pgf 2.0, third try

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

1 files changed, 970 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
new file mode 100644
index 00000000000..3d69d34b73c
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
@@ -0,0 +1,970 @@
+% Copyright 2007 Mark Wibrow
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+% This file parses/evaluates a decimal expression.
+%
+% Version 1.414213 29/9/2007
+
+% \pgfmathparse, \pgfmathqparse
+%
+% Evaluates a decimal expression.
+%
+% #1 - the expression.
+%
+% returns
+%
+% x = the result as a dimension.
+%
+% E.g.
+% \pgfmathparse{3pt*2cm+1.5}
+% \pgfmathqparse{3pt*2cm+1.5pt}
+%
+% Every number in \pgfmathqparse *must*
+% specify a unit.
+%
+\newif\ifpgfmath@quickparse
+
+\def\pgfmathparse{%
+	\pgfmath@quickparsefalse%
+	\pgfmathparse@}
+
+\def\pgfmathqparse{%
+	\pgfmath@quickparsetrue%
+	\pgfmathparse@}
+		
+\def\pgfmath@calcreal#1{#1}%
+\def\pgfmath@calcminof#1#2{min(#1,#2)}%
+\def\pgfmath@calcmaxof#1#2{max(#1,#2)}%
+\def\pgfmath@calcratio#1#2{#1/#2}%
+
+\def\pgfmathparse@#1{%
+  \begingroup%    
+    % Reinstall correct font, so that dimensions like 1em are correct
+    \pgfmath@selectfont%
+    \let\real\pgfmath@calcreal%
+    \let\minof\pgfmath@calcminof%
+    \let\maxof\pgfmath@calcmaxof%
+    \let\ratio\pgfmath@calcratio%
+    \edef\pgfmath@temp{#1}%
+    \pgfmath@resetparsingparameters%
+    \global\pgfmathunitsdeclaredfalse%
+    \ifpgfmath@quickparse%
+      \let\pgfmath@parseoperand\pgfmath@quickparseoperand%
+    \else%
+      \let\pgfmath@parseoperand\pgfmath@parseoperand%
+    \fi%
+    \let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+    \expandafter\pgfmath@parse@\pgfmath@temp @@@@@@@@@@@\pgfmath@empty}
+
+
+% \pgfmath@resetparsingparameters
+%
+% Reset the stack at the begining of the parse/group.
+%
+\def\pgfmath@resetparsingparameters{%
+	\pgfmath@stack{\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+	\def\pgfmath@stacknextoperator{\pgfmath@empty}% Will not work with \let
+}
+% \pgfmath@parse@
+%
+% Start parsing. Expect one of
+% 1) the end of the parse
+% 2) the start of a group
+% 3) a (possible) operand.
+%
+\def\pgfmath@parse@#1{%
+	\def\pgfmath@token{}%
+	\ifx#1@%
+		\let\pgfmath@parsenext\pgfmath@endparse%
+	\else%
+		\ifx#1(%
+			\let\pgfmath@parsenext\pgfmath@startparsegroup%
+		\else%
+			\edef\pgfmath@token{#1}%
+			\let\pgfmath@parsenext\pgfmath@parseoperand%
+	\fi\fi%
+	\pgfmath@parsenext%
+}
+
+% If no TeX units are declared *at any point* in the parse
+% the result is scaled by \pgfmathresultunitscale.
+\newif\ifpgfmathunitsdeclared
+\def\pgfmathsetresultunitscale#1{\def\pgfmathresultunitscale{#1}}
+\def\pgfmathresultunitscale{1}
+
+% \pgfmath@endparse
+%
+% Everything stops here.
+%
+\def\pgfmath@endparse#1\pgfmath@empty{%
+    \pgfmath@processalloperations%
+    \pgfmath@stackpop{\pgfmathresult}%
+    \begingroup%
+      \ifpgfmathunitsdeclared%
+        \pgfmath@x1pt\relax%
+      \else%
+        \afterassignment\pgfmath@gobbletilpgfmath@%
+        \pgfmath@x\pgfmathresultunitscale pt\relax\pgfmath@%
+      \fi%
+      \expandafter\pgfmath@x\pgfmathresult\pgfmath@x%
+      \pgfmath@returnone\pgfmath@x%
+    \endgroup%
+    \pgfmath@smuggleone{\pgfmathresult}%
+  \endgroup%
+  \ignorespaces%
+}
+
+% \pgfmath@startparsegroup
+%
+% When opening ( is scanned start a new group.
