pgf

git-svn-id: svn://tug.org/texlive/trunk@51107 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 543 insertions, 543 deletions

diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex
index b6ac16c8bf3..2dbf154d8be 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex
@@ -14,7 +14,7 @@
 % add function.
 %
 \pgfmathdeclarefunction{add}{2}{%
-	\begingroup%
+    \begingroup%
     \pgfmath@x=#1pt\relax%
     \pgfmath@y=#2pt\relax%
     \advance\pgfmath@x by\pgfmath@y%
@@ -26,7 +26,7 @@
 % subtract function.
 %
 \pgfmathdeclarefunction{subtract}{2}{%
-	\begingroup%
+    \begingroup%
     \pgfmath@x=#1pt\relax%
     \pgfmath@y=#2pt\relax%
     \advance\pgfmath@x by-\pgfmath@y%
@@ -37,11 +37,11 @@
 % neg function.
 %
 \pgfmathdeclarefunction{neg}{1}{%
-	\begingroup%
-		\pgfmath@x=-#1pt\relax%
-		\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
-		\pgfmath@smuggleone\pgfmathresult%
-	\endgroup%
+    \begingroup%
+        \pgfmath@x=-#1pt\relax%
+        \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
+        \pgfmath@smuggleone\pgfmathresult%
+    \endgroup%
 }
 % change the precedence for neg.
 % Otherwise, unary minus and exponentiation won't have the correct precedence
@@ -64,206 +64,206 @@
 \newif\ifpgfmath@divide@period
 
 \pgfmathdeclarefunction{divide}{2}{%
-	\begingroup%
-		\pgfmath@x=#1pt\relax%
-		\pgfmath@y=#2pt\relax%
-		\let\pgfmath@sign=\pgfmath@empty%
-		\ifdim0pt=\pgfmath@y%
-			\pgfmath@error{You've asked me to divide `#1' by `#2', %
-				but I cannot divide any number by `#2'}%				
-		\fi%
-		\afterassignment\pgfmath@xa%
-		\c@pgfmath@counta\the\pgfmath@y\relax%
-		\ifdim0pt=\pgfmath@xa%
-			\divide\pgfmath@x by\c@pgfmath@counta%
-		\else%
-			\ifdim0pt>\pgfmath@x%
-				\def\pgfmath@sign{-}%
-				\pgfmath@x=-\pgfmath@x%
-			\fi%
-			\ifdim0pt>\pgfmath@y%
-				\expandafter\def\expandafter\pgfmath@sign\expandafter{\pgfmath@sign-}%
-				\pgfmath@y=-\pgfmath@y%
-			\fi%
-			\ifdim1pt>\pgfmath@y%
-				\pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}%
-				\pgfmath@x=\pgfmath@sign\pgfmathresult\pgfmath@x%
-			\else%
-				\def\pgfmathresult{0}%
-				\pgfmath@divide@periodtrue%
-				\c@pgfmath@counta=0\relax%
-				\pgfmathdivide@@%
-				\pgfmath@x=\pgfmath@sign\pgfmathresult pt\relax%
-			\fi%
-		\fi%
-		\pgfmath@returnone\pgfmath@x%
-	\endgroup%	
+    \begingroup%
+        \pgfmath@x=#1pt\relax%
+        \pgfmath@y=#2pt\relax%
+        \let\pgfmath@sign=\pgfmath@empty%
+        \ifdim0pt=\pgfmath@y%
+            \pgfmath@error{You've asked me to divide `#1' by `#2', %
+                but I cannot divide any number by `#2'}%
+        \fi%
+        \afterassignment\pgfmath@xa%
+        \c@pgfmath@counta\the\pgfmath@y\relax%
+        \ifdim0pt=\pgfmath@xa%
+            \divide\pgfmath@x by\c@pgfmath@counta%
+        \else%
+            \ifdim0pt>\pgfmath@x%
+                \def\pgfmath@sign{-}%
+                \pgfmath@x=-\pgfmath@x%
+            \fi%
+            \ifdim0pt>\pgfmath@y%
+                \expandafter\def\expandafter\pgfmath@sign\expandafter{\pgfmath@sign-}%
+                \pgfmath@y=-\pgfmath@y%
+            \fi%
+            \ifdim1pt>\pgfmath@y%
+                \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}%
+                \pgfmath@x=\pgfmath@sign\pgfmathresult\pgfmath@x%
+            \else%
+                \def\pgfmathresult{0}%
+                \pgfmath@divide@periodtrue%
+                \c@pgfmath@counta=0\relax%
+                \pgfmathdivide@@%
+                \pgfmath@x=\pgfmath@sign\pgfmathresult pt\relax%
+            \fi%
+        \fi%
+        \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 \def\pgfmath@small@number{0.00002}
 
 \def\pgfmathdivide@@{%
-	\let\pgfmath@next=\relax%
-	\ifdim\pgfmath@small@number pt<\pgfmath@x%
-		\ifdim\pgfmath@small@number pt<\pgfmath@y%
-			\ifdim\pgfmath@y>\pgfmath@x%
-				\ifpgfmath@divide@period%
-					\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult.}%
-					\pgfmath@divide@periodfalse%
-				\fi%
-				\pgfmathdivide@dimenbyten\pgfmath@y%
-				\ifdim\pgfmath@y>\pgfmath@x%
-					\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult0}%
-				\fi%
-			\else%
-				\c@pgfmath@counta=\pgfmath@x%
-				\c@pgfmath@countb=\pgfmath@y%
-				\divide\c@pgfmath@counta by\c@pgfmath@countb%
-				\pgfmath@ya=\c@pgfmath@counta\pgfmath@y%
-				\advance\pgfmath@x by-\pgfmath@ya%
-				\def\pgfmath@next{%
-					\toks0=\expandafter{\pgfmathresult}%
-					\edef\pgfmathresult{\the\toks0 \the\c@pgfmath@counta}%
-				}%
-				\ifpgfmath@divide@period
-				\else
-					% we are behind the period. It may happen that the
-					% result is more than one digit - in that case,
-					% introduce special handling:
-					\ifnum\c@pgfmath@counta>9 %
-						\expandafter\pgfmathdivide@advance@last@digit\pgfmathresult CCCCC\@@
-						\advance\c@pgfmath@counta by-10 %
-						\ifnum\c@pgfmath@counta=0
-							\let\pgfmath@next=\relax
-						\fi
-					\fi
-				\fi
-				\pgfmath@next
-			\fi%
-			\let\pgfmath@next=\pgfmathdivide@@%
-		\fi%
-	\fi%
-	\pgfmath@next%
+    \let\pgfmath@next=\relax%
+    \ifdim\pgfmath@small@number pt<\pgfmath@x%
+        \ifdim\pgfmath@small@number pt<\pgfmath@y%
+            \ifdim\pgfmath@y>\pgfmath@x%
+                \ifpgfmath@divide@period%
+                    \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult.}%
+                    \pgfmath@divide@periodfalse%
+                \fi%
+                \pgfmathdivide@dimenbyten\pgfmath@y%
+                \ifdim\pgfmath@y>\pgfmath@x%
+                    \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult0}%
+                \fi%
+            \else%
+                \c@pgfmath@counta=\pgfmath@x%
+                \c@pgfmath@countb=\pgfmath@y%
+                \divide\c@pgfmath@counta by\c@pgfmath@countb%
+                \pgfmath@ya=\c@pgfmath@counta\pgfmath@y%
+                \advance\pgfmath@x by-\pgfmath@ya%
+                \def\pgfmath@next{%
+                    \toks0=\expandafter{\pgfmathresult}%
+                    \edef\pgfmathresult{\the\toks0 \the\c@pgfmath@counta}%
+                }%
+                \ifpgfmath@divide@period
+                \else
+                    % we are behind the period. It may happen that the
+                    % result is more than one digit - in that case,
+                    % introduce special handling:
+                    \ifnum\c@pgfmath@counta>9 %
+                        \expandafter\pgfmathdivide@advance@last@digit\pgfmathresult CCCCC\@@
+                        \advance\c@pgfmath@counta by-10 %
+                        \ifnum\c@pgfmath@counta=0
+                            \let\pgfmath@next=\relax
+                        \fi
+                    \fi
+                \fi
+                \pgfmath@next
+            \fi%
+            \let\pgfmath@next=\pgfmathdivide@@%
+        \fi%
+    \fi%
+    \pgfmath@next%
 }
 
