%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% This file is a copy of some part of PGF/Tikz.
%%% It has been copied here to provide :
%%%  - compatibility with older PGF versions
%%%  - availability of PGF contributions by Christian Feuersaenger
%%%    which are necessary or helpful for pgfplots.
%%%
%%% For reasons of simplicity, I have copied the whole file, including own contributions AND
%%% PGF parts. The copyrights are as they appear in PGF.
%%%
%%% Note that pgfplots has compatible licenses.
%%%
%%% This copy has been modified in the following ways:
%%%  - nested \input commands have been updated
%%%
%
% Support for the contents of this file will NOT be done by the PGF/TikZ team.
% Please contact the author and/or maintainer of pgfplots (Christian Feuersaenger) if you need assistance in conjunction
% with the deployment of this patch or partial content of PGF. Note that the author and/or maintainer of pgfplots has no obligation to fix anything:
% This file comes without any warranty as the rest of pgfplots; there is no obligation for help.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Date of this copy: Mo 30. Apr 17:24:35 CEST 2018 %%%



% Copyright 2011 by Christophe Jorssen and Mark Wibrow
% Copyright 2014 by Christian Feuersänger
%
% 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.
%
% $Id$
%
%
% This is a library for a LUA math parser and LUA math operations.
% Advantage compared to its TeX pendant:  it is FASTER and has HIGHER
% ACCURACY.
% Disadvantage: any function declared by means of
% \pgfmathdeclarefunction is NOT automatically transported to the LUA
% side (at the time of this writing).
% LUA functions need to be defined by means of LUA code
%
% function pgfluamathfunctions.myoperation(a,b)
%    return a*2*b
% end
%
% this will automatically set up 'myoperation' for use in
% \pgfluamathparse{myoperation(4,2)}
%
% The library has TWO use-cases which are more or less distinct: one
% is to use LUA for all math function, but not for math expression
% parsing -- this was still under control of the TeX math parser.
% This approach works like the 'fpu' library.
%
% The second approach is to use LUA to parse all math expressions -
% but if someone calls \pgfmathadd@{1}{2}, it would use the TeX
% command. This approach is relatively lightweight because it does not
% need to substitute all \pgfmath* macros.
%
% One can mix both modes.

% *******************************************************************
% Some luatex stuff. Should be put elsewhere (e.g. in
% pgfutil-luatex-engine).

\edef\pgfliblua@oldcatcodedoublequote{\the\catcode`\"}%
\catcode`\"=12

% We assume luatex version > 0.39:
%   - \directlua <general text> will work
%   - \directlua is the only luatex primitive that we can assume
%     accessible without being prefixed by the format via
%     tex.enableprimitives.
% Ideas taken from the ifluatex package (Heiko Oberdiek)
\let\pgfutil@ifluatex\iffalse
\begingroup\expandafter\expandafter\expandafter\endgroup
\expandafter\ifx\csname directlua\endcsname\relax
\else
  \expandafter\let\csname pgfutil@ifluatex\expandafter\endcsname
    \csname iftrue\endcsname
\fi

\pgfutil@ifluatex
  \let\pgfutil@directlua\directlua
  \pgfutil@directlua{%
    tex.enableprimitives('pgfutil@',{'luaescapestring'})}
\else
  \def\pgfutil@directlua#1{}
  \def\pgfutil@luaescapestring#1{}
\fi

\pgfutil@directlua{%
  pgfluamathfunctions = require("pgfplotsoldpgfsupp.luamath.functions")
  pgfluamathparser = require("pgfplotsoldpgfsupp.luamath.parser")}


% Patch some configuration macros such that the modifications are
% available in LUA as well:
\pgfkeys{
	/pgf/trig format/deg/.add code={}{\directlua{pgfluamathfunctions.setTrigFormat("deg")}\aftergroup\pgfmath@settrigformat},
	/pgf/trig format/rad/.add code={}{\directlua{pgfluamathfunctions.setTrigFormat("rad")}\aftergroup\pgfmath@settrigformat},
}
% ... and reactivate the key:
\pgfmathiftrigonometricusesdeg{%
	\pgfkeys{/pgf/trig format/deg}%
}{%
	\pgfkeys{/pgf/trig format/rad}%
}%