+%
+\def\pgfmath@startparsegroup{%
+	\begingroup%
+		\let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+		\pgfmath@resetparsingparameters%
+		\pgfmath@parse@}
+
+% \pgfmath@endparsegroup
+%
+% When closing ) is scanned, processes all waiting
+% operations (within the group) and close the group.
+%
+\def\pgfmath@endparsegroup{%
+		\pgfmath@processalloperations%
+		\pgfmath@stackpop{\pgfmathresult}%
+		\expandafter\pgfmath@x\pgfmathresult pt\relax%
+		\pgfmath@returnone\pgfmath@x%
+	\endgroup%
+	\pgfmath@parsepostgroup%
+}
+
+% \pgfmath@parseoperator
+%
+% An operator is expected here. 
+% Or the end of the parse or parse group.
+% 
+\def\pgfmath@parseoperator#1{%
+	\def\pgfmath@token{}%
+	% Push the operand in \pgfmathresult on to the stack. 
+	\expandafter\pgfmath@stackpushoperand\expandafter{\pgfmathresult}%
+	\ifx#1@%
+		\let\pgfmath@parsenext\pgfmath@endparse%
+	\else%
+		\ifx#1+%
+			\let\pgfmath@parsenext\pgfmath@parseadd%
+		\else%
+			\ifx#1-%
+				\let\pgfmath@parsenext\pgfmath@parsesubtract%
+			\else%
+				\ifx#1*%
+					\let\pgfmath@parsenext\pgfmath@parsemultiply%
+				\else%
+					\ifx#1/%
+						\let\pgfmath@parsenext\pgfmath@parsedivide%
+					\else
+						\ifx#1)%
+							\let\pgfmath@parsenext\pgfmath@endparsegroup%
+						\else%
+							\ifx#1r%
+								\let\pgfmath@parsenext\pgfmath@parseradians%
+							\else%
+								\ifx#1>%
+									\let\pgfmath@parsenext\pgfmath@parsegreaterthan%
+								\else%
+									\ifx#1<%
+										\let\pgfmath@parsenext\pgfmath@parselessthan%
+									\else%
+										\if#1=%
+											\let\pgfmath@parsenext\pgfmath@parseequalto%
+										\else%
+											\if#1^%
+												\let\pgfmath@parsenext\pgfmath@parsepower%
+											\else%
+												\pgfmath@error{Unknown operator `#1'}%
+												\let\pgfmath@parsenext\relax%
+	\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi%
+	\pgfmath@parsenext%
+}
+
+% Use a \toks register as a stack.
+\newtoks\pgfmath@stack
+
+% \pgfmath@stackpushoperator
+% 
+% Push an operator (actually its macro e.g., \pgfmathadd@)
+% on to the stack. And keep track of it using the macro
+% \pgfmath@stacknextoperator.
+%
+\def\pgfmath@stackpushoperator#1{%
+	\edef\pgfmath@temp{\noexpand#1\the\pgfmath@stack}%
+	\expandafter\pgfmath@stack\expandafter{\pgfmath@temp}%
+	\def\pgfmath@stacknextoperator{#1}}% <- Must \def. Cannot \let.
+
+% \pgfmath@stackpushoperand
+%
+% Push an operand (i.e. a number) on the stack. It is
+% put within a TeX group to make popping a lot simpler.
+%
+\def\pgfmath@stackpushoperand#1{%
+	\edef\pgfmath@temp{{#1}\the\pgfmath@stack}%
+	\expandafter\pgfmath@stack\expandafter{\pgfmath@temp}%
+}
+
+% \pgfmath@stackpeek
+%
+% Peek (i.e. without removal) at the top of the stack.
+%
+\def\pgfmath@stackpeek{\expandafter\pgfmath@stackpeek@\the\pgfmath@stack\pgfmath@}
+\def\pgfmath@stackpeek@#1#2\pgfmath@{#1}%
+
+% \pgfmath@stackpop
+%
+% Pop (i.e. remove) the top of the stack into #1.