 % advances the last digit found in the number. Any missing digits are
 % supposed to be filled with 'C'.
 \def\pgfmathdivide@advance@last@digit#1.#2#3#4#5#6#7\@@{%
-	\pgfmath@ya=\pgfmathresult pt %
-	\if#2C%
-		\pgfmath@xa=1pt %
-	\else
-		\if#3C%
-			\pgfmath@xa=0.1pt %
-		\else
-			\if#4C%
-				\pgfmath@xa=0.01pt %
-			\else
-				\if#5C%
-					\pgfmath@xa=0.001pt %
-				\else
-					\if#6C%
-						\pgfmath@xa=0.0001pt %
-					\else
-						\pgfmath@xa=0.00001pt %
-					\fi
-				\fi
-			\fi
-		\fi
-	\fi
-	\advance\pgfmath@ya by\pgfmath@xa
-	\edef\pgfmathresult{\pgfmath@tonumber@notrailingzero\pgfmath@ya}%
+    \pgfmath@ya=\pgfmathresult pt %
+    \if#2C%
+        \pgfmath@xa=1pt %
+    \else
+        \if#3C%
+            \pgfmath@xa=0.1pt %
+        \else
+            \if#4C%
+                \pgfmath@xa=0.01pt %
+            \else
+                \if#5C%
+                    \pgfmath@xa=0.001pt %
+                \else
+                    \if#6C%
+                        \pgfmath@xa=0.0001pt %
+                    \else
+                        \pgfmath@xa=0.00001pt %
+                    \fi
+                \fi
+            \fi
+        \fi
+    \fi
+    \advance\pgfmath@ya by\pgfmath@xa
+    \edef\pgfmathresult{\pgfmath@tonumber@notrailingzero\pgfmath@ya}%
 }%
 
 {
 \catcode`\p=12
 \catcode`\t=12
 \gdef\Pgf@geT@NO@TRAILING@ZERO#1.#2pt{%
-	#1.%
-	\ifnum#2=0 \else #2\fi
+    #1.%
+    \ifnum#2=0 \else #2\fi
 }
 }
 \def\pgfmath@tonumber@notrailingzero#1{\expandafter\Pgf@geT@NO@TRAILING@ZERO\the#1}
 
 
 \def\pgfmathdivide@dimenbyten#1{%
-	\edef\pgfmath@temp{\pgfmath@tonumber{#1}}%
-	\expandafter\pgfmathdivide@@dimenbyten\pgfmath@temp\@@#1\@@}
+    \edef\pgfmath@temp{\pgfmath@tonumber{#1}}%
+    \expandafter\pgfmathdivide@@dimenbyten\pgfmath@temp\@@#1\@@}
 \def\pgfmathdivide@@dimenbyten#1.#2\@@#3\@@{%
-	\pgfmath@tempcnta=#1\relax%
-	\divide\pgfmath@tempcnta by10\relax%
-	\pgfmath@tempcntb=\pgfmath@tempcnta%
-	\multiply\pgfmath@tempcnta by-10\relax%
-	\advance\pgfmath@tempcnta by#1\relax%
-	#3=\the\pgfmath@tempcntb.\the\pgfmath@tempcnta#2pt\relax%
+    \pgfmath@tempcnta=#1\relax%
+    \divide\pgfmath@tempcnta by10\relax%
+    \pgfmath@tempcntb=\pgfmath@tempcnta%
+    \multiply\pgfmath@tempcnta by-10\relax%
+    \advance\pgfmath@tempcnta by#1\relax%
+    #3=\the\pgfmath@tempcntb.\the\pgfmath@tempcnta#2pt\relax%
 }
 
