ifpgfplots@needsminorloop

\def\pgfplots@draw@tick@scale@label@for#1{%
	\csname ifpgfplots@#1islinear\endcsname
		\begingroup
			\def\pgfplots@temp@isbaseten{0}%
			\ifcase\csname pgfplots@scaled@ticks@#1@choice\endcsname
				\global\let\pgfplots@glob@TMPa=\pgfutil@empty
			\or
				\xdef\pgfplots@glob@TMPa{\csname pgfplots@tick@scale@#1\endcsname}%
				\def\pgfplots@temp@isbaseten{1}%
			\or
				\xdef\pgfplots@glob@TMPa{\csname pgfplots@tick@scale@#1\endcsname}%
				\def\pgfplots@temp@isbaseten{1}%
			\or
				\xdef\pgfplots@glob@TMPa{\csname pgfplots@tick@scale@#1\endcsname}%
				% real:
			\or
				% manual:
				\global\def\pgfplots@glob@TMPa{dummyargument}%
			\fi
			\if1\pgfplots@temp@isbaseten
				\expandafter\c@pgf@counta\pgfplots@glob@TMPa\relax
				\multiply\c@pgf@counta by-1
				\ifnum\c@pgf@counta=0\relax
					\global\let\pgfplots@glob@TMPa=\pgfutil@empty
				\else
					\xdef\pgfplots@glob@TMPa{\the\c@pgf@counta}%
				\fi
			\fi
		\endgroup
		\ifx\pgfplots@glob@TMPa\pgfutil@empty
		\else
			\begingroup
			\pgfkeysgetvalue{/pgfplots/#1tick scale label code/.@cmd}\pgfplots@loc@TMPa
			\ifx\pgfplots@loc@TMPa\pgfplots@empty@command@key
			\else
				\edef\pgfplots@tick@scale@labels{\noexpand\pgfplots@invoke@pgfkeyscode{/pgfplots/#1tick scale label code/.@cmd}{\pgfplots@glob@TMPa}}%
				%
				\pgfplots@change@pgfpoints@to@descriptioncs
				%
				\node[%
					/pgfplots/every tick label,%
					/pgfplots/every #1 tick label,%
					/pgfplots/every #1 tick scale label]
				{\pgfplots@tick@scale@labels};
			\fi
			\endgroup
		\fi
	\fi
}

% Check if the current tick position, stored in \pgfplots@tmpa, 
% does not cross the y-axis.
%
% This is just a special case for centered axis lines.
\def\pgfplots@xtick@check@tickshow{%
	\pgfplots@tickshowtrue
	\if\pgfplots@xaxislinesnum2% center
		\ifcase\pgfplots@yaxislinesnum\relax
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@xmin@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@xmax@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@xmin@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@logical@ZERO@x pt}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\or
			\pgfplotsmath@ifapproxequal@dim
				{\pgfplots@tmpa}{\pgfplots@xmax@reg}
				{\pgfplots@loc@tick@placement@tolerance}
				{%
					\pgfplots@tickshowfalse
				}{}%
		\fi
	\fi
}

% Draws extra ticks including grid lines, tick lines and tick labels
% along the current oriented surface.
%
% See \pgfplots@drawticklines@onorientedsurf@ for a description of the
% oriented surface.
%
% #1 : tick position list
\def\pgfplots@draw@extra@ticks@onorientedsurf{%
	\expandafter\pgfplots@draw@extra@ticks@onorientedsurf@\pgfplotspointonorientedsurfaceA
}%
% #1: axis (x or y)
% #2: tick position list
\def\pgfplots@draw@extra@ticks@onorientedsurf@#1#2{%
	\begingroup
	\def\pgfplots@scaled@ticks@x@choice{0}%
	\def\pgfplots@scaled@ticks@y@choice{0}%
	\def\pgfplots@scaled@ticks@z@choice{0}%
	\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
%	\pgfplotsset{/pgfplots/every extra #1 tick}%
	% use a scope here such that line width and draw color can be set.
	\scope[/pgfplots/.cd,/pgfplots/every extra #1 tick]
	\pgfplots@prepare@tick@coordlists@for{#1}{#2}%
	\pgfplots@drawgridlines@onorientedsurf%
	\pgfplots@drawticklines@onorientedsurf%
	\pgfplots@drawticklabels@onorientedsurf%
	\endscope
	\endgroup
}

% Computes final major and minor tick positions into global lists
% \pgfplots@prepared@tick@positions@major@x
% and
% \pgfplots@prepared@tick@positions@minor@x.
%
% The major tick list contains tuples (canvas position,logical position)
% while the minor tick list contains just the canvas position.
%
% #1: the axis
% #2: the tick list.
%
% PRECONDITION:  
% 	- \pgfplots@determinedefaultvalues has been executed.
% 		That means particularly that \pgfplots@[xy][min,max] are available in TeX point
% 		range (after datascaling and logs).
% POSTCONDITION:
% 	- the lists
% 		\pgfplots@prepared@tick@positions@major@x
% 		\pgfplots@prepared@tick@positions@major@tickindices@x
% 		\pgfplots@prepared@tick@positions@minor@x
% 	  are ready.
\def\pgfplots@prepare@tick@coordlists@for#1#2{%
	\begingroup
	\expandafter\let\expandafter\ifpgfplots@islinear\csname ifpgfplots@#1islinear\endcsname
	\expandafter\let\expandafter\ifpgfplots@minorticks\csname ifpgfplots@#1minorticks\endcsname
	\expandafter\let\expandafter\ifpgfplots@minorgrids\csname ifpgfplots@#1minorgrids\endcsname
	% these lists need to be global such that I can fill them inside
	% of \foreach statements. And, yes: I have also added a TeX group
	% on my own (but that's not the problem).