+%
+\def\pgfmath@stackpop#1{\expandafter\pgfmath@stackpop@\expandafter#1\the\pgfmath@stack\pgfmath@}
+\def\pgfmath@stackpop@#1#2#3\pgfmath@{\edef#1{#2}\pgfmath@stack{#3}}%
+
+% \pgfmath@stackpopoperation
+%
+% Remove and perform an operation from the stack.
+%
+\def\pgfmath@stackpopoperation{%
+	\expandafter\pgfmath@stackpopoperation@\the\pgfmath@stack\pgfmath@%
+}
+\def\pgfmath@stackpopoperation@#1#2#3#4#5\pgfmath@{%
+	\ifx\pgfmath@empty#1\relax%
+			\pgfmath@stack{\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+	\else%
+		\ifx\pgfmath@empty#2\relax%
+			\pgfmath@stack{{#1}\pgfmath@empty\pgfmath@empty\pgfmath@empty\pgfmath@empty}%
+		\else%
+			#2{#3}{#1}%
+			\pgfmath@stack{#4#5}%
+			\expandafter\pgfmath@stackpushoperand\expandafter{\pgfmathresult}%
+	\fi\fi%
+	\def\pgfmath@stacknextoperator{#4}}
+
+% \pgfmath@processalloperations
+%
+% Process all operation in the stack. The 
+% overall result is at the top of the stack.
+%
+\def\pgfmath@processalloperations{%
+	\expandafter\pgfmath@in@\pgfmath@stacknextoperator{\pgfmath@empty}%
+	\ifpgfmath@in@%
+		\let\pgfmath@processnext\relax%		
+	\else%
+		\pgfmath@stackpopoperation%
+		\let\pgfmath@processnext\pgfmath@processalloperations%
+	\fi%
+	\pgfmath@processnext}
+
+% \pgfmath@processoperationsuntil
+%
+% Process operations in the stack, until the specified
+% operation/s is/are encountered. The overall result is 
+% at the top of the stack.
+%
+\def\pgfmath@processoperationsuntil#1{%
+	\expandafter\pgfmath@in@\pgfmath@stacknextoperator{#1\pgfmath@empty}%
+	\ifpgfmath@in@%
+		\let\pgfmath@processnext\pgfmath@processoperationsuntil@end%		
+	\else%
+		\pgfmath@stackpopoperation%
+		\let\pgfmath@processnext\pgfmath@processoperationsuntil%
+	\fi%
+	\pgfmath@processnext{#1}}
+\def\pgfmath@processoperationsuntil@end#1{}
+
+
+% OK. Now the operators are parsed.
+% These correspond to the + - / * ^ < > = operators and r (postfix) function.
+%
+\def\pgfmath@parseadd{%	
+	% If no operator has been assigned (i.e. + is the first operator scanned),
+	% do nothing, except add addition to the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Empty the process stack up to any inequalities.
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathadd@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsesubtract{%	
+	% If no operator has been assigned (i.e. - is the first operator scanned),
+	% do nothing, except add subtract to the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Empty the process stack up to any inequalities.
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathsubtract@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsemultiply{%
+	% If no operator has been assigned (i.e. * is the first operator scanned),
+	% do nothing, except push multiply onto the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Process all operations up to inequalites or addition/subtraction
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathmultiply@}%
+	\pgfmath@parse@}
+	
+\def\pgfmath@parsedivide{%
+	% If no operator has been assigned (i.e. / is the first operator scanned),
+	% do nothing, except push divide onto the stack.
+	\ifx\pgfmath@stacknextoperator\pgfmath@empty%
+	\else%
+		% Process all operations up to inequalites or addition/subtraction
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%
+	\pgfmath@stackpushoperator{\pgfmathdivide@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parsegreaterthan{%
+	% On scanning an equality/inequality operator everything up to
+	% (but not including) the operator is evaluated... 
+	\pgfmath@processalloperations%
+	% ...and the operation pushed onto the stack.
+	\pgfmath@stackpushoperator{\pgfmathgreaterthan@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parselessthan{%
+	\pgfmath@processalloperations%
+	\pgfmath@stackpushoperator{\pgfmathlessthan@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parseequalto={%
+	\pgfmath@processalloperations%
+	\pgfmath@stackpushoperator{\pgfmathequalto@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parsepower{%
+	% Easy, just push power onto the stack.