 
 % reciprocal function.
 %
 \pgfmathdeclarefunction{reciprocal}{1}{%
-	\begingroup%
-		\expandafter\pgfmath@x#1pt\relax%
-		\ifdim\pgfmath@x=0pt\relax%
-			\pgfmath@error{You asked me to calculate `1/#1', but I cannot divide any number by zero}{}%
-		\fi%
-		\edef\pgfmath@reciprocaltemp{\pgfmath@tonumber{\pgfmath@x}}%
-		\expandafter\pgfmathreciprocal@@\pgfmath@reciprocaltemp0000000\pgfmath@}
+    \begingroup%
+        \expandafter\pgfmath@x#1pt\relax%
+        \ifdim\pgfmath@x=0pt\relax%
+            \pgfmath@error{You asked me to calculate `1/#1', but I cannot divide any number by zero}{}%
+        \fi%
+        \edef\pgfmath@reciprocaltemp{\pgfmath@tonumber{\pgfmath@x}}%
+        \expandafter\pgfmathreciprocal@@\pgfmath@reciprocaltemp0000000\pgfmath@}
 \def\pgfmathreciprocal@@#1.#2#3#4#5#6#7\pgfmath@{%
-		\c@pgfmath@counta#2#3#4#5#6\relax%
-		% If the number is an integer, use TeX arithmatic.
-		\ifnum\c@pgfmath@counta=0\relax%
-			\pgfmath@x1pt\relax%
-			\divide\pgfmath@x#1\relax%
-		\else%
-			\ifnum#1>100\relax%
-				\c@pgfmath@counta#1#2#3#4\relax%
-				\c@pgfmath@countb1000000000\relax%
-				\divide\c@pgfmath@countb\c@pgfmath@counta%
-				\c@pgfmath@counta\c@pgfmath@countb%
-				\divide\c@pgfmath@counta10000\relax%
-				\pgfmath@x\c@pgfmath@counta pt\relax%
-				\multiply\c@pgfmath@counta-10000\relax%
-				\advance\c@pgfmath@countb\c@pgfmath@counta%
-				\pgfmath@y\c@pgfmath@countb pt\relax%
-				\divide\pgfmath@y1000000\relax%		
-				\advance\pgfmath@x\pgfmath@y%
-			\else%
-				\c@pgfmath@counta#1#2#3#4#5#6\relax%
-				\c@pgfmath@countb1000000000\relax%
-				\divide\c@pgfmath@countb\c@pgfmath@counta%
-				\c@pgfmath@counta\c@pgfmath@countb%
-				\divide\c@pgfmath@counta10000\relax%
-				\pgfmath@x\c@pgfmath@counta pt\relax%
-				\multiply\c@pgfmath@counta-10000\relax%
-				\advance\c@pgfmath@countb\c@pgfmath@counta%
-				\pgfmath@y\c@pgfmath@countb pt\relax%
-				\pgfmath@y.1\pgfmath@y% Yes! This way is more accurate. Go figure...
-				\pgfmath@y.1\pgfmath@y%	
-				\pgfmath@y.1\pgfmath@y%	
-				\pgfmath@y.1\pgfmath@y%		
-				\advance\pgfmath@x\pgfmath@y%
-			\fi%
-		\fi%
-		\pgfmath@returnone\pgfmath@x%
-	\endgroup%
+        \c@pgfmath@counta#2#3#4#5#6\relax%
+        % If the number is an integer, use TeX arithmetic.
+        \ifnum\c@pgfmath@counta=0\relax%
+            \pgfmath@x1pt\relax%
+            \divide\pgfmath@x#1\relax%
+        \else%
+            \ifnum#1>100\relax%
+                \c@pgfmath@counta#1#2#3#4\relax%
+                \c@pgfmath@countb1000000000\relax%
+                \divide\c@pgfmath@countb\c@pgfmath@counta%
+                \c@pgfmath@counta\c@pgfmath@countb%
+                \divide\c@pgfmath@counta10000\relax%
+                \pgfmath@x\c@pgfmath@counta pt\relax%
+                \multiply\c@pgfmath@counta-10000\relax%
+                \advance\c@pgfmath@countb\c@pgfmath@counta%
+                \pgfmath@y\c@pgfmath@countb pt\relax%
+                \divide\pgfmath@y1000000\relax%
+                \advance\pgfmath@x\pgfmath@y%
+            \else%
+                \c@pgfmath@counta#1#2#3#4#5#6\relax%
+                \c@pgfmath@countb1000000000\relax%
+                \divide\c@pgfmath@countb\c@pgfmath@counta%
+                \c@pgfmath@counta\c@pgfmath@countb%
+                \divide\c@pgfmath@counta10000\relax%
+                \pgfmath@x\c@pgfmath@counta pt\relax%
+                \multiply\c@pgfmath@counta-10000\relax%
+                \advance\c@pgfmath@countb\c@pgfmath@counta%
+                \pgfmath@y\c@pgfmath@countb pt\relax%
+                \pgfmath@y.1\pgfmath@y% Yes! This way is more accurate. Go figure...
+                \pgfmath@y.1\pgfmath@y%
+                \pgfmath@y.1\pgfmath@y%
+                \pgfmath@y.1\pgfmath@y%
+                \advance\pgfmath@x\pgfmath@y%
+            \fi%
+        \fi%
+        \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 % div function.
 %
 \pgfmathdeclarefunction{div}{2}{%
-	\begingroup%
-		\pgfmathdivide@{#1}{#2}%
-		\ifdim\pgfmathresult pt<0pt\relax%
-			\pgfmathceil@{\pgfmathresult}%
-		\else%
-			\pgfmathfloor@{\pgfmathresult}%
-		\fi%
-		\afterassignment\pgfmath@gobbletilpgfmath@%
-		\c@pgfmath@counta=\pgfmathresult\relax\pgfmath@%
-		\edef\pgfmathresult{\the\c@pgfmath@counta}%
-		\pgfmath@smuggleone\pgfmathresult%
-	\endgroup%
+    \begingroup%
+        \pgfmathdivide@{#1}{#2}%
+        \ifdim\pgfmathresult pt<0pt\relax%
+            \pgfmathceil@{\pgfmathresult}%
+        \else%
+            \pgfmathfloor@{\pgfmathresult}%
+        \fi%
+        \afterassignment\pgfmath@gobbletilpgfmath@%
+        \c@pgfmath@counta=\pgfmathresult\relax\pgfmath@%
+        \edef\pgfmathresult{\the\c@pgfmath@counta}%
+        \pgfmath@smuggleone\pgfmathresult%
+    \endgroup%
 }
 
 % mod function.
@@ -285,27 +285,27 @@
 % Mod function (never negative).
 %
 \pgfmathdeclarefunction{Mod}{2}{%
-	\begingroup%
-		\pgfmathmod@{#1}{#2}%
-		\pgfmath@x=\pgfmathresult pt\relax%
-		\ifdim\pgfmath@x<0pt\relax%
-			\advance\pgfmath@x by#2pt\relax%
-		\fi%
-		\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
-		\pgfmath@smuggleone\pgfmathresult%
-	\endgroup%
+    \begingroup%
+        \pgfmathmod@{#1}{#2}%
+        \pgfmath@x=\pgfmathresult pt\relax%
+        \ifdim\pgfmath@x<0pt\relax%
+            \advance\pgfmath@x by#2pt\relax%
+        \fi%
+        \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
+        \pgfmath@smuggleone\pgfmathresult%
+    \endgroup%
 }
 