% re-activates the current trig format. This is important after a TeX
% group has been closed.
\def\pgfmath@settrigformat{%
	\pgfmathiftrigonometricusesdeg{%
		\directlua{pgfluamathfunctions.setTrigFormat("deg")}%
	}{%
		\directlua{pgfluamathfunctions.setTrigFormat("rad")}%
	}%
}%

\let\pgfmathsetseed@pgfbasic = \pgfmathsetseed
\def\pgfmathsetseed#1{%
	\pgfmathsetseed@pgfbasic{#1}%
	\directlua{pgfluamathfunctions.setRandomSeed(pgfluamathfunctions.tonumber("\pgfmathresult"))}%
}%

% Patch 'declare function' such that it communicates the function
% directly to LUA.
\let\pgfmathnotifynewdeclarefunction@orig=\pgfmathnotifynewdeclarefunction
\def\pgfmathnotifynewdeclarefunction#1#2#3{%
	\pgfmathnotifynewdeclarefunction@orig{#1}{#2}{#3}%
	%
	% we have to check if '#3' contains control sequences.
	% this is highly tricky as it may contain '#1'...
	\begingroup
		\toks0={#3}%
		\xdef\pgf@marshal@glob{\the\toks0 }%
	\endgroup
	\pgfutil@command@to@string\pgf@marshal@glob\pgf@marshal
	\expandafter\pgfutilifcontainsmacro\expandafter{\pgf@marshal}{%
		\def\pgf@temp{1}%
	}{%
		\def\pgf@temp{0}%
	}%
	\if1\pgf@temp
		% let lua produce an error when evaluating this function -- we cannot possibly expand the macro to its current state:
		\directlua{pgfluamathparser.pushLocalExpressionFunction(%
			"\pgfutil@luaescapestring{#1}",%
			#2,%
			"functionMustBeEvaluatedInTeX")}%
	\else
		\directlua{pgfluamathparser.pushLocalExpressionFunction(%
			"\pgfutil@luaescapestring{#1}",%
			#2,%
			"\pgfutil@luaescapestring{#3}")}%
	\fi
	%
	% ensure that the local function is removed at the end of the
	% scope. To this end, we maintain a stack on the LUA side.
	\aftergroup\pgfluamathparse@pop@local@function
}%

\def\pgfluamathparse@pop@local@function{%
	\directlua{pgfluamathparser.popLocalExpressionFunction()}%
}%

% End of luatex stuff
% *******************************************************************

% Loading part: based on fpu library


% if LUA failed to evaluate the expression, it will be evaluated in
% TeX as fallback. This boolean defines if the error message shall be
% shown or suppressed. The default is to suppress it and show any
% resulting TeX errors.
%
% If LUA fails \pgfmathresult will be empty.
%
% This is actually only for debugging; it will be set implicitly when
% activating/deactivating TeX fallback.
\newif\ifpgfluamathshowerrormessage

% Defines what happens if LUA failed to evaluate the expression: if
% this is true, the TeX parser will be invoked as fallback.
%
% This happens
% - for \chardef'ed boxes for which LUA lacks evaluation capabilities
% - if the expression includes some function which is unavailable in
%   LUA (defined only in TeX)
% - some special cases which simply haven't been added to the LUA
%   parser (yet).
%   At the time of this writing, this includes
% -- arrays created via '{}' and indexed with '[]'
% -- strings with "<str>"
% -- 'scalar' function
% -- hex/octal/binary input
\newif\ifpgfluamathenableTeXfallback

\newif\ifpgfluamathcomputationactive
\newif\ifpgfluamathparseractive

\def\pgfluamath@makecomputationactive{%
  \ifpgfluamathcomputationactive
  \else
    \pgfluamath@checkuninstallcmd%
    \pgfluamath@install%
    \pgfluamathcomputationactivetrue
  \fi}