+	\pgfmath@stackpushoperator{\pgfmathpow@}%
+	\pgfmath@parse@}
+
+\def\pgfmath@parseradians{%
+	% r is a post-fix function...
+	\ifx\pgfmath@primaryoperation\pgfmath@empty%
+	\else%
+		\pgfmath@processoperationsuntil{\pgfmathequalto@\pgfmathlessthan@\pgfmathgreaterthan@%
+			\pgfmathadd@\pgfmathsubtract@}%
+	\fi%	
+	\pgfmath@stackpop{\pgfmath@temp}%
+	\pgfmathdeg@{\pgfmath@temp}%
+	% ...so processing returns to \pgfmath@parseoperator
+	\pgfmath@parseoperator}
+	
+\newcount\c@pgfmath@parsecounta
+\newcount\c@pgfmath@parsecountb
+\newcount\c@pgfmath@parsecountc
+\newdimen\pgfmath@parsex
+
+% \pgfmath@quickparseoperand
+%
+% An operand can *only* be a dimension.
+%
+\def\pgfmath@quickparseoperand{%
+	\afterassignment\pgfmath@quickparseoperand@%
+	\pgfmath@parsex\pgfmath@token}
+\def\pgfmath@quickparseoperand@{%
+	\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+	\pgfmath@parseoperator%
+}
+	
+% \pgfmath@parseoperand
+%
+% An operand can be an ASCII number (with or without dimensions, with
+% or without a decimal point), a TeX register (count, dimen or skip,
+% which may have expanded with \the), or a function e.g. sin(X).
+%
+% It is assumed that after \edef-ing, the only unexpanded tokens are registers. 
+%
+\def\pgfmath@parseoperand{%
+	\def\pgfmath@sign{}%
+	\expandafter\pgfmath@parseoperandsign\pgfmath@token}
+\def\pgfmath@parseoperandsign#1{%
+	\pgfmath@in@#1{-+}% 
+	\ifpgfmath@in@
+		% Gobble multiple signs.
+		\edef\pgfmath@sign{\pgfmath@sign#1}%
+		\expandafter\pgfmath@parseoperandsign%
+	\else%
+		\expandafter\pgfmath@parsenumberorfunction\expandafter#1%
+	\fi%
+}
+
+\newif\ifpgfmath@dimen@
+
+\def\pgfmath@ifregisterdimen@#1\pgfmath@{%
+	\pgfmath@in@{p}{#1}%
+	\ifpgfmath@in@%
+		\pgfmath@dimen@true%
+	\else%
+		\pgfmath@dimen@false%
+	\fi} 			
+
+\def\pgfmath@parsenumberorfunction#1{%
+  \let\pgfmath@parsenext\pgfmath@parsenumberorfunction@simple%
+  \ifx#1\wd\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \ifx#1\ht\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \ifx#1\dp\let\pgfmath@parsenext\pgfmath@boxdimen\fi%
+  \pgfmath@parsenext#1%
+}
+
+\def\pgfmath@boxdimen#1#2{%
+  \pgfmath@parsex=\pgfmath@sign#1#2%
+  \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+  \global\pgfmathunitsdeclaredtrue% a dimension has units 
+  \pgfmath@parseoperator%
+}
+
+\def\pgfmath@parsenumberorfunction@simple#1{%	
+	\expandafter\ifcat#1\relax%
+		% So, a TeX register.
+		\afterassignment\pgfmath@ifregisterdimen@%
+		\pgfmath@parsex\pgfmath@sign#1pt\relax\pgfmath@%
+		\ifpgfmath@dimen@% 
+			% A dimension! So stop scanning operand here.
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+         \global\pgfmathunitsdeclaredtrue% a dimension has units
+			\def\pgfmath@temp{}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+		\else%
+			% A count! Expand it, but carry on as usual as it might
+			% be immediately followed by a dimension.
+			\ifdim\pgfmath@parsex<0pt\relax%
+				\edef\pgfmath@sign{\pgfmath@sign-}%
+				\pgfmath@parsex-\pgfmath@parsex%
+			\fi%
+			\edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parsenumberorfunction@%
+		\fi%
+	\else%
+		% Could be a number or a function...?