 % abs function.
 %
 \pgfmathdeclarefunction{abs}{1}{%
-	\begingroup%
-		\expandafter\pgfmath@x#1pt\relax%
-		\ifdim\pgfmath@x<0pt\relax%
-			\pgfmath@x-\pgfmath@x%
-		\fi%
-	\pgfmath@returnone\pgfmath@x%
-	\endgroup%
+    \begingroup%
+        \expandafter\pgfmath@x#1pt\relax%
+        \ifdim\pgfmath@x<0pt\relax%
+            \pgfmath@x-\pgfmath@x%
+        \fi%
+    \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 % sign(x)
@@ -334,189 +334,189 @@
 % uses coefficients contributed by Alain Matthes.
 %
 \pgfmathdeclarefunction{ln}{1}{%
-	\begingroup%
-		\expandafter\pgfmath@x#1pt\relax%
-		\ifdim\pgfmath@x>0pt\else%
-			\pgfmath@error{I cannot calculate the logarithm of `#1'}{}%
-		\fi%		
-		\c@pgfmath@counta=0\relax%
-		\ifdim\pgfmath@x>2pt\relax%
-			\ifdim\pgfmath@x<128pt\relax%
-				\ifdim\pgfmath@x<8pt\relax%
-					\ifdim\pgfmath@x<4pt\relax%
-						\divide\pgfmath@x by2\relax%
-						\c@pgfmath@counta=1\relax%
-					\else%
-						\divide\pgfmath@x by4\relax%
-						\c@pgfmath@counta=2\relax%
-					\fi%
-				\else%
-					\ifdim\pgfmath@x<32pt\relax%
-						\ifdim\pgfmath@x<16pt\relax%
-							\divide\pgfmath@x by8\relax%
-							\c@pgfmath@counta=3\relax%
-						\else%
-							\divide\pgfmath@x by16\relax%
-							\c@pgfmath@counta=4\relax%
-						\fi%
-					\else%
-						\ifdim\pgfmath@x<64pt\relax%
-							\divide\pgfmath@x by32\relax%
-							\c@pgfmath@counta=5\relax%
-						\else%
-							\divide\pgfmath@x by64\relax%
-							\c@pgfmath@counta=6\relax%
-						\fi%
-					\fi%
-				\fi%
-			\else%
-				\ifdim\pgfmath@x<2048pt\relax%
-					\ifdim\pgfmath@x<512pt\relax%
-						\ifdim\pgfmath@x<256pt\relax%
-							\divide\pgfmath@x by128\relax%
-							\c@pgfmath@counta=7\relax%
-						\else%
-							\divide\pgfmath@x by256\relax%
-							\c@pgfmath@counta=8\relax%
-						\fi%
-					\else%
-						\ifdim\pgfmath@x<1024pt\relax%
-							\divide\pgfmath@x by512\relax%
-							\c@pgfmath@counta=9\relax%
-						\else%
-							\divide\pgfmath@x by1024\relax%
-							\c@pgfmath@counta=10\relax%
-						\fi%
-					\fi%
-				\else%
-					\ifdim\pgfmath@x<8192pt\relax%
-						\ifdim\pgfmath@x<4096pt\relax%
-							\divide\pgfmath@x by2048\relax%
-							\c@pgfmath@counta=11\relax%
-						\else%
-							\divide\pgfmath@x by4096\relax%
-							\c@pgfmath@counta =12\relax%
-						\fi%
-					\else%
-						\divide\pgfmath@x by8192\relax%
-						\c@pgfmath@counta=13\relax%
-					\fi%
-				\fi%
-			\fi%	
-		\else%
-			\ifdim\pgfmath@x<1pt\relax%
-				\ifdim\pgfmath@x>0.0078125pt\relax% 2^-7
-					\ifdim\pgfmath@x>0.125pt\relax% 2^-3
-						\ifdim\pgfmath@x>0.5pt\relax% 2^-1
-							\multiply\pgfmath@x by2\relax%
-							\c@pgfmath@counta=-1\relax%
-						\else%
-							\multiply\pgfmath@x by4\relax%
-							\c@pgfmath@counta=-2\relax%
-						\fi%
-					\else%
-						\ifdim\pgfmath@x>0.03125pt\relax% 2^-5
-							\ifdim\pgfmath@x>0.0625pt\relax%
-								\multiply\pgfmath@x by8\relax%
-								\c@pgfmath@counta=-3\relax%
-							\else%
-								\multiply\pgfmath@x by16\relax%
-								\c@pgfmath@counta=-4\relax%
-							\fi%
-						\else%
-							\ifdim\pgfmath@x>0.015625pt\relax% 2^-6
-								\multiply\pgfmath@x by32\relax%
-								\c@pgfmath@counta=-5\relax%
-							\else%
-								\multiply\pgfmath@x by64\relax%
-								\c@pgfmath@counta=-6\relax%
-							\fi%
-						\fi%
-					\fi%
-				\else%
-					\ifdim\pgfmath@x>0.000244140625pt\relax% 2^-11
-						\ifdim\pgfmath@x>0.001953125pt\relax% 2^-9
-							\ifdim\pgfmath@x>0.00390625pt\relax% 2^-8
-								\multiply\pgfmath@x by128\relax%
-								\c@pgfmath@counta=-7\relax%
-							\else%
-								\multiply\pgfmath@x by256\relax%
-								\c@pgfmath@counta=-8\relax%
-							\fi%
-						\else%
-							\ifdim\pgfmath@x>0.0009765625pt\relax% 2^-10
-								\multiply\pgfmath@x by512\relax%
-								\c@pgfmath@counta=-9\relax%
-							\else%
-								\multiply\pgfmath@x by1024\relax%
-								\c@pgfmath@counta=-10\relax%
-							\fi%
-						\fi%
-					\else%
-						\ifdim\pgfmath@x>0.0001220703125pt\relax% 2^13
-							\ifdim\pgfmath@x>0.0002441406256pt\relax% 2^12
-								\multiply\pgfmath@x by2048\relax%
-								\c@pgfmath@counta=-11\relax%
-							\else%
-								\multiply\pgfmath@x by4096\relax%
-								\c@pgfmath@counta=-12\relax%
-							\fi%
-						\else%
-							\multiply\pgfmath@x by8192\relax%
-							\c@pgfmath@counta=-13\relax%
-						\fi%
-					\fi%
-				\fi%
-			\fi%	
-		\fi%
-		%
-		% Use A+(B+(C+(D+(E+F*x)*x)*x)*x)*x
-		%
-		% where:
-		% A = -2.787927935
-		% B =  5.047861502
-		% C = -3.489886985
-		% D =  1.589480044
-		% E = -.4025153233
-		% F =  0.04300521312
-		%
-		\edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
-		\pgfmath@x=0.04300521312\pgfmath@x%
-		\advance\pgfmath@x by-.4025153233pt\relax%
-		\pgfmath@x=\pgfmath@temp\pgfmath@x%
-		\advance\pgfmath@x by1.589480044pt\relax%
-		\pgfmath@x=\pgfmath@temp\pgfmath@x%
-		\advance\pgfmath@x by-3.489886985pt\relax%
-		\pgfmath@x=\pgfmath@temp\pgfmath@x%
-		\advance\pgfmath@x by5.047861502pt\relax%
-		\pgfmath@x=\pgfmath@temp\pgfmath@x%
-		\advance\pgfmath@x by-2.787927935pt\relax%
-		\advance\pgfmath@x by\c@pgfmath@counta pt\relax%
-		\pgfmath@x=0.6931471806\pgfmath@x%	
-		\pgfmath@returnone\pgfmath@x%
-	\endgroup%
+    \begingroup%
+        \expandafter\pgfmath@x#1pt\relax%
+        \ifdim\pgfmath@x>0pt\else%
+            \pgfmath@error{I cannot calculate the logarithm of `#1'}{}%
+        \fi%
+        \c@pgfmath@counta=0\relax%
+        \ifdim\pgfmath@x>2pt\relax%
+            \ifdim\pgfmath@x<128pt\relax%
+                \ifdim\pgfmath@x<8pt\relax%
+                    \ifdim\pgfmath@x<4pt\relax%
+                        \divide\pgfmath@x by2\relax%
+                        \c@pgfmath@counta=1\relax%
+                    \else%
+                        \divide\pgfmath@x by4\relax%
+                        \c@pgfmath@counta=2\relax%
+                    \fi%
+                \else%
+                    \ifdim\pgfmath@x<32pt\relax%
+                        \ifdim\pgfmath@x<16pt\relax%
+                            \divide\pgfmath@x by8\relax%
+                            \c@pgfmath@counta=3\relax%
+                        \else%
+                            \divide\pgfmath@x by16\relax%
+                            \c@pgfmath@counta=4\relax%
+                        \fi%
+                    \else%
+                        \ifdim\pgfmath@x<64pt\relax%
+                            \divide\pgfmath@x by32\relax%
+                            \c@pgfmath@counta=5\relax%
+                        \else%
+                            \divide\pgfmath@x by64\relax%
+                            \c@pgfmath@counta=6\relax%
+                        \fi%