\def\pgfluamath@makecomputationinactive{%
  \ifpgfluamathcomputationactive
    \pgfluamath@uninstall%
    \pgfluamathcomputationactivefalse
  \fi}

\let\pgfluamath@pgfmathparse\pgfmathparse
\def\pgfluamath@makeparseractive{%
  \ifpgfluamathparseractive
  \else
    \let\pgfluamath@pgfmathparse\pgfmathparse
    \let\pgfmathparse\pgfluamathparse
    \let\pgfmath@iftrue=\pgfmathluamath@iftrue
    \pgfluamathparseractivetrue
  \fi}

\let\pgfmath@iftrue@basic=\pgfmath@iftrue

\def\pgfluamath@makeparserinactive{%
  \ifpgfluamathparseractive
    \let\pgfmathparse\pgfluamath@pgfmathparse
    \let\pgfmath@iftrue=\pgfmath@iftrue@basic
    \pgfluamathparseractivefalse
  \fi}

\pgfqkeys{/pgf}{%
  % Enable lua-side computation of \pgfmathresult
  % (will be deactivated after the current TeX group)
  luamath/.is choice,
  luamath/only computation/.code={%
    \pgfutil@ifluatex
      \pgfluamath@makecomputationactive
      \pgfluamath@makeparserinactive
    \else
      \pgfmath@error{Sorry, you need the luaTeX engine to use the
        luamath library}%
    \fi},
  luamath/parser and computation/.code={%
    \pgfutil@ifluatex
      \pgfluamath@makecomputationactive
      \pgfluamath@makeparseractive
    \else
      \pgfmath@error{Sorry, you need the luaTeX engine to use the
        luamath library}%
    \fi},
  luamath/off/.code={%
    \pgfluamath@makecomputationinactive
    \pgfluamath@makeparserinactive},
  luamath/.default=only computation,
  %
  % activates ONLY the parser. This is fast and does not replace the
  % \pgfmath* functions.
  % @see |parser and computation| which also allows to write
  % \pgfmathadd{1}{2} to call LUA
  luamath/parser/.code={%
    \pgfutil@ifluatex
      \pgfluamath@makeparseractive
    \else
      \pgfmath@error{Sorry, you need the luaTeX engine to use the
        luamath library}%
    \fi
  },
	luamath/output format/.is choice,
	luamath/output format/fixed/.code=	{\def\pgfluamath@outputformat@choice{0}},
	% returns results for use in the FPU
	luamath/output format/float/.code=	{\def\pgfluamath@outputformat@choice{1}},
	luamath/output format/fixed,
	% this is merely useful for debugging purposes, I guess.
	luamath/show error message/.is if=pgfluamathshowerrormessage,
	luamath/enable TeX fallback/.is choice,
	luamath/enable TeX fallback/true/.code={\pgfluamathenableTeXfallbacktrue\pgfluamathshowerrormessagefalse},
	luamath/enable TeX fallback/false/.code={\pgfluamathenableTeXfallbackfalse\pgfluamathshowerrormessagetrue},
	luamath/enable TeX fallback/.default=true,
	luamath/enable TeX fallback=true,
}

\def\pgfluamath@uninstall@appendcmd#1{%
  \expandafter\gdef\expandafter\pgfluamath@uninstall\expandafter{%
    \pgfluamath@uninstall #1}}

% If the uninstall command is already assembled, it will skip the
% uninstall assemblation.
\def\pgfluamath@checkuninstallcmd{%
  \pgfutil@ifundefined{pgfluamath@uninstall}{%
    \global\let\pgfluamath@uninstall=\pgfutil@empty
  }{%
    % We already HAVE an uninstall command (prepared globally).
    % So: don't waste time assembling one!
    \def\pgfluamath@uninstall@appendcmd##1{}%
    \def\pgfluamath@prepareuninstallcmd##1{}%
  }%
}