+		\edef\pgfmath@temp{#1}%
+		\let\pgfmath@parsenext\pgfmath@parsenumberorfunction@%
+	\fi%
+	\expandafter\pgfmath@parsenext\pgfmath@temp%
+}%
+
+\def\pgfmath@parsenumberorfunction@#1{%
+	\ifx#1(% It might be a group e.g. -(1+2)...
+		\let\pgfmath@parsenext\pgfmath@parseoperandgroup%
+	\else%
+		\pgfmath@in@{#1}{.0123456789}% 
+		\ifpgfmath@in@% ... or a number...
+			\let\pgfmath@parsenext\pgfmath@parsenumber%
+		\else% ... or a function.
+			\let\pgfmath@parsenext\pgfmath@parsefunction%
+		\fi%
+	\fi%
+	\pgfmath@parsenext#1%
+}%
+
+\def\pgfmath@parseoperandgroup({%
+	\let\pgfmath@postparsegroup\pgfmath@@parseoperandgroup%
+	\pgfmath@startparsegroup%
+}
+
+\def\pgfmath@@parseoperandgroup{%
+	\let\pgfmath@postparsegroup\pgfmath@parseoperator%
+	\edef\pgfmathresult{\pgfmath@sign\pgfmathresult}%
+	\pgfmath@parseoperator%
+}
+
+\def\pgfmath@parsenumber{% 
+	% Consider the number 3.14159
+	% 3 is parsed by assignment to a, then '.' is absorbed and 14159
+	% parsed by assignement to b (actually b=114159, see below). 
+	\c@pgfmath@parsecountc0\relax%
+	\afterassignment\pgfmath@parsedecimalpoint%
+	\c@pgfmath@parsecounta0}
+
+\def\pgfmath@parsedecimalpoint#1{%
+	\ifx#1.% Is there a decimal point? If not, see if there are any units.
+		\let\pgfmath@parsenext\pgfmath@parsemantissa%
+	\else%
+		\c@pgfmath@parsecountb10\relax% The first digit of b is gobbled (see below). 
+		\let\pgfmath@parsenext\pgfmath@parseunits%
+	\fi%
+	\pgfmath@parsenext#1}
+
+
+
+% We would like to assign the following number (which is the mantisse)
+% to a number. However, for a very long mantisse as in 3.141592653589793238462643
+% this will fail since the number becomes too large.
+%
+% Because of this, we have to do some ``magic'': We scan 9 tokens and
+% then do an assignment with a guard after 9 tokens so that the
+% assigment cannot fail.
+%
+\def\pgfmath@parsemantissa.#1#2#3#4#5#6#7#8#9{%
+  \afterassignment\pgfmath@checkforguard%    
+  % Consider the number: 2.005
+  % 2 is assigned to a, but b will be assigned 5, which is *not right*. 
+  % So using 1 here hereresults in  b=1005. The first digit is then  
+  % gobbled later, when expanded with \the.
+  \c@pgfmath@parsecountb1#1#2#3#4#5#6#7#8#9\relax}%
+
+\def\pgfmath@checkforguard{%
+  \pgfmath@ifnextchar\relax%
+  {%
+    % Ok, this is a looong mantisse. Start gobbling all following
+    % numbers
+    \pgfmath@gobblemantisse%
+  }%
+  {%
+    \pgfmath@removeguard%
+  }%
+}
+
+\def\pgfmath@gobblemantisse\relax#1#2#3#4#5#6#7#8#9{%
+  \afterassignment\pgfmath@checkforguard%
+  \c@pgfmath@parsecountc0#1#2#3#4#5#6#7#8#9\relax% these digits are ignored
+}
+
+\def\pgfmath@removeguard#1\relax{\pgfmath@parseunits#1}
+
+ 
+\def\pgfmath@parseunits#1{%
+  % Here the extra first digit in b is gobbled. 