+                    \fi%
+                \fi%
+            \else%
+                \ifdim\pgfmath@x<2048pt\relax%
+                    \ifdim\pgfmath@x<512pt\relax%
+                        \ifdim\pgfmath@x<256pt\relax%
+                            \divide\pgfmath@x by128\relax%
+                            \c@pgfmath@counta=7\relax%
+                        \else%
+                            \divide\pgfmath@x by256\relax%
+                            \c@pgfmath@counta=8\relax%
+                        \fi%
+                    \else%
+                        \ifdim\pgfmath@x<1024pt\relax%
+                            \divide\pgfmath@x by512\relax%
+                            \c@pgfmath@counta=9\relax%
+                        \else%
+                            \divide\pgfmath@x by1024\relax%
+                            \c@pgfmath@counta=10\relax%
+                        \fi%
+                    \fi%
+                \else%
+                    \ifdim\pgfmath@x<8192pt\relax%
+                        \ifdim\pgfmath@x<4096pt\relax%
+                            \divide\pgfmath@x by2048\relax%
+                            \c@pgfmath@counta=11\relax%
+                        \else%
+                            \divide\pgfmath@x by4096\relax%
+                            \c@pgfmath@counta =12\relax%
+                        \fi%
+                    \else%
+                        \divide\pgfmath@x by8192\relax%
+                        \c@pgfmath@counta=13\relax%
+                    \fi%
+                \fi%
+            \fi%
+        \else%
+            \ifdim\pgfmath@x<1pt\relax%
+                \ifdim\pgfmath@x>0.0078125pt\relax% 2^-7
+                    \ifdim\pgfmath@x>0.125pt\relax% 2^-3
+                        \ifdim\pgfmath@x>0.5pt\relax% 2^-1
+                            \multiply\pgfmath@x by2\relax%
+                            \c@pgfmath@counta=-1\relax%
+                        \else%
+                            \multiply\pgfmath@x by4\relax%
+                            \c@pgfmath@counta=-2\relax%
+                        \fi%
+                    \else%
+                        \ifdim\pgfmath@x>0.03125pt\relax% 2^-5
+                            \ifdim\pgfmath@x>0.0625pt\relax%
+                                \multiply\pgfmath@x by8\relax%
+                                \c@pgfmath@counta=-3\relax%
+                            \else%
+                                \multiply\pgfmath@x by16\relax%
+                                \c@pgfmath@counta=-4\relax%
+                            \fi%
+                        \else%
+                            \ifdim\pgfmath@x>0.015625pt\relax% 2^-6
+                                \multiply\pgfmath@x by32\relax%
+                                \c@pgfmath@counta=-5\relax%
+                            \else%
+                                \multiply\pgfmath@x by64\relax%
+                                \c@pgfmath@counta=-6\relax%
+                            \fi%
+                        \fi%
+                    \fi%
+                \else%
+                    \ifdim\pgfmath@x>0.000244140625pt\relax% 2^-11
+                        \ifdim\pgfmath@x>0.001953125pt\relax% 2^-9
+                            \ifdim\pgfmath@x>0.00390625pt\relax% 2^-8
+                                \multiply\pgfmath@x by128\relax%
+                                \c@pgfmath@counta=-7\relax%
+                            \else%
+                                \multiply\pgfmath@x by256\relax%
+                                \c@pgfmath@counta=-8\relax%
+                            \fi%
+                        \else%
+                            \ifdim\pgfmath@x>0.0009765625pt\relax% 2^-10
+                                \multiply\pgfmath@x by512\relax%
+                                \c@pgfmath@counta=-9\relax%
+                            \else%
+                                \multiply\pgfmath@x by1024\relax%
+                                \c@pgfmath@counta=-10\relax%
+                            \fi%
+                        \fi%
+                    \else%
+                        \ifdim\pgfmath@x>0.0001220703125pt\relax% 2^13
+                            \ifdim\pgfmath@x>0.0002441406256pt\relax% 2^12
+                                \multiply\pgfmath@x by2048\relax%
+                                \c@pgfmath@counta=-11\relax%
+                            \else%
+                                \multiply\pgfmath@x by4096\relax%
+                                \c@pgfmath@counta=-12\relax%
+                            \fi%
+                        \else%
+                            \multiply\pgfmath@x by8192\relax%
+                            \c@pgfmath@counta=-13\relax%
+                        \fi%
+                    \fi%
+                \fi%
+            \fi%
+        \fi%
+        %
+        % Use A+(B+(C+(D+(E+F*x)*x)*x)*x)*x
+        %
+        % where:
+        % A = -2.787927935
+        % B =  5.047861502
+        % C = -3.489886985
+        % D =  1.589480044
+        % E = -.4025153233
+        % F =  0.04300521312
+        %
+        \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
+        \pgfmath@x=0.04300521312\pgfmath@x%
+        \advance\pgfmath@x by-.4025153233pt\relax%
+        \pgfmath@x=\pgfmath@temp\pgfmath@x%
+        \advance\pgfmath@x by1.589480044pt\relax%
+        \pgfmath@x=\pgfmath@temp\pgfmath@x%
+        \advance\pgfmath@x by-3.489886985pt\relax%
+        \pgfmath@x=\pgfmath@temp\pgfmath@x%
+        \advance\pgfmath@x by5.047861502pt\relax%
+        \pgfmath@x=\pgfmath@temp\pgfmath@x%
+        \advance\pgfmath@x by-2.787927935pt\relax%
+        \advance\pgfmath@x by\c@pgfmath@counta pt\relax%
+        \pgfmath@x=0.6931471806\pgfmath@x%
+        \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 % log2 function.
 %
 \pgfmathdeclarefunction{log2}{1}{%
-	\begingroup%
-		\pgfmathln@{#1}%
-		\pgfmath@x=\pgfmathresult pt\relax%
-		\pgfmath@x=1.442695041\pgfmath@x% 1/ln(2).
-		\pgfmath@returnone\pgfmath@x%
-	\endgroup%
+    \begingroup%
+        \pgfmathln@{#1}%
+        \pgfmath@x=\pgfmathresult pt\relax%
+        \pgfmath@x=1.442695041\pgfmath@x% 1/ln(2).
+        \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 % log10 function
 %
-\pgfmathdeclarefunction{log10}{1}{%	
-	\begingroup%
-		\pgfmathln@{#1}%
-		\pgfmath@x=\pgfmathresult pt\relax%
-		\pgfmath@x=0.43429441\pgfmath@x% 1/ln(10).
-		\pgfmath@returnone\pgfmath@x%
-	\endgroup%
+\pgfmathdeclarefunction{log10}{1}{%
+    \begingroup%
+        \pgfmathln@{#1}%
+        \pgfmath@x=\pgfmathresult pt\relax%
+        \pgfmath@x=0.43429441\pgfmath@x% 1/ln(10).
+        \pgfmath@returnone\pgfmath@x%
+    \endgroup%
 }
 