% This assembles an uninstall command globally ON FIRST USAGE.
% See \pgfmathfloat@plots@checkuninstallcmd
\def\pgfluamath@prepareuninstallcmd#1{%
  \expandafter\global\expandafter\let
    \csname pgfluamath@backup@\string#1\endcsname=#1%
  \expandafter\gdef\expandafter\pgfluamath@uninstall\expandafter{%
    \pgfluamath@uninstall
    \expandafter\let\expandafter#1\csname pgfluamath@backup@\string#1\endcsname}%
}

\def\pgfluamath@install@function#1=#2{%
  \pgfluamath@prepareuninstallcmd{#1}%
  \let#1=#2%
}

\def\pgfluamath@install{%
  \pgfluamath@install@function\pgfmathadd@=\pgfluamathadd@%
  \pgfluamath@install@function\pgfmathsubtract@=\pgfluamathsubtract@%
  \pgfluamath@install@function\pgfmathneg@=\pgfluamathneg@%
  \pgfluamath@install@function\pgfmathmultiply@=\pgfluamathmultiply@%
  \pgfmathfloat@install\pgfmath@iftrue=\pgfmathluamath@iftrue
  \pgfluamath@install@function\pgfmathdivide@=\pgfluamathdivide@%
  % \pgfluamath@install@function\pgfmathdiv@=\pgfluamathdiv@%
  \pgfluamath@install@function\pgfmathfactorial@=\pgfluamathfactorial@%
  \pgfluamath@install@function\pgfmathsqrt@=\pgfluamathsqrt@%
  % \pgfluamath@install@function\pgfmathpow@=\pgfluamathpow@%
  \pgfluamath@install@function\pgfmathe@=\pgfluamathe@%
  \pgfluamath@install@function\pgfmathexp@=\pgfluamathexp@%
  \pgfluamath@install@function\pgfmathln@=\pgfluamathln@%
  \pgfluamath@install@function\pgfmathlogten@=\pgfluamathlogten@%
  % \pgfluamath@install@function\pgfmathlogtwo@=\pgfluamathlogtwo@%
  \pgfluamath@install@function\pgfmathabs@=\pgfluamathabs@%
  \pgfluamath@install@function\pgfmathmod@=\pgfluamathmod@%
  \pgfluamath@install@function\pgfmathMod@=\pgfluamathMod@%
  \pgfluamath@install@function\pgfmathround@=\pgfluamathround@%
  \pgfluamath@install@function\pgfmathfloor@=\pgfluamathfloor@%
  \pgfluamath@install@function\pgfmathceil@=\pgfluamathceil@%
  % \pgfluamath@install@function\pgfmathint@=\pgfluamathint@%
  % \pgfluamath@install@function\pgfmathfrac@=\pgfluamathfrac@%
  % \pgfluamath@install@function\pgfmathreal@=\pgfluamathreal@%
  \pgfluamath@install@function\pgfmathgcd@=\pgfluamathgcd@%
  \pgfluamath@install@function\pgfmathisprime@=\pgfluamathisprime@%
  \pgfluamath@install@function\pgfmathpi@=\pgfluamathpi@%
  \pgfluamath@install@function\pgfmathrad@=\pgfluamathrad@%
  \pgfluamath@install@function\pgfmathdeg@=\pgfluamathdeg@%
  \pgfluamath@install@function\pgfmathsin@=\pgfluamathsin@%
  \pgfluamath@install@function\pgfmathcos@=\pgfluamathcos@%
  \pgfluamath@install@function\pgfmathtan@=\pgfluamathtan@%
  \pgfluamath@install@function\pgfmathsec@=\pgfluamathsec@%
  \pgfluamath@install@function\pgfmathcosec@=\pgfluamathcosec@%
  \pgfluamath@install@function\pgfmathcot@=\pgfluamathcot@%
  \pgfluamath@install@function\pgfmathasin@=\pgfluamathasin@%