+  \edef\pgfmath@resulttemp{%
+    \pgfmath@sign\the\c@pgfmath@parsecounta.\expandafter\pgfmath@gobbleone\the\c@pgfmath@parsecountb}%
+  % Check whether #1 is a \dp, \wd, or \ht
+  \let\pgfmath@parsenext=\pgfmath@parseunits@simple%
+  \ifx#1\wd\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \ifx#1\ht\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \ifx#1\dp\let\pgfmath@parsenext=\pgfmath@parseunits@boxdimen\fi%
+  \pgfmath@parsenext#1%
+}
+
+\def\pgfmath@parseunits@boxdimen#1#2{%
+  \pgfmath@parsex=\pgfmath@sign#1#2%
+  \pgfmath@parsex\pgfmath@resulttemp\pgfmath@parsex%
+  \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+  \global\pgfmathunitsdeclaredtrue% a dimension has units 
+  \pgfmath@parseoperator%
+}
+
+\def\pgfmath@parseunits@simple#1{%
+	% Now check if #1 is actually a register.
+	\ifcat#1\relax%
+		\afterassignment\pgfmath@ifregisterdimen@%
+		\pgfmath@parsex#1pt\relax\pgfmath@%
+		\pgfmath@parsex\pgfmath@resulttemp\pgfmath@parsex%
+		\ifpgfmath@dimen@% If it's a dimen stop scanning operand here.
+      \global\pgfmathunitsdeclaredtrue% a dimension has units
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+		\else
+			\edef\pgfmath@resulttemp{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\let\pgfmath@parsenext\pgfmath@parseunits@%
+		\fi%
+		\expandafter\pgfmath@parsenext%
+	\else%
+		\expandafter\pgfmath@parseunits@\expandafter#1%
+	\fi}
+
+\def\pgfmath@parseunits@#1#2{%
+	% Check if #1 is an operator, or the character `@' indicating the end of the parse.
+	\pgfmath@in@#1{@+-*/^r<>=()}%
+	\ifpgfmath@in@%
+		\edef\pgfmath@tokens{#1#2}%
+		\edef\pgfmathresult{\pgfmath@resulttemp}%
+		\let\pgfmath@parsenext\pgfmath@parseoperator%
+	\else%
+		\pgfmath@in@#1{Ee}% e+0X
+		\ifpgfmath@in@%
+			% Oh no! It might be and em or an ex...
+			\pgfmath@in@#2{mx}%
+			\ifpgfmath@in@%
+				\global\pgfmathunitsdeclaredtrue%
+				\pgfmath@parsex\pgfmath@resulttemp#1#2\relax%
+				\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+				\edef\pgfmath@tokens{}%
+				\let\pgfmath@parsenext\pgfmath@parseoperator%
+			\else%
+				\edef\pgfmath@tokens{#2}%
+				\let\pgfmath@parsenext\pgfmath@parsescientific%
+			\fi%
+		\else
+			% Anything else *should* be a TeX unit.
+			\global\pgfmathunitsdeclaredtrue%
+			\pgfmath@parsex\pgfmath@resulttemp#1#2\relax%
+			\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@parsex}}%
+			\edef\pgfmath@tokens{}%
+			\let\pgfmath@parsenext\pgfmath@parseoperator%
+	\fi\fi%
+	\expandafter\pgfmath@parsenext\pgfmath@tokens%
+}
+
+% Parse 'Scientific' notation in the form xEyy
+%
+\def\pgfmath@parsescientific{%
+	\afterassignment\pgfmath@parsescientific@%
+	\c@pgfmath@parsecounta}
+
+\def\pgfmath@parsescientific@{%
+	\edef\pgfmath@parsesci@temp{\pgfmath@resulttemp\the\c@pgfmath@parsecountc}%
+	\expandafter\pgfmathscientific\expandafter{\pgfmath@parsesci@temp}%
+		{\the\c@pgfmath@parsecounta}%
+	\edef\pgfmath@resulttemp{\pgfmathresult}%
+	\pgfmath@parseunits@}
+
+% Functions parsed (not calculated) here are:
+%
+% round(X)         'half-up' rounding.
+% floor(X)         floor function.
+% ciel(X)          ceiling function.
+% abs(X)           absolute function.
+%
+% exp(X)           e^X (0 <= X <~= 9.7).
+% ln(X)            logarithm of X.
+% pow(X,Y)         X^Y,
+%
+% sin(X)           sine function.
+% cos(X)           cosine function.
+% tan(X)           tan function.