 % This is needed since \pgfmathlog2 and \pgfmathlog10 are not legal macro names
@@ -527,7 +527,7 @@
 
 % exp function.
 %
-\pgfmathdeclarefunction{exp}{1}{%	
+\pgfmathdeclarefunction{exp}{1}{%
   \begingroup
     \pgfmath@xc=#1pt\relax
     \pgfmath@yc=#1pt\relax
@@ -559,186 +559,186 @@
 
 % sqrt function.
 %
-\pgfmathdeclarefunction{sqrt}{1}{%	
-	\begingroup%
-		\expandafter\pgfmath@x#1pt\relax%
-		\ifdim\pgfmath@x<0pt\relax%
-			\pgfmath@error{I cannot calculate the square-root of the negative number `#1'}{}%
-		\else%
-			\ifdim\pgfmath@x<10pt\relax%
-				\def\pgfmath@zeros{0}%
-				\def\pgfmath@targetiterations{1}%
-			\else%
-				\ifdim\pgfmath@x<100pt\relax%
-					\def\pgfmath@zeros{}%
-					\def\pgfmath@targetiterations{1}%
-				\else%
-					\ifdim\pgfmath@x<1000pt\relax%
-						\def\pgfmath@zeros{0}%
-						\def\pgfmath@targetiterations{2}%
-					\else%
-						\ifdim\pgfmath@x<10000pt\relax%
-							\def\pgfmath@zeros{}%
-							\def\pgfmath@targetiterations{2}%
-					\else%
-							\def\pgfmath@zeros{0}%
-							\def\pgfmath@targetiterations{3}%
-		\fi\fi\fi\fi\fi%
-		\edef\pgfmath@temp{\pgfmath@zeros\pgfmath@tonumber{\pgfmath@x}}%
-		\expandafter\pgfmath@sqrt@\pgfmath@temp\pgfmath@%
+\pgfmathdeclarefunction{sqrt}{1}{%
+    \begingroup%
+        \expandafter\pgfmath@x#1pt\relax%
+        \ifdim\pgfmath@x<0pt\relax%
+            \pgfmath@error{I cannot calculate the square-root of the negative number `#1'}{}%
+        \else%
+            \ifdim\pgfmath@x<10pt\relax%
+                \def\pgfmath@zeros{0}%
+                \def\pgfmath@targetiterations{1}%
+            \else%
+                \ifdim\pgfmath@x<100pt\relax%
+                    \def\pgfmath@zeros{}%
+                    \def\pgfmath@targetiterations{1}%
+                \else%
+                    \ifdim\pgfmath@x<1000pt\relax%
+                        \def\pgfmath@zeros{0}%
+                        \def\pgfmath@targetiterations{2}%
+                    \else%
+                        \ifdim\pgfmath@x<10000pt\relax%
+                            \def\pgfmath@zeros{}%
+                            \def\pgfmath@targetiterations{2}%
+                    \else%
+                            \def\pgfmath@zeros{0}%
+                            \def\pgfmath@targetiterations{3}%
+        \fi\fi\fi\fi\fi%
+        \edef\pgfmath@temp{\pgfmath@zeros\pgfmath@tonumber{\pgfmath@x}}%
+        \expandafter\pgfmath@sqrt@\pgfmath@temp\pgfmath@%
 }
 \def\pgfmath@sqrt@#1.#2\pgfmath@{\pgfmath@@sqrt@#1#2\pgfmath@empty\pgfmath@empty\pgfmath@}
 