  \pgfluamath@install@function\pgfmathacos@=\pgfluamathacos@%
  \pgfluamath@install@function\pgfmathatan@=\pgfluamathatan@%
  \pgfluamath@install@function\pgfmathatantwo@=\pgfluamathatantwo@%
  \pgfluamath@install@function\pgfmathmax@=\pgfluamathmax@%
  \pgfluamath@install@function\pgfmathmin@=\pgfluamathmin@%
  % \pgfluamath@install@function\pgfmath@pi=\pgfluamathpi@%
  % \pgfluamath@install@function\pgfmathpi=\pgfluamathpi@%
  % \pgfluamath@install@function\pgfmathe@=\pgfluamathe@%
  % \pgfluamath@install@function\pgfmathe=\pgfluamathe@%
  % \pgfluamath@install@function\pgfmathlessthan@=\pgfluamathlessthan@%
  % \pgfluamath@install@function\pgfmathless@=\pgfluamathlessthan@%
  % \pgfluamath@install@function\pgfmathgreaterthan@=\pgfluamathgreaterthan@%
  % \pgfluamath@install@function\pgfmathgreater@=\pgfluamathgreaterthan@%
  % \pgfluamath@install@function\pgfmathpow@=\pgfluamathpow@
  \pgfluamath@install@function\pgfmathrand@=\pgfluamathrand@
  \pgfluamath@install@function\pgfmathrand=\pgfluamathrand@
  \pgfluamath@install@function\pgfmathrnd@=\pgfluamathrnd@
  \pgfluamath@install@function\pgfmathrnd=\pgfluamathrnd@
  % \pgfluamath@install@function\pgfmathtrue@=\pgfluamathtrue@
  % \pgfluamath@install@function\pgfmathfalse@=\pgfluamathfalse@
  % \pgfluamath@install@function\pgfmathnot@=\pgfluamathnot@
  % \pgfluamath@install@function\pgfmathhex@=\pgfluamathhex@
  % \pgfluamath@install@function\pgfmathHex@=\pgfluamathHex@
  % \pgfluamath@install@function\pgfmathoct@=\pgfluamathoct@
  % \pgfluamath@install@function\pgfmathbin@=\pgfluamathbin@
  % \pgfluamath@install@function\pgfmathand@=\pgfluamathand@
  % \pgfluamath@install@function\pgfmathor@=\pgfluamathor@
  % \pgfluamath@install@function\pgfmathfactorial@=\pgfluamathfactorial@
  % \pgfluamath@install@function\pgfmathveclen@=\pgfluamathveclen@
  % \pgfluamath@install@function\pgfmathcosh@=\pgfluamathcosh@
  % \pgfluamath@install@function\pgfmathsinh@=\pgfluamathsinh@
  % \pgfluamath@install@function\pgfmathtanh@=\pgfluamathtanh@
  % \pgfluamath@install@function@unimplemented{ceil}%
  % \pgfluamath@install@function@unimplemented{frac}%
  % \pgfluamath@install@function@unimplemented{log2}%
  % \pgfluamath@install@function@unimplemented{log10}%
  % \pgfluamath@install@function@unimplemented{equalto}%
  % \pgfluamath@install@function@unimplemented{random}%
  % \pgfluamath@install@function@unimplemented{setseed}%
  % \pgfluamath@install@function@unimplemented{Mod}%
  % \pgfluamath@install@function@unimplemented{real}%
  % \pgfluamath@install@function@unimplemented{notequal}%
  \pgfluamath@install@function\pgfmathreciprocal=\pgfluamathreciprocal%
  \pgfluamath@install@function\pgfpointnormalised=\pgfluamathpointnormalised
}

\def\pgfluamathgetresult#1{%
  \edef\pgfmathresult{\pgfutil@directlua{tex.print(-1,#1)}}}