+% asin(X)          arcsine of X (in radians)    -1 <= X <= 1
+% acos(X)          arccosine of X (in radians)  -1 <= X <= 1
+% atan(X)          arctangent of X (in radians) -1 <= X <= 1
+% veclen(X,Y)      the length Z where Z^2 = X^2 + Y^2
+% mod(X,Y)         X modulo Y
+% max(X,Y)         the maximum of X or Y
+% min(X,Y)         the minimum of X or Y
+%
+% NB veclen, mod, max, and min *cannot* be nested.
+%
+% deg(X)           converts X to degrees (X in radians)
+% rad(X)           converts X to radians (X in degrees)
+%
+% rnd              generate pseudo-random number X (0 <= X <= 1).
+% rand             generate pseudo-random number X (1 <= X <= -1).
+% sqrt(X)          square root.
+% 
+% pi               the constant PI.
+
+\def\pgfmath@parsefunction{%
+	\def\pgfmath@parsedfunctionname{}%
+	\futurelet\pgfmath@parsetoken\pgfmath@parsefunction@@}
+\def\pgfmath@parsefunction@@#1{%
+	\pgfmath@in@#1{()@+-*/^<>=}% A function name ends with one of these...
+	\ifpgfmath@in@%
+		\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@end%
+	\else%
+		\ifx\pgfmath@parsetoken\pgfmath@sptoken% ...or a space.
+			\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@end%
+		\else%
+			\let\pgfmath@parsefunctionnext\pgfmath@parsefunction@continue%
+	\fi\fi%
+	\pgfmath@parsefunctionnext#1}
+
+\def\pgfmath@parsefunction@end#1{%
+	\expandafter\ifx\csname pgfmath@parsefunction@\pgfmath@parsedfunctionname\endcsname\relax%
+		\pgfmath@reportunknownfunction%
+		\let\pgfmath@parsefunctionnext\relax%
+	\else%
+		\let\pgfmath@parsefunctionnext\pgfmath@executeparsefunction@%
+	\fi%
+	\pgfmath@parsefunctionnext#1}
+
+\def\pgfmath@parsefunction@continue#1{%
+	\edef\pgfmath@parsedfunctionname{\pgfmath@parsedfunctionname#1}%
+	\futurelet\pgfmath@parsetoken\pgfmath@parsefunction@@}
+	
+\def\pgfmath@executeparsefunction@{\csname pgfmath@parsefunction@\pgfmath@parsedfunctionname\endcsname}
+		
+		
+\def\pgfmath@reportunknownfunction{%
+	\pgfmath@error{Unknown function `\pgfmath@parsedfunctionname'}{}%
+}
+
+% \pgfmath@postfunction
+% 
+% In scanning a function e.g. sin(40), we subvert the normal parsing 
+% group mechanism by messing around with \pgfmath@parsepostgroup, so 
+% that after scanning ), the parser doesn't scan for an operator, but 
+% returns to the macros scanning the function. 
+% Here the mechanism is restored, and the value of the function is 
+% stored along with the approprate sign, which was saved earlier.
+%
+\def\pgfmath@postfunction{%
+	\let\pgfmath@parsepostgroup\pgfmath@parseoperator%
+	\edef\pgfmathresult{\pgfmath@sign\pgfmathresult}%
+	\pgfmath@parseoperator}
+	
+
+% \pgfmath@parsefunction@abs
+%
+\def\pgfmath@parsefunction@abs{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@abs@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@abs@{%	
+	\expandafter\pgfmathabs@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sqrt
+%
+\def\pgfmath@parsefunction@sqrt{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sqrt@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sqrt@{%	
+	\expandafter\pgfmathsqrt@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@round
+%
+\def\pgfmath@parsefunction@round{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@round@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@round@{%	
+	\expandafter\pgfmathround@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@floor
+%
+\def\pgfmath@parsefunction@floor{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@floor@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@floor@{%	
+	\expandafter\pgfmathfloor@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@ceil
+%
+\def\pgfmath@parsefunction@ceil{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@ceil@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@ceil@{%	
+	\expandafter\pgfmathceil@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sin
+%
+\def\pgfmath@parsefunction@sin{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sin@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sin@{%	
+	\expandafter\pgfmathsin@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cos
+%
+\def\pgfmath@parsefunction@cos{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cos@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cos@{%	
+	\expandafter\pgfmathcos@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@asin
+%
+\def\pgfmath@parsefunction@asin{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@asin@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@asin@{%	
+	\expandafter\pgfmathasin@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@acos
+%
+\def\pgfmath@parsefunction@acos{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@acos@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@acos@{%	
+	\expandafter\pgfmathacos@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@atan
+%
+\def\pgfmath@parsefunction@atan{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@atan@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@atan@{%	
+	\expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@tan
+%
+\def\pgfmath@parsefunction@tan{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@tan@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@tan@{%	
+	\expandafter\pgfmathtan@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cot
+%
+\def\pgfmath@parsefunction@cot{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cot@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cot@{%	
+	\expandafter\pgfmathcot@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@sec
+%
+\def\pgfmath@parsefunction@sec{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@sec@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@sec@{%	
+	\expandafter\pgfmathsec@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@cosec
+%
+\def\pgfmath@parsefunction@cosec{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@cosec@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@cosec@{%	
+	\expandafter\pgfmathcosec@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@rad
+%
+\def\pgfmath@parsefunction@rad{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@rad@%
+	\pgfmath@parse@}
+\def\pgfmath@parsefunction@rad@{%
+	\expandafter\pgfmathrad@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}%
+	
+% \pgfmath@parsefunction@rad
+%
+\def\pgfmath@parsefunction@deg{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@deg@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@deg@{%
+	\expandafter\pgfmathdeg@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction}%
+	
+% \pgfmath@parsefunction@rnd
+%
+\def\pgfmath@parsefunction@rnd{%
+	\expandafter\pgfmathrnd%
+	\expandafter\pgfmath@postfunction}
+			
+% \pgfmath@parsefunction@rand
+%
+\def\pgfmath@parsefunction@rand{%
+	\expandafter\pgfmathrand%
+	\expandafter\pgfmath@postfunction}%
+			
+% \pgfmath@parsefunction@exp
+%
+\def\pgfmath@parsefunction@exp{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@exp@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@exp@{%	
+	\expandafter\pgfmathexp@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@ln
+%
+\def\pgfmath@parsefunction@ln{%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@ln@%
+	\expandafter\pgfmath@parse@}
+\def\pgfmath@parsefunction@ln@{%	
+	\expandafter\pgfmathln@\expandafter{\pgfmathresult}%
+	\pgfmath@postfunction%
+}
+	
+% \pgfmath@parsefunction@pi
+%
+\def\pgfmath@parsefunction@pi{%
+	\pgfmathpi%
+	\pgfmath@postfunction%
+}
+
+% \pgfmath@parsefunction@veclen
+%
+\def\pgfmath@parsefunction@veclen{%
+	\expandafter\pgfmath@parsefunction@veclen@}
+\def\pgfmath@parsefunction@veclen@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@veclen@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@veclen@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathveclen@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@mod 
+%
+\def\pgfmath@parsefunction@mod{%
+	\expandafter\pgfmath@parsefunction@mod@}
+\def\pgfmath@parsefunction@mod@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@mod@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@mod@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmod@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+
+% \pgfmath@parsefunction@max
+%
+\def\pgfmath@parsefunction@max{%
+	\expandafter\pgfmath@parsefunction@max@}
+\def\pgfmath@parsefunction@max@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@max@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@max@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmax@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}	
+
+% \pgfmath@parsefunction@min 
+%
+\def\pgfmath@parsefunction@min{%
+	\expandafter\pgfmath@parsefunction@min@}
+\def\pgfmath@parsefunction@min@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@min@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@min@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathmin@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}
+	
+% \pgfmath@parsefunction@pow 
+%
+\def\pgfmath@parsefunction@pow{%
+	\expandafter\pgfmath@parsefunction@pow@}
+\def\pgfmath@parsefunction@pow@(#1,{%
+	\pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}%
+	\let\pgfmath@parsepostgroup\pgfmath@parsefunction@pow@@
+	\pgfmath@startparsegroup}
+\def\pgfmath@parsefunction@pow@@{%
+	\edef\pgfmath@secondoperand{\pgfmathresult}%
+	\pgfmathpow@{\pgfmath@firstoperand}{\pgfmath@secondoperand}%
+	\pgfmath@postfunction}	
\ No newline at end of file