	\global\pgfplotslistnewempty\pgfplots@prepared@tick@positions@major
	\global\pgfplotslistnewempty\pgfplots@prepared@tick@positions@major@tickindices
	\global\pgfplotslistnewempty\pgfplots@prepared@tick@positions@minor
	%
	\afterassignment\pgfplots@gobble@until@relax
	\pgfplots@tmpa=\pgfkeysvalueof{/pgfplots/#1tick placement tolerance}pt\relax
	\pgfplots@tmpa=\csname pgfplots@#1@inverseveclength\endcsname\pgfplots@tmpa
	\edef\pgfplots@loc@tick@placement@tolerance{\the\pgfplots@tmpa}%
	%
	\advance\csname pgfplots@#1min@reg\endcsname by-\pgfplots@tmpa
	\advance\csname pgfplots@#1max@reg\endcsname by\pgfplots@tmpa
	%
	\edef\pgfplots@loc@TMPa{#2}%
	\ifx\pgfplots@loc@TMPa\pgfutil@empty
	\else
		\ifpgfplots@minorticks
			\pgfplots@needsminorlooptrue
		\else
			\ifpgfplots@minorgrids
				\pgfplots@needsminorlooptrue
			\else
				\pgfplots@needsminorloopfalse
			\fi
		\fi
		\ifpgfplots@needsminorloop
			\ifpgfplots@islinear
				\expandafter\let\expandafter\pgfplots@minor@tick@num\csname pgfplots@minor@#1tick@num\endcsname
				\begingroup
				\c@pgf@counta=\pgfplots@minor@tick@num\relax
				\advance\c@pgf@counta by1\relax
				\pgfplots@tmpa=\csname pgfplots@tick@distance@#1\endcsname pt %
				\divide\pgfplots@tmpa by\c@pgf@counta
				\edef\pgfmathresult{\pgf@sys@tonumber{\pgfplots@tmpa}}%
				\pgfmath@smuggleone\pgfmathresult
				\endgroup
				\let\pgfplots@minor@tick@dist=\pgfmathresult
			\else
				\def\pgfplots@minor@tick@num{9}%
			\fi
		\fi
		%
		% Prepare the [xy]tick[min|max] key processing:
		\let\pgfplots@checktickminmax=\pgfutil@empty
		\expandafter\ifx\csname pgfplots@#1tickmin\endcsname\pgfutil@empty
		\else
			\expandafter\def\expandafter\pgfplots@checktickminmax\expandafter{%
				\pgfplots@checktickminmax
				\ifdim\pgfplots@tmpa<\csname pgfplots@#1tickmin\endcsname pt
					\pgfplots@tickshowfalse
				\fi
			}%
		\fi
		\expandafter\ifx\csname pgfplots@#1tickmax\endcsname\pgfutil@empty
		\else
			\expandafter\def\expandafter\pgfplots@checktickminmax\expandafter{%
				\pgfplots@checktickminmax
				\ifdim\pgfplots@tmpa>\csname pgfplots@#1tickmax\endcsname pt
					\pgfplots@tickshowfalse
				\fi
			}%
		\fi
		%
		%
		\gdef\pgfplots@glob@TMPa{0}%
		\foreach \x in {#2} {%
			\let\pgfplots@ticknum=\pgfplots@glob@TMPa
			%
			\pgfplots@tmpa=\x pt %
			\csname pgfplots@#1tick@check@tickshow\endcsname
			\pgfplots@checktickminmax
			%
			\ifpgfplots@tickshow
				\ifdim\pgfplots@tmpa<\csname pgfplots@#1min@reg\endcsname
				\else
					\ifdim\pgfplots@tmpa>\csname pgfplots@#1max@reg\endcsname
					\else
						\expandafter\pgfplotslistpushbackglobal\x\to\pgfplots@prepared@tick@positions@major
						\expandafter\pgfplotslistpushbackglobal\pgfplots@ticknum\to\pgfplots@prepared@tick@positions@major@tickindices
					\fi
				\fi
			\fi
			% X-Axis ticks bottom and top
			% in log:
			%  log( i*10^k ) = log\pgfplots@i + k\log10 -> draw ticks for i=1..9
			\ifpgfplots@needsminorloop
				\foreach \pgfplots@i in {1,...,\pgfplots@minor@tick@num} {%
					\begingroup
					\ifpgfplots@islinear
						\pgfplots@tmpa=\pgfplots@minor@tick@dist pt %
						\pgfplots@tmpa=\pgfplots@i\pgfplots@tmpa
					\else
						\pgfplots@tmpa=\csname pgfplotsmathlogi@#1\endcsname\pgfplots@i pt %
					\fi
					\edef\pgfmathresult{\the\pgfplots@tmpa}%
					\pgfmath@smuggleone\pgfmathresult
					\endgroup
					\advance\pgfplots@tmpa by\pgfmathresult\relax
					\pgfplots@tickshowtrue
					\pgfplots@checktickminmax
					\ifpgfplots@tickshow
						\ifdim\pgfplots@tmpa<\csname pgfplots@#1min@reg\endcsname
						\else
							\ifdim\pgfplots@tmpa>\csname pgfplots@#1max@reg\endcsname
							\else
								\edef\pgfmathresult{\pgf@sys@tonumber{\pgfplots@tmpa}}%
								\expandafter\pgfplotslistpushbackglobal\pgfmathresult\to\pgfplots@prepared@tick@positions@minor
							\fi
						\fi
					\fi
				}%
			\fi
			\pgfplotsutil@advancestringcounter\pgfplots@ticknum
			% carry \ticknum outside of this scope:
			\global\let\pgfplots@glob@TMPa=\pgfplots@ticknum
		}%
	\fi
	\endgroup
	\expandafter\let\csname pgfplots@prepared@tick@positions@minor@#1\endcsname=\pgfplots@prepared@tick@positions@minor
	\expandafter\let\csname pgfplots@prepared@tick@positions@major@#1\endcsname=\pgfplots@prepared@tick@positions@major
	\expandafter\let\csname pgfplots@prepared@tick@positions@major@tickindices@#1\endcsname=\pgfplots@prepared@tick@positions@major@tickindices
	\global\let\pgfplots@prepared@tick@positions@major=\relax
	\global\let\pgfplots@prepared@tick@positions@major@tickindices=\relax
	\global\let\pgfplots@prepared@tick@positions@minor=\relax
}%

% Draws grid lines at the a-positions of the currently set oriented
% surface.
%
% Tick positions are taken out of the already precomputed list
% \pgfplots@prepared@tick@positions@major@...
%
% See \pgfplots@drawticklines@onorientedsurf@ for a description of the
% oriented surface.