\def\pgfmathluamath@iftrue{%
	\if 0\pgfluamath@outputformat@choice
		\let\pgfmathluamath@@iftrue@v=\pgfluamathone
	\else
		\let\pgfmathluamath@@iftrue@v=\pgfluamathfloatone
	\fi
	\pgfmathluamath@iftrue@
}%
\def\pgfluamathone{1.0}%
\def\pgfluamathfloatone{1Y1.0e+00]}%
\def\pgfmathluamath@iftrue@#1#2{%
	\ifx\pgfmathresult\pgfmathluamath@@iftrue@v
		\def\pgfmath@next{#1}%
	\else
		\def\pgfmath@next{#2}%
	\fi
	\pgfmath@next
}%

\def\pgfluamathpi@{%
  \pgfluamathgetresult{pgfluamathfunctions.pi()}}
\def\pgfluamathe@{%
  \pgfluamathgetresult{pgfluamathfunctions.e()}}
\def\pgfluamathadd@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.add(#1,#2)}}
\def\pgfluamathsubtract@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.substract(#1,#2)}}
\def\pgfluamathneg@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.neg(#1)}}
\def\pgfluamathmultiply@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.multiply(#1,#2)}}
\def\pgfluamathdivide@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.divide(#1,#2)}}
\def\pgfluamathabs@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.abs(#1)}}
\def\pgfluamathround@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.round(#1)}}
\def\pgfluamathfloor@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.floor(#1)}}
\def\pgfluamathceil@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.ceil(#1)}}
\def\pgfluamathgcd@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.gcd(#1,#2)}}
\def\pgfluamathisprime@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.isprime(#1)}}
\def\pgfluamathmax@#1{%
  \pgfluamathgetresult{%
    math.max(pgfluamathfunctions.split_braces_to_explist("#1"))}}
\def\pgfluamathmin@#1{%
  \pgfluamathgetresult{%
    math.min(pgfluamathfunctions.split_braces_to_explist("#1"))}}
\def\pgfluamathsin@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.Sin(#1)}}
\def\pgfluamathcos@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.Cos(#1)}}
\def\pgfluamathtan@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.Tan(#1)}}
\def\pgfluamathmod@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.mod(#1,#2)}}
\def\pgfluamathMod@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.Mod(#1,#2)}}
\def\pgfluamathrad@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.rad(#1)}}
\def\pgfluamathdeg@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.deg(#1)}}
\def\pgfluamathatan@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.aTan(#1)}}
\def\pgfluamathatantwo@#1#2{%
  \pgfluamathgetresult{pgfluamathfunctions.aTan2(#1,#2)}}
\def\pgfluamathasin@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.aSin(#1)}}
\def\pgfluamathacos@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.aCos(#1)}}
\def\pgfluamathcot@#1{%
  \pgfluamathgetresult{1/pgfluamathfunctions.Tan(#1)}}
\def\pgfluamathsec@#1{%
  \pgfluamathgetresult{1/pgfluamathfunctions.Cos(#1)}}
\def\pgfluamathcosec@#1{%
  \pgfluamathgetresult{1/pgfluamathfunctions.Sin(#1)}}
\def\pgfluamathexp@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.exp(#1)}}
\def\pgfluamathln@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.log(#1)}}
\def\pgfluamathlogten@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.log10(#1)}}
\def\pgfluamathsqrt@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.sqrt(#1)}}
\def\pgfluamathrnd@{%
  \pgfluamathgetresult{pgfluamathfunctions.rnd()}}
\def\pgfluamathrand@{%
  \pgfluamathgetresult{pgfluamathfunctions.rand(-1,1)}}
\def\pgfluamathfactorial@#1{%
  \pgfluamathgetresult{pgfluamathfunctions.factorial(#1)}}
\def\pgfluamathreciprocal#1{%
  \pgfluamathgetresult{1/#1}}
% \pgfluamath@install@function\pgfmath@pi=\pgfluamathpi@%
% \pgfluamath@install@function\pgfmathpi=\pgfluamathpi@%
% \pgfluamath@install@function\pgfmathe@=\pgfluamathe@%
% \pgfluamath@install@function\pgfmathe=\pgfluamathe@%
% \pgfluamath@install@function\pgfmathlessthan@=\pgfluamathlessthan@%
% \pgfluamath@install@function\pgfmathless@=\pgfluamathlessthan@%
% \pgfluamath@install@function\pgfmathgreaterthan@=\pgfluamathgreaterthan@%
% \pgfluamath@install@function\pgfmathgreater@=\pgfluamathgreaterthan@%
% \pgfluamath@install@function\pgfmathpow@=\pgfluamathpow@
% \pgfluamath@install@function\pgfmathrand@=\pgfluamathrand@
% \pgfluamath@install@function\pgfmathrand=\pgfluamathrand@
% \pgfluamath@install@function\pgfmathrnd@=\pgfluamathrnd@
% \pgfluamath@install@function\pgfmathrnd=\pgfluamathrnd@
% \pgfluamath@install@function\pgfmathtrue@=\pgfluamathtrue@
% \pgfluamath@install@function\pgfmathfalse@=\pgfluamathfalse@
% \pgfluamath@install@function\pgfmathnot@=\pgfluamathnot@
% \pgfluamath@install@function\pgfmathhex@=\pgfluamathhex@
% \pgfluamath@install@function\pgfmathHex@=\pgfluamathHex@
% \pgfluamath@install@function\pgfmathoct@=\pgfluamathoct@
% \pgfluamath@install@function\pgfmathbin@=\pgfluamathbin@
% \pgfluamath@install@function\pgfmathand@=\pgfluamathand@
% \pgfluamath@install@function\pgfmathor@=\pgfluamathor@
% \pgfluamath@install@function\pgfmathfactorial@=\pgfluamathfactorial@
% \pgfluamath@install@function\pgfmathveclen@=\pgfluamathveclen@
% \pgfluamath@install@function\pgfmathcosh@=\pgfluamathcosh@
% \pgfluamath@install@function\pgfmathsinh@=\pgfluamathsinh@
% \pgfluamath@install@function\pgfmathtanh@=\pgfluamathtanh@

\def\pgfluamathpointnormalised#1{%
  \pgf@process{#1}%
  \pgfutil@directlua{%
    pgfluamathfunctions.pointnormalised(%
      \pgf@sys@tonumber{\pgf@x},\pgf@sys@tonumber{\pgf@y})}%
  \ignorespaces}

% Parser

\newif\ifpgfluamathunitsdeclared

% true if and only if LUA failed to evaluate the expression and the
% expression was evaluated by means of the TeX parser as fallback.
%
% This happens
% - for \chardef'ed boxes for which LUA lacks evaluation capabilities
% - if the expression includes some function which is unavailable in
%   LUA (defined only in TeX)
% - some special cases which simply haven't been added to the LUA
%   parser (yet).
%   At the time of this writing, this includes
% -- arrays created via '{}' and indexed with '[]'
% -- strings with "<str>"
% -- 'scalar' function
% -- hex/octal/binary input
\newif\ifpgfluamathusedTeXfallback

% Parses the math expression and defines \pgfmathresult and
% \ifpgfmathunitsdeclared to contain the result.
%
% If \ifpgfluamathparseractive then the result is also assigned to
% \pgfmathresult. Furthermore, if the expression cannot be evaluated (because LUA does not support
% it), it will be evaluated by mean of TeX as fallback.
%
% @see \ifpgfluamathusedTeXfallback
% @see \ifpgfluamathshowerrormessage
\def\pgfluamathparse#1{%
  \pgfluamathusedTeXfallbackfalse
  \pgfutil@directlua{pgfluamathparser.texCallParser(
    "\pgfutil@luaescapestring{#1}",
    \pgfluamath@outputformat@choice,
    \ifpgfluamathshowerrormessage true\else false\fi)%
  }%
  \ifx\pgfmathresult\pgfutil@empty
    \ifpgfluamathenableTeXfallback
       \pgfluamathusedTeXfallbacktrue
       \pgfluamath@pgfmathparse{#1}%
    \fi
  \fi
}

\catcode`\"=\pgfliblua@oldcatcodedoublequote
\endinput