 \def\pgfmath@@sqrt@#1#2{%
-		\c@pgfmath@countb=#1#2\relax%
-		\ifnum\c@pgfmath@countb>35\relax%
-			\ifnum\c@pgfmath@countb>63\relax%
-				\ifnum\c@pgfmath@countb>80\relax%
-					\c@pgfmath@counta=9\relax%
-				\else%
-					\c@pgfmath@counta=8\relax%
-				\fi%
-			\else%
-				\ifnum\c@pgfmath@countb>48\relax%
-					\c@pgfmath@counta=7\relax%
-				\else%
-					\c@pgfmath@counta=6\relax%
-				\fi%
-			\fi%
-		\else%
-			\ifnum\c@pgfmath@countb>15\relax%
-				\ifnum\c@pgfmath@countb>24\relax%
-					\c@pgfmath@counta5\relax%
-				\else%
-					\c@pgfmath@counta=4\relax%
-				\fi%
-			\else%
-				\ifnum\c@pgfmath@countb>3\relax%
-					\ifnum\c@pgfmath@countb>8\relax%
-						\c@pgfmath@counta=3\relax%
-					\else%
-						\c@pgfmath@counta=2\relax%
-					\fi%
-				\else%
-					\ifnum\c@pgfmath@countb>0\relax%
-						\c@pgfmath@counta=1\relax%
-					\else%
-						\c@pgfmath@counta=0\relax%
-					\fi%
-				\fi%
-			\fi%
-		\fi%
-		\edef\pgfmath@root{\the\c@pgfmath@counta}%
-		\edef\pgfmath@rootspecial{\the\c@pgfmath@counta}%
-		\multiply\c@pgfmath@counta by-\c@pgfmath@counta\relax%
-		\advance\c@pgfmath@counta by#1#2\relax%
-		\edef\pgfmath@remainder{\the\c@pgfmath@counta}%
-		\pgfmath@@@sqrt@%
+        \c@pgfmath@countb=#1#2\relax%
+        \ifnum\c@pgfmath@countb>35\relax%
+            \ifnum\c@pgfmath@countb>63\relax%
+                \ifnum\c@pgfmath@countb>80\relax%
+                    \c@pgfmath@counta=9\relax%
+                \else%
+                    \c@pgfmath@counta=8\relax%
+                \fi%
+            \else%
+                \ifnum\c@pgfmath@countb>48\relax%
+                    \c@pgfmath@counta=7\relax%
+                \else%
+                    \c@pgfmath@counta=6\relax%
+                \fi%
+            \fi%
+        \else%
+            \ifnum\c@pgfmath@countb>15\relax%
+                \ifnum\c@pgfmath@countb>24\relax%
+                    \c@pgfmath@counta5\relax%
+                \else%
+                    \c@pgfmath@counta=4\relax%
+                \fi%
+            \else%
+                \ifnum\c@pgfmath@countb>3\relax%
+                    \ifnum\c@pgfmath@countb>8\relax%
+                        \c@pgfmath@counta=3\relax%
+                    \else%
+                        \c@pgfmath@counta=2\relax%
+                    \fi%
+                \else%
+                    \ifnum\c@pgfmath@countb>0\relax%
+                        \c@pgfmath@counta=1\relax%
+                    \else%
+                        \c@pgfmath@counta=0\relax%
+                    \fi%
+                \fi%
+            \fi%
+        \fi%
+        \edef\pgfmath@root{\the\c@pgfmath@counta}%
+        \edef\pgfmath@rootspecial{\the\c@pgfmath@counta}%
+        \multiply\c@pgfmath@counta by-\c@pgfmath@counta\relax%
+        \advance\c@pgfmath@counta by#1#2\relax%
+        \edef\pgfmath@remainder{\the\c@pgfmath@counta}%
+        \pgfmath@@@sqrt@%
 }
 