%
% #1 : the verbatim axis name (either 'x' or 'y')
% #2 : the index of the axis  (either 0 or 1)
\def\pgfplots@drawgridlines@onorientedsurf{%
	\expandafter\pgfplots@drawgridlines@onorientedsurf@\pgfplotspointonorientedsurfaceA
}%
\def\pgfplots@drawgridlines@onorientedsurf@#1{%
	\pgfplots@if{pgfplots@shownothingof@\pgfplotspointonorientedsurfaceB}{%
		\relax
	}{%
		\begingroup
		\pgfplots@ifgridlines@onorientedsurf@should@be@drawn{%
			\expandafter\let\expandafter\pgfplots@prepared@tick@positions@major@\csname pgfplots@prepared@tick@positions@major@#1\endcsname
			\expandafter\let\expandafter\pgfplots@prepared@tick@positions@minor@\csname pgfplots@prepared@tick@positions@minor@#1\endcsname
			\pgfplots@loop@CONTINUEfalse
			\pgfplots@if{pgfplots@#1majorgrids}{\pgfplots@loop@CONTINUEtrue}{}%
			\pgfplots@if{pgfplots@#1minorgrids}{\pgfplots@loop@CONTINUEtrue}{}%
			\ifpgfplots@loop@CONTINUE
				\scope
				\pgfplots@drawtickgridlines@INSTALLCLIP@onorientedsurf#1
				%
				\pgfplots@if{pgfplots@#1minorgrids}{%
					\draw[%
						/pgfplots/every axis grid,
						/pgfplots/every minor grid,
						/pgfplots/every axis #1 grid,
						/pgfplots/every minor #1 grid]%
					\pgfextra
					\pgfplotslistforeach\pgfplots@prepared@tick@positions@minor@\as\pgfplots@curgridpos{%
						\pgfpathmoveto{\pgfplotspointonorientedsurfaceab{\pgfplots@curgridpos}{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}}%
						\pgfpathlineto{\pgfplotspointonorientedsurfaceab{\pgfplots@curgridpos}{\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname}}%
					}%
					\endpgfextra;
				}{}%
				%
				\pgfplots@if{pgfplots@#1majorgrids}{%
					\draw[%
						/pgfplots/every axis grid,
						/pgfplots/every major grid,
						/pgfplots/every axis #1 grid,
						/pgfplots/every major #1 grid]%
					\pgfextra
					\pgfplotslistforeach\pgfplots@prepared@tick@positions@major@\as\pgfplots@curgridpos{%
						\pgfpathmoveto{\pgfplotspointonorientedsurfaceab{\pgfplots@curgridpos}{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}}%
						\pgfpathlineto{\pgfplotspointonorientedsurfaceab{\pgfplots@curgridpos}{\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname}}%
					}%
					\endpgfextra;
				}{}%
				%
				\endscope
			\fi
		}{}%
		\endgroup
	}%
}

% Draws ticks on the currently active "oriented surface".
%
% The oriented surface is two dimensional and has been initialised
% with \pgfplotspointonorientedsurfaceabsetupfor*** somehow.
%
% The idea is now the following: 
% - the tick positions change along the FIRST coordinate of this
%   surface:
%
%   x ---- x ---- x ---- x
%   --> FIRST -->
%
% - the tick lines are drawn along the SECOND coordinate of this
%   surface:
%
%   | ---- | ---- | ---- |   | SECOND
%   |      |      |      |   v
%
% for example, 
% \pgfplotspointonorientedsurfaceab@setupfor@xyZ{1}
% \pgfplots@drawticklines@onorientedsurf
% will draw ticks at x-positions designated by \pgfplots@xtick. The
% small tick lines will be drawn along the y axis.  For each processed
% point, the z coordinate will be fixed to '1'.
%
% Another example:
% \pgfplotspointonorientedsurfaceab@setupfor@yxZ{-1}
% \pgfplots@drawticklines@onorientedsurf
% will draw ticks at y-positions designated by \pgfplots@ytick. The
% small tick lines will be drawn along the x axis.  For each processed
% point, the z coordinate will be fixed to '-1'.
% 
% Tick positions are taken out of the already precomputed list
% \pgfplots@prepared@tick@positions@major@...
\def\pgfplots@drawticklines@onorientedsurf{%
	\expandafter\pgfplots@drawticklines@onorientedsurf@\pgfplotspointonorientedsurfaceA
}%

% Avoids tick lines which are too thick by introducing a clipping
% region. Tick lines (and grid lines) won't extend to the left or
% right of axis #1.
\def\pgfplots@drawtickgridlines@INSTALLCLIP@onorientedsurf#1{%
	\pgfinterruptboundingbox%
	\begingroup
		\pgf@xa=5cm
		\edef\pgfplots@loc@TMPc{\pgf@sys@tonumber{\pgf@xa}}%
		% the case ||e_b|| == 0 should never happen here! Should be
		% caught before entering this routine.
		\pgfmathmultiply@{\pgfplots@loc@TMPc}{\csname pgfplots@\pgfplotspointonorientedsurfaceB @inverseveclength\endcsname}%
		\let\pgfplots@loc@LENGTH=\pgfmathresult
		\pgfmathsubtract@{\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname}{\pgfplots@loc@LENGTH}%
		\let\pgfplots@loc@MIN=\pgfmathresult
		\pgfmathadd@{\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname}{\pgfplots@loc@LENGTH}%
		\let\pgfplots@loc@MAX=\pgfmathresult
		\pgfpathmoveto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1min\endcsname}{\pgfplots@loc@MIN}}%
		\pgfpathlineto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1max\endcsname}{\pgfplots@loc@MIN}}%
		\pgfpathlineto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1max\endcsname}{\pgfplots@loc@MAX}}%
		\pgfpathlineto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1min\endcsname}{\pgfplots@loc@MAX}}%
		\pgfusepath{clip}%
	\endgroup
	\endpgfinterruptboundingbox%
}%

\def\pgfplots@drawticklines@onorientedsurf@#1{%
	\pgfplots@if{pgfplots@shownothingof@\pgfplotspointonorientedsurfaceB}{%
		\relax
	}{%
		\scope
		\pgfplots@ifaxisline@B@onorientedsurf@should@be@drawn{0}{%
			\def\pgfplots@drawticklines@for@placecomputedtick@LOWEROK{1}%
		}{%
			\def\pgfplots@drawticklines@for@placecomputedtick@LOWEROK{0}%
		}%
		\pgfplots@ifaxisline@B@onorientedsurf@should@be@drawn{1}{%
			\def\pgfplots@drawticklines@for@placecomputedtick@UPPEROK{1}%
		}{%
			\def\pgfplots@drawticklines@for@placecomputedtick@UPPEROK{0}%
		}%
		\if\pgfkeysvalueof{/pgfplots/\pgfplotspointonorientedsurfaceB\space dir/value}r%
			% local special handling for reversed axes: exchange
			% meaning of 'left' and 'right' here.
			%
			% the rest of the pgfplots code does that automatically because
			% there, tickposnum is relevant to determine the axes
			% which contains tick labels. And this algorithm checks
			% for reversed axes implicitly.
			%
			\if1\csname pgfplots@\pgfplotspointonorientedsurfaceA tickposnum\endcsname
				\expandafter\def\csname pgfplots@\pgfplotspointonorientedsurfaceA tickposnum\endcsname{3}%
			\else
				\if3\csname pgfplots@\pgfplotspointonorientedsurfaceA tickposnum\endcsname
					\expandafter\def\csname pgfplots@\pgfplotspointonorientedsurfaceA tickposnum\endcsname{1}%
				\fi
			\fi
		\fi
		\ifcase\csname pgfplots@\pgfplotspointonorientedsurfaceA tickposnum\endcsname\relax
			% both
		\or
			% lower
			\def\pgfplots@drawticklines@for@placecomputedtick@UPPEROK{0}%
		\or
			% center
			\def\pgfplots@drawticklines@for@placecomputedtick@UPPEROK{0}%
		\or
			% upper
			\def\pgfplots@drawticklines@for@placecomputedtick@LOWEROK{0}%
		\else
			% never used?
			\def\pgfplots@drawticklines@for@placecomputedtick@UPPEROK{0}%
		\fi
		\begingroup
			% Assemble the \pgfplots@drawticklines@for@placecomputedtick
			% command.
			\let\E=\noexpand
			\xdef\pgfplots@drawticklines@for@placecomputedtick{%
				\if\pgfplots@drawticklines@for@placecomputedtick@LOWEROK1%
					\E\pgfpathmoveto{\E\pgfplotspointonorientedsurfaceab{\E\pgfplots@curtickpos}{\E\pgfplots@tick@beg@a}}%
					\E\pgfpathlineto{\E\pgfplotspointonorientedsurfaceab{\E\pgfplots@curtickpos}{\E\pgfplots@tick@end@a}}%
				\fi
				\if\pgfplots@drawticklines@for@placecomputedtick@UPPEROK1%
					\E\pgfpathmoveto{\E\pgfplotspointonorientedsurfaceab{\E\pgfplots@curtickpos}{\E\pgfplots@tick@beg@b}}%
					\E\pgfpathlineto{\E\pgfplotspointonorientedsurfaceab{\E\pgfplots@curtickpos}{\E\pgfplots@tick@end@b}}%
				\fi
			}%
		\endgroup
		\expandafter\let\expandafter\pgfplots@prepared@tick@positions@major@\csname pgfplots@prepared@tick@positions@major@#1\endcsname
		\expandafter\let\expandafter\pgfplots@prepared@tick@positions@minor@\csname pgfplots@prepared@tick@positions@minor@#1\endcsname
		\pgfplots@drawtickgridlines@INSTALLCLIP@onorientedsurf#1
		%
		\pgfplots@if{pgfplots@#1minorticks}{%
			\draw[%
				/pgfplots/every tick,
				/pgfplots/every minor tick,
				/pgfplots/every #1 tick,
				/pgfplots/every minor #1 tick]%
			\pgfextra
			\pgfmathparse{\pgfplots@subtickwidth}%
			\let\pgfplots@subtickwidth@=\pgfmathresult
			\pgfmathmultiply@{\pgfplots@subtickwidth@}{\csname pgfplots@\pgfplotspointonorientedsurfaceB @inverseveclength\endcsname}%
			\let\pgfplots@subtickwidth@=\pgfmathresult
			\let\pgfplots@subtickwidth=\pgfmathresult
			\ifcase\csname pgfplots@#1tickalignnum\endcsname\relax
				\def\pgfplots@tick@offset{0}%
			\or
				\let\pgfplots@tick@offset=\pgfplots@subtickwidth@%
			\or
				\pgfmathmultiply@{0.5}{\pgfplots@subtickwidth@}%
				\let\pgfplots@tick@offset=\pgfmathresult%
			\fi
			\pgfplots@prepare@tick@offsets@for@{#1}{\pgfplots@subtickwidth@}%
			\pgfplotslistforeach\pgfplots@prepared@tick@positions@minor@\as\pgfplots@curtickpos{%
				\pgfplots@drawticklines@for@placecomputedtick
			}%
			\endpgfextra;
		}{}%
		%
		\pgfplots@if{pgfplots@#1majorticks}{%
			\draw[%
				/pgfplots/every tick,
				/pgfplots/every major tick,
				/pgfplots/every #1 tick,
				/pgfplots/every major #1 tick]%
			\pgfextra
			\pgfmathparse{\pgfplots@tickwidth}%
			\let\pgfplots@tickwidth@=\pgfmathresult
			\pgfmathmultiply@{\pgfplots@tickwidth@}{\csname pgfplots@\pgfplotspointonorientedsurfaceB @inverseveclength\endcsname}%
			\let\pgfplots@tickwidth@=\pgfmathresult
			\let\pgfplots@tickwidth=\pgfmathresult
			\ifcase\csname pgfplots@#1tickalignnum\endcsname\relax
				\def\pgfplots@tick@offset{0}%
			\or
				\let\pgfplots@tick@offset=\pgfplots@tickwidth@%
			\or
				\pgfmathmultiply@{0.5}{\pgfplots@tickwidth@}%
				\let\pgfplots@tick@offset=\pgfmathresult%
			\fi
			\pgfplots@prepare@tick@offsets@for@{#1}{\pgfplots@tickwidth@}%
			\pgfplotslistforeach\pgfplots@prepared@tick@positions@major@\as\pgfplots@curtickpos{%
				\pgfplots@drawticklines@for@placecomputedtick
			}%
			\endpgfextra;
		}{}%
		%
		\endscope
	}%
}

% Draws tick labels at the positions of the currently set oriented
% surface.
%
% Tick positions are taken out of the already precomputed list
% \pgfplots@prepared@tick@positions@major@...
%
% For 2D axes, this task is relatively simple:
% we iterate through every prepared major tick position and place a
% tick label. Open points, however, are the question whether to use
% the RIGHT or the LEFT axis line on the current oriented surface:
%
%        direction 'b' (second oriented)
% |-------------------------|
% |                         |
% |                         |
% |                         |direction 'a' (first oriented)
% |                         |
% |                         |
% |                         |
% |-------------------------|
% Left                  Right
%
% Given the axis line which shall contain the labels, we have to
% decide how to align the tick label nodes: on the left or on the
% right? Of course, we want to align them such that they are "outside"
% of the figure! That's simple as well: "Left axis line => outside
% means left", "Right axis line => outside means right".
%
% That's all, basically.
%
% For 3D axes, all these points are basically ... the same! 
% Now it can happen that the current oriented surface shall
% not contain ANY tick label. In that case, we do nothing.
% Furthermore, the "outside" direction (i.e. the anchoring of the
% label nodes) is a little bit more difficult.
% 
%
% See \pgfplots@drawticklines@onorientedsurf@ for a description of the
% oriented surface.
\def\pgfplots@drawticklabels@onorientedsurf{%
	\expandafter\pgfplots@drawticklabels@onorientedsurf@\pgfplotspointonorientedsurfaceA
}
\def\pgfplots@drawticklabels@onorientedsurf@#1{%
	\begingroup
	\expandafter\let\expandafter\pgfplots@prepared@tick@positions@major@\csname pgfplots@prepared@tick@positions@major@#1\endcsname
	% check whether
	% - we need to place tick labels on the LEFT side,
	% - we need to place tick labels on the RIGHT side,
	% - we don't need tick labels for the current surface at all:
	\pgfplotspointonorientedsurfaceabmatchaxisline{\csname pgfplots@#1ticklabelaxisspec\endcsname}{\pgfplots@ticklabelside}%
	\ifx\pgfplots@ticklabelside\pgfutil@empty
		% SKIP. The current oriented surface shall not get tick labels
		% for #1.
	\else
		\pgfplots@if{pgfplots@#1majorticks}{%
			\pgfplots@if{pgfplots@#1islinear}{%
				\pgfplots@init@scaled@tick@for{#1}%
			}{\relax}%
			\begingroup
			\pgfkeysalso{/tikz/every node/.append style={/pgfplots/every tick label,/pgfplots/every #1 tick label}}%
			\pgfplots@drawticklabels@onorientedsurf@prepareanchor#1%
			%
			\pgfplotsmath@ifzero{\csname pgfplots@\pgfplotspointonorientedsurfaceB @veclength\endcsname}{%
				\def\pgfplots@tick@offset{0}%
			}{%
				\ifcase\csname pgfplots@#1tickalignnum\endcsname\relax
					\def\pgfmathresult{0}%
				\or
					\pgfmathparse{\pgfplots@tickwidth}%
				\or
					\pgfmathmultiply{0.5}{\pgfplots@tickwidth}%
				\fi
				\let\pgfplots@tick@offset=\pgfmathresult
				\pgfplots@ticklabel@maxtickdimen@extrashift{#1}{\pgfplots@tick@offset}%
				\pgfmathmultiply@{\pgfplots@tick@offset}{\csname pgfplots@\pgfplotspointonorientedsurfaceB @inverseveclength\endcsname}%
				\let\pgfplots@tick@offset=\pgfmathresult
			}%
			%				
			\if2\csname pgfplots@#1axislinesnum\endcsname % Centered axis lines?
				\expandafter\let\expandafter\pgfplots@tick@origin\csname pgfplots@logical@ZERO@\pgfplotspointonorientedsurfaceB\endcsname%
				% FIXME : that stuff here does not respect
				% '[xyz]tickpos num' keys!
				\pgfplots@tickposchoiceb
				\if r\pgfkeysvalueof{/pgfplots/\pgfplotspointonorientedsurfaceB\space dir/value}%
					% special handling for reversed axes.
					\pgfmathmultiply{-1}{\pgfplots@tick@offset}%
					\let\pgfplots@tick@offset=\pgfmathresult
				\fi
				\pgfmathsubtract@{\pgfplots@tick@origin}{\pgfplots@tick@offset}%
			\else
				\if0\pgfplots@ticklabelside
				 	\expandafter\let\expandafter\pgfplots@tick@origin\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname%
					\pgfplots@tickposchoiceb
					\pgfmathsubtract@{\pgfplots@tick@origin}{\pgfplots@tick@offset}%
				\else
					\if1\pgfplots@ticklabelside
						\expandafter\let\expandafter\pgfplots@tick@origin\csname pgfplots@\pgfplotspointonorientedsurfaceB max\endcsname%
						\pgfplots@tickposchoicea
						\pgfmathadd@{\pgfplots@tick@origin}{\pgfplots@tick@offset}%
					\else
						% Should never happen.
						\pgfplots@error{Internal logic error during tick label placement (got placement character '\pgfplots@ticklabelside'). 
								Please report this as a bug or verify your input arguments to #1ticklabel pos.}%
						\expandafter\let\expandafter\pgfplots@tick@origin\csname pgfplots@\pgfplotspointonorientedsurfaceB min\endcsname%
						\pgfplots@tickposchoiceb
						\pgfmathsubtract@{\pgfplots@tick@origin}{\pgfplots@tick@offset}%
					\fi
				\fi
			\fi
			%
			% make sure the \pgfmathlogtologten method works even for
			% non-standard 'log basis #1':
			\expandafter\let\expandafter\pgfmathlogtologten@\csname pgfplotsmathlogtologten@#1@\endcsname
			%
			\let\pgfplots@tick@origin=\pgfmathresult%
			\xdef\pgfplots@show@ticklabel@LASTTICK{}%
			\pgfplotslistforeachungrouped\pgfplots@prepared@tick@positions@major@\as\pgfplots@curtickpos{%
				\expandafter\pgfplotslistpopfront\csname pgfplots@prepared@tick@positions@major@tickindices@#1\endcsname\to\pgfplots@ticknum
				\pgfplots@show@ticklabel
					{#1}{\pgfplots@curtickpos}(\pgfplots@curtickpos,\pgfplots@tick@origin)%
					{\pgfplots@ticknum}%
			}%
			\pgfplots@ticklabel@maxtickdimen@finish{#1}%
			\endgroup
			\pgfplots@draw@tick@scale@label@for #1%
		}%
		{\relax}% if...@major==false
	\fi
	\endgroup
}

% This here does the main work for any tick label ANCHORING.
%
% FIXME : the new 'near ticklabel' anchors are now the default method
% to place tick labels.
%
% This feature here can be used to disable this anchoring, i.e. set
% 'ticklabel anchor=tikz' to use a stupid heuristics.
%
% There are actually two choices:
% Choice 1: near ticklabel
% 	This choice places tick labels fully automatic outside of the
% 	figure, all on a line which is parallel to the axis which
% 	contains the corresponding tick labels.
%
% 	Since we are currently working on a restricted surface, we have
% 	three direction related to that surface:
% 		'a': this is the direction in which tick positions are known.
% 		'b': the 'orthogonal' axis to 'a' which is also in the surface.
% 		'n': the surface normal.
% 	Now, the idea for tick labels is to place them at 
% 		SCALE_b * b + SCALE_n * n,
% 	where the SCALE_[bn] numbers are choosen such that the label is
% 	outside of the axis.
%
% 	The offset is simply added to the transformation matrix (as a
% 	shift).
%
% Choice 2: tikz.
%   This is more or less a backwards compatibility feature. It does
%   not change the transformation matrix. It simply sets the 'at' key
%   of each node to the tick position and prepares the correct anchors
%   for the TikZ '\node' commands.
%   That's all here.
%
% PRECONDITION:
%   - called inside of  \pgfplots@drawticklabels@onorientedsurf@
% POSTCONDITION:
% 	- defines 
% 		- \pgfplots@tickposchoicea
% 			if called, sets keys such that tick labels are RIGHT (TOP) of
% 			the axis,
%
% 		- \pgfplots@tickposchoiceb
% 			if called, sets keys such that tick labels are LEFT
% 			(BOTTOM) of the axis,
\def\pgfplots@drawticklabels@onorientedsurf@prepareanchor#1{%
	\if\csname pgfplots@ticklabel@anchor@#1\endcsname0%
		% auto is the same as 'near ticklabel':
		\expandafter\def\csname pgfplots@ticklabel@anchor@#1\endcsname{1}%
	\fi
	\ifcase\csname pgfplots@ticklabel@anchor@#1\endcsname%
		% 0: doesn't happen, see above.
	\or
		% 1: near ticklabel.
		% The following code contains automatically
		% aligned tick labels (especially for 3D axes). 
		% see the manual for the |near ticklabel| anchors.
		\pgfkeys{/tikz/anchor=near #1ticklabel}%
		%
		% process the (optional) ticklabel distance:
		\begingroup
			\pgfkeysgetvalue{/pgfplots/#1ticklabel shift}\pgfmathresult
			\ifx\pgfmathresult\pgfutil@empty
			\else
				\afterassignment\pgfplots@gobble@until@relax
				\pgf@xa=\pgfkeysvalueof{/pgfplots/#1ticklabel shift}pt\relax
				\multiply\pgf@xa by-1 % the direction vector points to the INSIDE. the shift should have opposite sign.
				\edef\pgfmathresult{\pgf@sys@tonumber\pgf@xa}%
			\fi
			\pgfmath@smuggleone\pgfmathresult
		\endgroup
		\let\pgfplots@loc@TMPc=\pgfmathresult
		\ifx\pgfplots@loc@TMPc\pgfutil@empty
		\else
			\pgftransformshift{%
				\pgfplotspointouternormalvectorofticklabelaxis{#1}%
				\pgfqpointscale{-\pgfplots@loc@TMPc}{}%
			}%
		\fi
		%
		% these things are irrelevant here:
		\let\pgfplots@tickposchoicea=\pgfutil@empty
		\let\pgfplots@tickposchoiceb=\pgfutil@empty
	\or
		% 2: tikz.
		% We simply prepare the default anchor.
		% Actually, this code is just for backwards compatibility -
		% there may be people who prefer to set anchors. The
		% 'near ticklabel' implementation is much more general, however.
		\if\pgfplotspointonorientedsurfaceB x
			\def\pgfplots@tickposchoicea{\tikzset{right}}%
			\def\pgfplots@tickposchoiceb{\tikzset{left}}%
		\else
			\if\pgfplotspointonorientedsurfaceB y
				\def\pgfplots@tickposchoicea{\tikzset{above}}%
				\def\pgfplots@tickposchoiceb{\tikzset{below}}%
			\else
				\def\pgfplots@tickposchoicea{\tikzset{anchor=north east}}%
				\def\pgfplots@tickposchoiceb{\tikzset{anchor=south east}}%
			\fi
		\fi
	\fi
	\pgfplots@ticklabel@maxtickdimen@prepare@for@normalvec
		{#1}%
		{\pgfplotspointouternormalvectorofticklabelaxis{#1}}%
}%

\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@glob@TMPb)
		\ifpgfplots@checkuniform@isfirst
			\global\pgfplots@checkuniform@isfirstfalse
		\else
			\pgfmathsubtract@\cur\pgfplots@glob@TMPb%
			\pgfmathapproxequalto@\pgfmathresult{1.0}%
			\ifpgfmathcomparison
			\else
				\global\pgfplots@isuniformtickfalse
				\breakforeach
			\fi
		\fi
		\global\let\pgfplots@glob@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.
%
% #1: a tick sequence (expanded)
% #2: a macro which will be filled with the tick distance. This is
% only valid if \pgfplots@isuniformticktrue.
\def\pgfplots@checkisuniformLINEARtick#1#2{%
	\begingroup
	\global\pgfplots@isuniformticktrue
	\pgfplots@checkuniform@isfirsttrue
	\global\let\pgfplots@glob@TMPb=\pgfutil@empty
	\global\def\pgfplots@glob@TMPa{1}%
	\foreach \x in {#1}{%
		\ifx\pgfplots@glob@TMPb\pgfutil@empty
		\else
			\pgfmathsubtract@\x\pgfplots@glob@TMPb
			\ifpgfplots@checkuniform@isfirst
				% remember first distance h = x_1 - x_0
				\global\let\pgfplots@glob@TMPa=\pgfmathresult
				\global\pgfplots@checkuniform@isfirstfalse
			\else
				% check whether x_i - x_{i-1} = h
				\pgfmathapproxequalto@\pgfmathresult\pgfplots@glob@TMPa%
				\ifpgfmathcomparison
				\else
					\global\pgfplots@isuniformtickfalse
					\breakforeach
				\fi
			\fi
		\fi
		\global\let\pgfplots@glob@TMPb=\x%
	}%
	\endgroup
	\let#2=\pgfplots@glob@TMPa
}

% helper method which computes log10*\x foreach \x in {#1}.
% The result will be \xdef'ed into #2.
%
% #1: the ticks
% #2: the output macro
% #3: the axis
\def\pgfplots@compute@tick@times@logten#1\to#2#3{%
	\global\let#2=\pgfutil@empty
	\foreach \pgfplots@loc@TMPb in {#1} {%
		\pgfmathmultiply@{\pgfplots@loc@TMPb}{\csname pgfplots@log@scale@todisplaylog@#3\endcsname}%
		\ifx#2\pgfutil@empty
			\xdef#2{\pgfmathresult}%
		\else
			\xdef#2{#2,\pgfmathresult}%
		\fi
	}%
}

% 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!
% This yields H (for example as 2*10^e). Then, compute i*H, i \in \Z
%
% The data scaling transformation T(x) makes things more complicated.
% Now, T(x) = q * x - p  and we need to check for problems with large
% numbers:
%   - q* H = ( T(Max) - T(Min) ) / desirednumticks = q * (Max - Min) / desirednumticks.
%   - Using floating point arithmetics, (Max-Min)/desirednumticks (unscaled!)
%   is analysed to restrict H to {1*10^e, 2*10^e, 5*10^e}.
%   - So, we get  q * H  (we can't use the 'p' shift of the affine trafo here).
%   - The next problem is to compute { I*H, I in \Z } because
%   	I = trunc( Min / H )  = trunc(  ( T(Min) + p ) / (q*H) ).
%     This can be seen by Min = I*H + rest   and thus T(Min) = I*q*H + q*rest -p.
%     The Problem: (T(min)+p ) / (q*H) can be TOO BIG for pgfmath.
%   -> for the data scaling case, I will use floating point
%   arithmetics to compute that last step.
%   I will acquire \pgfplots@[xy]min@unscaled@as@float here.
%     
%
%
%
%
% 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 pgfplotspoint#1axislength\endcsname\relax
	% r = max place without ticks in pt -> choose desirednumticks >= W/r
	\divide\Wr by\axisdefaulttickwidth\relax
	\afterassignment\pgfplots@gobble@until@relax
	\desirednumticks=\the\Wr\relax
	\advance\desirednumticks by1
	\csname ifpgfplots@#1islinear\endcsname
		\ifnum\axisdefaulttryminticks>\desirednumticks\relax
			\desirednumticks=\axisdefaulttryminticks\relax
		\fi
	\else
		\ifnum\pgfplots@default@try@minticks@log>\desirednumticks\relax
			\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@loc@TMPa{\csname pgfplots@#1tickten\endcsname}%
			\expandafter\pgfplots@compute@tick@times@logten\pgfplots@loc@TMPa\to\pgfplots@glob@TMPa{#1}%
			\expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplots@glob@TMPa
		\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=\pgf@ya
		\let\MIN=\pgf@yb
		% 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
%\message{Axis limit #1: [\the\MIN:\the\MAX], diff = \the\H.}%
		\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
			\aftergroup\pgfplots@isuniformticktrue
			\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgf@sys@tonumber{\H}}{\the\pgfmathfloat@a@E}%
			\let\Hmacro=\pgfmathresult
			% The following code is carried out in floating point
			% arithmetics because it requires large data ranges.
			%
			% I want to compute MIN@new := I*H  where I is chosen
			% such that MIN = I*H + rest with rest < H.
			% The problem is the possibly large range of MIN. I
			% can't work completely in the transformed datarange,
			% so numbers get too large.
			%
			% So, compute I := int( MIN / H )  (integer truncation)
			% in float arithmetics and then MIN@new := I*H
			\pgfmathfloatdivide@{\csname pgfplots@#1min@unscaled@as@float\endcsname}{\Hmacro}%
			\pgfmathfloatint@{\pgfmathresult}%
			\pgfmathfloatmultiply@{\pgfmathresult}{\Hmacro}%
			\let\MIN@new=\pgfmathresult
			% Ok, we are ready.
			% Now, convert everything into the fixed point data
			% range:
			\ifpgfplots@is@datascaled
				\csname pgfplots@datascaletrafo@#1\endcsname{\MIN@new}%
				\MIN=\pgfmathresult pt
				\pgfplots@data@scale@trafo\Hmacro
				\H=\pgfmathresult pt
			\else
				\pgfmathfloattofixed\MIN@new
				\MIN=\pgfmathresult pt
				\pgfmathfloattofixed\Hmacro
				\H=\pgfmathresult pt
			\fi
			%
			% And, since we have used finite precision, I is most
			% likely to be large. So: subtract one H. In the worst
			% case, this produces one tick position too much (but
			% it won't be printed).
			\advance\MIN by-\H\relax
		\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}{\csname pgfplots@log@scale@todisplaylog@#1@inv\endcsname}%
			\let\Hmacrobaseten=\pgfmathresult
			\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
				\aftergroup\pgfplots@isuniformticktrue
				\pgfplots@isuniformticktrue
			\else
				\aftergroup\pgfplots@isuniformtickfalse
				\pgfplots@isuniformtickfalse
			\fi
%\message{final H=\pgf@sys@tonumber{\H} * log(10)}%
			\H=\csname pgfplots@log@scale@todisplaylog@#1\endcsname\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:
			\MIN=\csname pgfplots@log@scale@todisplaylog@#1@inv\endcsname\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
			\MIN=\csname pgfplots@log@scale@todisplaylog@#1\endcsname 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
					\advance\MIN \csname pgfplots@log@scale@todisplaylog@#1\endcsname pt
				\fi
			\fi
		\fi
		\MINH=\MIN
		\advance\MINH by\H
		% Ok, now it can happen that only ONE tick label is placed in
		% this range.
		% That's useless, so check for it.
		%
		% That's the case if
		%    MIN < ORIGMIN && MAX < MIN+2 H 
		% MIN < ORIGMIN by construction (ok, MIN <= ORIGMIN by
		% construction, but I don't care about this case). 
		% So: check only the second condition.
		\def\pgfplots@tick@returnval@ready{0}%
		\pgfplots@tmpa=\MINH
		\advance\pgfplots@tmpa by\H
		\ifdim\MAX<\pgfplots@tmpa
			\pgfplots@if{pgfplots@#1islinear}{%
				\def\pgfplots@tick@returnval@ready{1}%
				\begingroup
					\c@pgf@counta=\axisdefaulttryminticks\relax
					\advance\c@pgf@counta by1
					\edef\axisdefaulttryminticks{\the\c@pgf@counta}%
%\message{**TOO FEW TICK LABELS. RECURSION with try min ticks=\axisdefaulttryminticks.**}%
					% recurse.
					\pgfplots@assign@default@tick@foraxis{#1}%
					\expandafter\global\expandafter\let\expandafter\pgfplots@glob@TMPa\csname pgfplots@#1tick\endcsname
					\expandafter\global\expandafter\let\expandafter\pgfplots@glob@TMPb\csname pgfplots@tick@distance@#1\endcsname
				\endgroup
			}{%
				\aftergroup\pgfplots@isuniformtickfalse
				% ok, do something special.
				%
				% The idea is now to place ticks at
				% 10^{i*h} with properly choosen 'h'.
				%
				% So: apply basically the SAME code as above for linear
				% axis, just everything log 10!  And keep in mind that all
				% coordinates are actually given as natural logarithms.
				\expandafter\MIN\csname pgfplots@#1min\endcsname pt
				\H=\MAX
				\advance\H by-\MIN
				\H=\csname pgfplots@log@scale@todisplaylog@#1@inv\endcsname\H
%\message{Axis limit #1: [\the\MIN:\the\MAX], diff/log(10) = \the\H.}%
				\c@pgf@counta=\desirednumticks\relax
				\advance\c@pgf@counta by-1
				\ifnum\c@pgf@counta>2
					% subtract one more. This algorithm here produces more
					% ticks than the normal one which is designed for 10^i
					\advance\c@pgf@counta by-1
				\fi
				\divide\H by\c@pgf@counta\relax
%\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}%
				\pgfmathfloatparsenumber{\Hmacro}%
				\expandafter\pgfmathfloat@decompose\pgfmathresult\relax\pgfmathfloat@a@S\H\pgfmathfloat@a@E
				% Determine properly snapped 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
				\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgf@sys@tonumber{\H}}{\the\pgfmathfloat@a@E}%
				\expandafter\pgfmathfloattofixed\expandafter{\pgfmathresult}%
				\let\Hmacro=\pgfmathresult
				\H=\Hmacro pt %
				% Ok, our step size h for 10^{i*h} is ready!
%\message{determined step size 10^{\Hmacro}}%
				% Now, we want to activate the Tick set {10^{i*H}, i in \Z}
				% compute I such that
				%   10^{min} = 10^{I * H + rest};  |rest| < H
				% -> I = round(xmin/H)
				% -> MIN = I * H
				% BUT EVERYTHING to log(10) basis!
				\MIN=\csname pgfplots@log@scale@todisplaylog@#1@inv\endcsname \MIN\relax
				\pgfmathlog@invoke@expanded\pgfmathdivide@{%
					{\pgf@sys@tonumber\MIN}%
					{\Hmacro}%
				}%
				\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\relax
				\multiply\MIN by\c@pgf@counta\relax
				%
				% convert back to basis 'e':
				\MIN=\csname pgfplots@log@scale@todisplaylog@#1\endcsname\MIN\relax
				\H=\csname pgfplots@log@scale@todisplaylog@#1\endcsname\H\relax
				\MINH=\MIN\relax
				\advance\MINH by\H\relax
			}%
		\fi
%\message{final H=\the\H.}%
		\if0\pgfplots@tick@returnval@ready
			\xdef\pgfplots@glob@TMPb{\pgf@sys@tonumber{\H}}%
			\advance\MAX by0.5\H % avoid rounding inaccuracies:
			\xdef\pgfplots@glob@TMPa{\pgf@sys@tonumber{\MIN},\pgf@sys@tonumber{\MINH},...,\pgf@sys@tonumber{\MAX}}%
		\fi
		\aftergroup\pgfplots@determinedefaultvalues@needs@check@uniformtickfalse
	\else
		\expandafter\global\expandafter\let\expandafter\pgfplots@glob@TMPa\csname pgfplots@#1tick\endcsname
		\gdef\pgfplots@glob@TMPb{}% will be computed later, in 'check uniform tick'
		\aftergroup\pgfplots@determinedefaultvalues@needs@check@uniformticktrue
	\fi
	\endgroup
	\expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplots@glob@TMPa
	\expandafter\let\csname pgfplots@tick@distance@#1\endcsname=\pgfplots@glob@TMPb
%\message{pgfplots.sty: #1tick set to \csname pgfplots@#1tick\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@loc@TMPb in {#1} {%
		\pgfmathfloatparsenumber{\pgfplots@loc@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@loc@TMPb in {#1} {%
		#2{\pgfplots@loc@TMPb}%
		\ifx#3\pgfutil@empty
			\xdef#3{\pgfmathresult}%
		\else
			\xdef#3{#3,\pgfmathresult}%
		\fi
	}%
	%
}%

% Adds a further, temporary anchor to every node which will be
% processed. The anchor will be named '#2'. It is placed such that
% 1. the node's center is on a line in direction of the inwards normal
% vector of the #1 ticklabel axis and the 'at' position of the node,
% 2. the node does not intrude the axis.
%
% In effect, one of the node's standard anchors (north, east, ... )
% will be placed on the line
%    \draw[blue,thick,->] (xticklabel cs:0,0) -- (xticklabel cs:1,0);
%
% This command is identical to calling
% \pgfplotsdeclareborderanchorforaxis{#1}{<three-char-string-of-#1-ticklabel-axis>}{#2}
%
% @REMARKS:
% 	- it is -by no means- necessary that any ticks or tick labels are
% 	drawn or defined for this method.
% 	- in fact, tick labels use such an anchor (the 'near #1ticklabel'
% 	anchor is defined in this way)
\def\pgfplotsdeclareborderanchorforticklabelaxis#1#2{%
	\pgfplotsdeclareborderanchorforaxis{#1}{\pgfplotsticklabelaxisspec{#1}}{#2}%
}