 \def\pgfmath@@@sqrt@#1#2{%
-		\ifx\pgfmath@empty#1%
-			\edef\pgfmath@remainder{\pgfmath@remainder00}%
-			\def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
-		\else%
-			\ifx\pgfmath@empty#2%
-				\edef\pgfmath@remainder{\pgfmath@remainder#10}%
-				\def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
-			\else%
-				\edef\pgfmath@remainder{\pgfmath@remainder#1#2}%
-				\def\pgfmath@tokens{}%
-		\fi\fi%
-		\c@pgfmath@counta=\pgfmath@rootspecial\relax%
-		\multiply\c@pgfmath@counta by20\relax%
-		\c@pgfmath@countb=\c@pgfmath@counta%
-		\multiply\c@pgfmath@countb by6\relax%
-		\advance\c@pgfmath@countb by36\relax%
-		\c@pgfmath@countc=\c@pgfmath@counta%
-		\multiply\c@pgfmath@countc by2\relax%
-		\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% 
-			\advance\c@pgfmath@countb by-\c@pgfmath@countc%
-			\advance\c@pgfmath@countb by-20\relax%
-			\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-				\advance\c@pgfmath@countb by-\c@pgfmath@countc%
-				\advance\c@pgfmath@countb by-12\relax%
-				\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-					\advance\c@pgfmath@countb by-\c@pgfmath@counta%
-					\advance\c@pgfmath@countb by-3\relax%
-					\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-						\def\pgfmath@digit{0}%
-					\else%
-						\def\pgfmath@digit{1}%
-					\fi%
-				\else%
-					\advance\c@pgfmath@countb by\c@pgfmath@counta%
-					\advance\c@pgfmath@countb by5\relax%
-					\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-						\def\pgfmath@digit{2}%
-					\else%
-						\def\pgfmath@digit{3}%
-					\fi%
-				\fi%
-			\else%
-				\advance\c@pgfmath@countb by\c@pgfmath@counta%
-				\advance\c@pgfmath@countb by9\relax%
-				\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-					\def\pgfmath@digit{4}%
-				\else%
-					\def\pgfmath@digit{5}%
-				\fi%
-			\fi%
-		\else%
-			\advance\c@pgfmath@countb by\c@pgfmath@countc%
-			\advance\c@pgfmath@countb by28\relax%
-			\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-				\advance\c@pgfmath@countb by-\c@pgfmath@counta%
-				\advance\c@pgfmath@countb by-15\relax%
-				\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-					\def\pgfmath@digit{6}%
-				\else%
-					\def\pgfmath@digit{7}%
-				\fi%
-			\else%
-				\advance\c@pgfmath@countb by\c@pgfmath@counta%
-				\advance\c@pgfmath@countb by17\relax%
-				\ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
-					\def\pgfmath@digit{8}%
-				\else%
-					\def\pgfmath@digit{9}%
-				\fi%
-			\fi%
-		\fi%
-		\edef\pgfmath@rootspecial{\pgfmath@rootspecial\pgfmath@digit}%
-		\advance\c@pgfmath@counta by\pgfmath@digit\relax%
-		\multiply\c@pgfmath@counta by-\pgfmath@digit\relax%
-		\advance\c@pgfmath@counta by\pgfmath@remainder\relax%
-		\edef\pgfmath@remainder{\the\c@pgfmath@counta}%
-		\c@pgfmath@counta=\pgfmath@targetiterations\relax%
-		\advance\c@pgfmath@counta by-1\relax%
-		\edef\pgfmath@targetiterations{\the\c@pgfmath@counta}%
-		\ifnum\c@pgfmath@counta=0\relax%
-			\edef\pgfmath@root{\pgfmath@root.\pgfmath@digit}%
-		\else%
-			\edef\pgfmath@root{\pgfmath@root\pgfmath@digit}%
-		\fi%
-		\ifnum\c@pgfmath@counta=-4\relax% -n+1 digits of precision.
-			\let\pgfmath@next\pgfmath@sqrt@end%
-		\else%
-			\let\pgfmath@next\pgfmath@@@sqrt@%
-		\fi%
-		\expandafter\pgfmath@next\pgfmath@tokens%
+        \ifx\pgfmath@empty#1%
+            \edef\pgfmath@remainder{\pgfmath@remainder00}%
+            \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
+        \else%
+            \ifx\pgfmath@empty#2%
+                \edef\pgfmath@remainder{\pgfmath@remainder#10}%
+                \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}%
+            \else%
+                \edef\pgfmath@remainder{\pgfmath@remainder#1#2}%
+                \def\pgfmath@tokens{}%
+        \fi\fi%
+        \c@pgfmath@counta=\pgfmath@rootspecial\relax%
+        \multiply\c@pgfmath@counta by20\relax%
+        \c@pgfmath@countb=\c@pgfmath@counta%
+        \multiply\c@pgfmath@countb by6\relax%
+        \advance\c@pgfmath@countb by36\relax%
+        \c@pgfmath@countc=\c@pgfmath@counta%
+        \multiply\c@pgfmath@countc by2\relax%
+        \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+            \advance\c@pgfmath@countb by-\c@pgfmath@countc%
+            \advance\c@pgfmath@countb by-20\relax%
+            \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                \advance\c@pgfmath@countb by-\c@pgfmath@countc%
+                \advance\c@pgfmath@countb by-12\relax%
+                \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                    \advance\c@pgfmath@countb by-\c@pgfmath@counta%
+                    \advance\c@pgfmath@countb by-3\relax%
+                    \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                        \def\pgfmath@digit{0}%
+                    \else%
+                        \def\pgfmath@digit{1}%
+                    \fi%
+                \else%
+                    \advance\c@pgfmath@countb by\c@pgfmath@counta%
+                    \advance\c@pgfmath@countb by5\relax%
+                    \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                        \def\pgfmath@digit{2}%
+                    \else%
+                        \def\pgfmath@digit{3}%
+                    \fi%
+                \fi%
+            \else%
+                \advance\c@pgfmath@countb by\c@pgfmath@counta%
+                \advance\c@pgfmath@countb by9\relax%
+                \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                    \def\pgfmath@digit{4}%
+                \else%
+                    \def\pgfmath@digit{5}%
+                \fi%
+            \fi%
+        \else%
+            \advance\c@pgfmath@countb by\c@pgfmath@countc%
+            \advance\c@pgfmath@countb by28\relax%
+            \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                \advance\c@pgfmath@countb by-\c@pgfmath@counta%
+                \advance\c@pgfmath@countb by-15\relax%
+                \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                    \def\pgfmath@digit{6}%
+                \else%
+                    \def\pgfmath@digit{7}%
+                \fi%
+            \else%
+                \advance\c@pgfmath@countb by\c@pgfmath@counta%
+                \advance\c@pgfmath@countb by17\relax%
+                \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax%
+                    \def\pgfmath@digit{8}%
+                \else%
+                    \def\pgfmath@digit{9}%
+                \fi%
+            \fi%
+        \fi%
+        \edef\pgfmath@rootspecial{\pgfmath@rootspecial\pgfmath@digit}%
+        \advance\c@pgfmath@counta by\pgfmath@digit\relax%
+        \multiply\c@pgfmath@counta by-\pgfmath@digit\relax%
+        \advance\c@pgfmath@counta by\pgfmath@remainder\relax%
+        \edef\pgfmath@remainder{\the\c@pgfmath@counta}%
+        \c@pgfmath@counta=\pgfmath@targetiterations\relax%
+        \advance\c@pgfmath@counta by-1\relax%
+        \edef\pgfmath@targetiterations{\the\c@pgfmath@counta}%
+        \ifnum\c@pgfmath@counta=0\relax%
+            \edef\pgfmath@root{\pgfmath@root.\pgfmath@digit}%
+        \else%
+            \edef\pgfmath@root{\pgfmath@root\pgfmath@digit}%
+        \fi%
+        \ifnum\c@pgfmath@counta=-4\relax% -n+1 digits of precision.
+            \let\pgfmath@next\pgfmath@sqrt@end%
+        \else%
+            \let\pgfmath@next\pgfmath@@@sqrt@%
+        \fi%
+        \expandafter\pgfmath@next\pgfmath@tokens%
 }
 
 \def\pgfmath@sqrt@end#1\pgfmath@{%
-		\edef\pgfmathresult{\pgfmath@root}%
-		\pgfmath@smuggleone\pgfmathresult%
-	\endgroup}
+        \edef\pgfmathresult{\pgfmath@root}%
+        \pgfmath@smuggleone\pgfmathresult%
+    \endgroup}
 
 % \pgfmathpow
 %
 % Calculates #1 ^ #2
 %
-\pgfmathdeclarefunction{pow}{2}{%	
+\pgfmathdeclarefunction{pow}{2}{%
   \begingroup%
     \pgfmath@xa=#1pt%
     \pgfmath@xb=#2pt%
@@ -775,27 +775,27 @@
         \pgfmathexp@{\pgfmath@tonumber{\pgfmath@x}}%
         \pgfmath@x=\pgfmathresult pt\relax%
       \fi%
-    \fi              
+    \fi
     \pgfmath@returnone\pgf@x%
   \endgroup%
 }
 
 % factorial function.
 %
-\pgfmathdeclarefunction{factorial}{1}{%	
-	\begingroup%
-		\afterassignment\pgfmath@gobbletilpgfmath@%
-		\c@pgfmath@counta=#1\relax\pgfmath@%
-		\pgfmath@x=1pt\relax%
-		\pgfmathloop%
-		\ifnum\c@pgfmath@counta<2\relax%
-		\else%
-			\multiply\pgfmath@x by\c@pgfmath@counta%
-			\advance\c@pgfmath@counta by-1\relax%
-		\repeatpgfmathloop%
-		\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
-		\pgfmath@smuggleone\pgfmathresult%
-	\endgroup%
+\pgfmathdeclarefunction{factorial}{1}{%
+    \begingroup%
+        \afterassignment\pgfmath@gobbletilpgfmath@%
+        \c@pgfmath@counta=#1\relax\pgfmath@%
+        \pgfmath@x=1pt\relax%
+        \pgfmathloop%
+        \ifnum\c@pgfmath@counta<2\relax%
+        \else%
+            \multiply\pgfmath@x by\c@pgfmath@counta%
+            \advance\c@pgfmath@counta by-1\relax%
+        \repeatpgfmathloop%
+        \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
+        \pgfmath@smuggleone\pgfmathresult%
+    \endgroup%
 }
 
 % Local Variables: