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authorKarl Berry <karl@freefriends.org>2014-02-27 00:01:50 +0000
committerKarl Berry <karl@freefriends.org>2014-02-27 00:01:50 +0000
commit90ae413a94da014dbf7a6a8ab584f7c668483a5a (patch)
tree4e0528a2b2fb2004988e7fc804ea2f1354f1f5d5 /Master/texmf-dist/tex/generic/pgf/math
parent800cc56380d1edfe567a6a66bef13e8950eb2b0c (diff)
pgf 3.0.0
git-svn-id: svn://tug.org/texlive/trunk@33057 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/generic/pgf/math')
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex6
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex598
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex245
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex28
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex172
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex7
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex124
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex27
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex2761
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex178
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex1073
-rw-r--r--Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex4
12 files changed, 3007 insertions, 2216 deletions
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
index 9c51dc46117..0c11f544594 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
@@ -7,6 +7,11 @@
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
+\ifx\pgfmathsetlength\undefined
+\else
+ \expandafter\endinput
+\fi
+
\input pgfmathcalc.code.tex
\ifx\pgfkeysloaded\undefined
@@ -15,3 +20,4 @@
\expandafter\input pgfmathfloat.code.tex
\fi
+\endinput \ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
index c1f099ce160..5cc58e62e5d 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
@@ -33,21 +33,24 @@
% parsed assignment.
\def\pgfmathsetlength#1#2{%
- \expandafter\pgfmath@onquick#2\pgfmath@%
- {%
- % Ok, quick version:
- \begingroup%
- \pgfmath@selectfont%
- \pgfmath@x#2\unskip%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
- #1\pgfmathresult pt\relax%
- }%
- {%
- \pgfmathparse{#2}%
- #1\pgfmathresult pt\relax%
- }%
- \ignorespaces%
+ \expandafter\pgfmath@onquick#2\pgfmath@%
+ {%
+ % Ok, quick version:
+ \begingroup%
+ \pgfmath@selectfont%
+ #1#2\unskip%
+ \expandafter\endgroup%
+ \expandafter#1\the#1\relax%
+ }%
+ {%
+ \pgfmathparse{#2}%
+ \ifpgfmathmathunitsdeclared%
+ #1\pgfmathresult mu\relax%
+ \else%
+ #1\pgfmathresult pt\relax%
+ \fi%
+ }%
+ \ignorespaces%
}
% \pgfmathaddtolength
@@ -58,19 +61,22 @@
% #2 - an expression
%
\def\pgfmathaddtolength#1#2{%
- \expandafter\pgfmath@onquick#2\pgfmath@%
+ \expandafter\pgfmath@onquick#2\pgfmath@%
{%
- \begingroup%
- \pgfmath@selectfont%
- \pgfmath@x#1\relax%
- \advance\pgfmath@x#2\unskip%
- \pgfmath@returnone\pgfmath@x%
+ \begingroup%
+ \pgfmath@selectfont%
+ \advance#1#2\unskip%
+ \expandafter%
\endgroup%
- #1\pgfmathresult pt\relax%
+ \expandafter#1\the#1\relax%
}%
{%
- \pgfmathparse{#2}%
- \advance#1\pgfmathresult pt\relax%
+ \pgfmathparse{#2}%
+ \ifpgfmathmathunitsdeclared%
+ \advance#1\pgfmathresult mu\relax%
+ \else%
+ \advance#1\pgfmathresult pt\relax%
+ \fi%
}%
\ignorespaces%
}
@@ -135,11 +141,11 @@
% \thecounter (same as \the\c@counter)
%
\def\pgfmathnewcounter#1{%
- \expandafter\ifx\csname c@#1\endcsname\relax%
- \def\pgfmath@marshal{\csname newcount\endcsname}% Ha! Who cares about \outer?
- \expandafter\pgfmath@marshal\csname c@#1\endcsname%
- \expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}%
- \fi%
+ \expandafter\ifx\csname c@#1\endcsname\relax%
+ \def\pgfmath@marshal{\csname newcount\endcsname}% Ha! Who cares about \outer?
+ \expandafter\pgfmath@marshal\csname c@#1\endcsname%
+ \expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}%
+ \fi%
}
% \pgfmathsetcounter
@@ -150,7 +156,7 @@
% #2 - an expression
%
\def\pgfmathsetcounter#1#2{%
- \expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}%
+ \expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}%
}
% \pgfmathaddtocounter
@@ -173,17 +179,17 @@
\def\pgfmath@pgftext{pgf}
\def\pgfmath@tikztext{tikz}
\def\pgfmathmakecounterglobal#1{%
- \pgfmath@ifundefined{c@#1}{}{%
- \expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}%
- \ifpgfmath@in@%
- \else%
- \expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}%
- \ifpgfmath@in@%
- \else%
- \expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax%
- \fi%
- \fi%
- }%
+ \pgfmath@ifundefined{c@#1}{}{%
+ \expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}%
+ \ifpgfmath@in@%
+ \else%
+ \expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}%
+ \ifpgfmath@in@%
+ \else%
+ \expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax%
+ \fi%
+ \fi%
+ }%
}
% \pgfmathsetmacro
@@ -194,11 +200,11 @@
% #2 - an expression
%
\def\pgfmathsetmacro#1#2{%
- \begingroup%
- \pgfmathsetlength\pgfmath@x{#2}%
- \edef#1{\pgfmath@tonumber{\pgfmath@x}}%
- \pgfmath@smuggleone{#1}%
- \endgroup%
+ \begingroup%
+ \pgfmathparse{#2}%
+ \let#1=\pgfmathresult
+ \pgfmath@smuggleone{#1}%
+ \endgroup%
}
% \pgfmathsetlengthmacro
@@ -209,11 +215,11 @@
% #2 - an expression
%
\def\pgfmathsetlengthmacro#1#2{%
- \begingroup%
- \pgfmathsetlength\pgfmath@x{#2}%
- \edef#1{\the\pgfmath@x}%
- \pgfmath@smuggleone{#1}%
- \endgroup%
+ \begingroup%
+ \pgfmathsetlength\pgfmath@x{#2}%
+ \edef#1{\the\pgfmath@x}%
+ \pgfmath@smuggleone{#1}%
+ \endgroup%
}
% \pgfmathtruncatemacro
@@ -224,11 +230,11 @@
% #2 - an expression
%
\def\pgfmathtruncatemacro#1#2{%
- \begingroup%
- \pgfmathsetcount\c@pgfmath@counta{#2}%
- \edef#1{\the\c@pgfmath@counta}%
- \pgfmath@smuggleone{#1}%
- \endgroup%
+ \begingroup%
+ \pgfmathsetcount\c@pgfmath@counta{#2}%
+ \edef#1{\the\c@pgfmath@counta}%
+ \pgfmath@smuggleone{#1}%
+ \endgroup%
}
% Check whether a given parameter starts with quick.
@@ -247,72 +253,33 @@
\futurelet\pgfmath@next%
\pgfmath@@onquick}
\def\pgfmath@@onquick#1\pgfmath@{%
- \ifx\pgfmath@next+%
- \let\pgfmath@next=\pgfmath@firstoftwo%
- \else%
- \let\pgfmath@next=\pgfmath@secondoftwo%
- \fi%
- \pgfmath@next%
+ \ifx\pgfmath@next+%
+ \let\pgfmath@next=\pgfmath@firstoftwo%
+ \else%
+ \let\pgfmath@next=\pgfmath@secondoftwo%
+ \fi%
+ \pgfmath@next%
}
% *** The following commands DO NOT WORK without the rest of PGF ***
%
% (a dumping ground for stuff that doesn't really belong anywhere else)
-
+
% \pgfmathanglebetweenpoints
%
% Define \pgfmathresult as the angle between points #1 and #2
% Should get the quadrants right as well.
%
\def\pgfmathanglebetweenpoints#1#2{%
- \begingroup%
- \pgf@process{\pgfpointdiff{#1}{#2}}%
- %
- % First approximate the angle of the external point...
- %
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@xb\pgf@x%
- \pgf@yb\pgf@y%
- \ifdim\pgf@xa<0pt\relax%
- \pgf@xa-\pgf@xa%
- \fi%
- \ifdim\pgf@ya<0pt\relax%
- \pgf@ya-\pgf@ya%
- \fi%
- \ifdim\pgf@ya>\pgf@xa%
- \pgf@x\pgf@xa%
- \pgf@y\pgf@ya%
- \else%
- \pgf@x\pgf@ya%
- \pgf@y\pgf@xa%
- \fi%
- \ifdim\pgf@y=0pt\relax%
- \pgf@x0pt%
- \else%
- \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}%
- \pgf@x\pgfmathresult\pgf@x%
- \fi%
- \multiply\pgf@x1000\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgf@counta\the\pgf@x\relax\pgfmath@%
- \expandafter\pgf@x\csname pgfmath@atan@\the\c@pgf@counta\endcsname pt\relax%
- \ifdim\pgfmath@ya>\pgfmath@xa\relax%
- \pgf@x-\pgf@x%
- \advance\pgf@x90pt%
- \fi%
- \ifdim\pgf@xb<0pt%
- \ifdim\pgf@yb>0pt%
- \pgf@x-\pgf@x%
- \fi%
- \advance\pgf@x180pt\relax%
- \else%
- \ifdim\pgf@yb<0pt%
- \pgf@x-\pgf@x%
- \advance\pgf@x360pt\relax%
- \fi\fi%
- \pgfmath@returnone\pgf@x%
- \endgroup%
+ \begingroup%
+ \pgf@process{\pgfpointdiff{#1}{#2}}%
+ \edef\pgf@marshall{\expandafter\noexpand\csname pgfmathatan2@\endcsname{\expandafter\Pgf@geT\the\pgf@y}{\expandafter\Pgf@geT\the\pgf@x}}%
+ \pgf@marshall%
+ \ifdim\pgfmathresult pt<0pt%
+ \pgfmathparse{\pgfmathresult+360}%
+ \fi%
+ \expandafter%
+ \endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult}%
}
%
@@ -321,33 +288,33 @@
% Rotate point #1 about point #2 by #3 degrees.
%
\def\pgfmathrotatepointaround#1#2#3{%
- \pgf@process{%
- \pgf@process{#1}%
- \pgf@xc=\pgf@x%
- \pgf@yc=\pgf@y%
- \pgf@process{#2}%
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@xb\pgf@x%
- \pgf@yb\pgf@y%
- \pgf@x=\pgf@xc%
- \pgf@y=\pgf@yc%
- \advance\pgf@x-\pgf@xa%
- \advance\pgf@y-\pgf@ya%
- \pgfmathsetmacro\angle{#3}%
- \pgfmathsin@{\angle}%
- \let\sineangle\pgfmathresult%
- \pgfmathcos@{\angle}%
- \let\cosineangle\pgfmathresult%
- \pgf@xa\cosineangle\pgf@x%
- \advance\pgf@xa-\sineangle\pgf@y%
- \pgf@ya\sineangle\pgf@x%
- \advance\pgf@ya\cosineangle\pgf@y%
- \pgf@x\pgf@xb%
- \pgf@y\pgf@yb%
- \advance\pgf@x\pgf@xa%
- \advance\pgf@y\pgf@ya%
- }%
+ \pgf@process{%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@process{#2}%
+ \pgf@xa\pgf@x%
+ \pgf@ya\pgf@y%
+ \pgf@xb\pgf@x%
+ \pgf@yb\pgf@y%
+ \pgf@x=\pgf@xc%
+ \pgf@y=\pgf@yc%
+ \advance\pgf@x-\pgf@xa%
+ \advance\pgf@y-\pgf@ya%
+ \pgfmathsetmacro\angle{#3}%
+ \pgfmathsin@{\angle}%
+ \let\sineangle\pgfmathresult%
+ \pgfmathcos@{\angle}%
+ \let\cosineangle\pgfmathresult%
+ \pgf@xa\cosineangle\pgf@x%
+ \advance\pgf@xa-\sineangle\pgf@y%
+ \pgf@ya\sineangle\pgf@x%
+ \advance\pgf@ya\cosineangle\pgf@y%
+ \pgf@x\pgf@xb%
+ \pgf@y\pgf@yb%
+ \advance\pgf@x\pgf@xa%
+ \advance\pgf@y\pgf@ya%
+ }%
}
% \pgfmathanglebetweenlines
@@ -356,18 +323,18 @@
% to point #2 and a line from #3 to point #4.
%
\def\pgfmathanglebetweenlines#1#2#3#4{%
- \begingroup%
- \pgfmathanglebetweenpoints{#1}{#2}%
- \let\firstangle\pgfmathresult%
- \pgfmathanglebetweenpoints{#3}{#4}%
- \let\secondangle\pgfmathresult%
- \ifdim\firstangle pt>\secondangle pt\relax%
- \pgfmathadd@{\secondangle}{360}%
- \let\secondangle\pgfmathresult%
- \fi%
- \pgfmathsubtract@{\secondangle}{\firstangle}%
- \pgfmath@smuggleone\pgfmathresult%
- \endgroup%
+ \begingroup%
+ \pgfmathanglebetweenpoints{#1}{#2}%
+ \let\firstangle\pgfmathresult%
+ \pgfmathanglebetweenpoints{#3}{#4}%
+ \let\secondangle\pgfmathresult%
+ \ifdim\firstangle pt>\secondangle pt\relax%
+ \pgfmathadd@{\secondangle}{360}%
+ \let\secondangle\pgfmathresult%
+ \fi%
+ \pgfmathsubtract@{\secondangle}{\firstangle}%
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup%
}
% \pgfmathpointreflectalongaxis
@@ -375,14 +342,14 @@
% Reflects point #2 around an axis centered on #2 at an angle #3.
%
\def\pgfmathreflectpointalongaxis#1#2#3{%
- \pgf@process{%
- \pgfmathanglebetweenpoints{#2}{#1}%
- \pgfmath@tempdima\pgfmathresult pt\relax%
- \pgfmathparse{#3}%
- \advance\pgfmath@tempdima-\pgfmathresult pt\relax%
- \pgfmath@tempdima-2.0\pgfmath@tempdima%
- \pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}%
- }%
+ \pgf@process{%
+ \pgfmathanglebetweenpoints{#2}{#1}%
+ \pgfmath@tempdima\pgfmathresult pt\relax%
+ \pgfmathparse{#3}%
+ \advance\pgfmath@tempdima-\pgfmathresult pt\relax%
+ \pgfmath@tempdima-2.0\pgfmath@tempdima%
+ \pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}%
+ }%
}
@@ -402,107 +369,107 @@
% #6 radii of the arc.
%
\def\pgfmathpointintersectionoflineandarc#1#2#3#4#5#6{%
- \pgf@process{%
- %
- % Get the required angle.
- %
- \pgfmathanglebetweenpoints{#2}{#1}%
- \let\x\pgfmathresult%
- %
- % Get the radii of the arc.
- %
- \pgfmath@in@{and }{#6}%
- \ifpgfmath@in@%
- \pgf@polar@#6\@@%
- \else%
- \pgf@polar@#6 and #6\@@%
- \fi%
- \edef\xarcradius{\the\pgf@x}%
- \edef\yarcradius{\the\pgf@y}%
- %
- % Get the start and end angles of the arc...
- %
- \pgfmathsetmacro\s{#4}%
- \pgfmathsetmacro\e{#5}%
- %
- % ...and also with rounding.
- %
- \pgfmathmod@{\s}{360}%
- \ifdim\pgfmathresult pt<0pt\relax%
- \pgfmathadd@{\pgfmathresult}{360}%
- \fi%
- \let\ss\pgfmathresult%
- \pgfmathmod@{\e}{360}%
- \ifdim\pgfmathresult pt<0pt\relax%
- \pgfmathadd@{\pgfmathresult}{360}%
- \fi%
- \let\ee\pgfmathresult%
- %
- % Hackery for when arc straddles zero.
- %
- \ifdim\ee pt<\ss pt\relax%
- \pgfmathadd@{\x}{180}%
- \pgfmathmod@{\pgfmathresult}{360}%
- \let\x\pgfmathresult%
- \fi%
- \def\m{360}% Measure of nearness.
- \pgfmathadd@{\s}{\e}%
- \pgfmathdivide@{\pgfmathresult}{2}%
- \let\n\pgfmathresult% The best estimate (default to middle of arc).
- \pgfmathloop%
- \pgfmathadd@{\s}{\e}%
- \pgfmathdivide@{\pgfmathresult}{2}%
- \let\p\pgfmathresult%
- \ifdim\p pt=\s pt\relax%
- \else%
- \pgfmathanglebetweenpoints{#2}{%
- \pgfpointadd{#3}{%
- \pgf@x\xarcradius\relax%
- \pgfmathcos@{\p}%
- \pgf@x\pgfmathresult\pgf@x%
- \pgf@y\yarcradius\relax%
- \pgfmathsin@{\p}%
- \pgf@y\pgfmathresult\pgf@y%
- }%
- }%
- %
- % Hackery for when arc straddles zero.
- %
- \ifdim\ee pt<\ss pt\relax%
- \pgfmathadd@{\pgfmathresult}{180}%
- \pgfmathmod@{\pgfmathresult}{360}%
- \fi%
- \let\q\pgfmathresult%
- %
- % More hackery...
- %
- \ifdim\x pt>335pt\relax%
- \ifdim\q pt<45pt\relax%
- \pgfmathadd@{\q}{360}%
- \let\q\pgfmathresult%
- \fi%
- \fi%
- \ifdim\x pt=\q pt% Found it!
- \pgfmathbreakloop% Breaks after current iteration is complete.
- \else
- \ifdim\x pt<\q pt\relax%
- \let\e\p%
- \else%
- \let\s\p%
- \fi%
- \fi%
- \pgfmathsubtract@{\x}{\q}%
- \pgfmathabs@{\pgfmathresult}%
- %
- % Save the estimate if it is better than any previous estimate.
- %
- \ifdim\pgfmathresult pt<\m pt\relax%
- \let\m\pgfmathresult%
- \let\n\p%
- \fi%
- \repeatpgfmathloop%
- \pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}%
- }%
+ \pgf@process{%
+ %
+ % Get the required angle.
+ %
+ \pgfmathanglebetweenpoints{#2}{#1}%
+ \let\x\pgfmathresult%
+ %
+ % Get the radii of the arc.
+ %
+ \pgfmath@in@{and }{#6}%
+ \ifpgfmath@in@%
+ \pgf@polar@#6\@@%
+ \else%
+ \pgf@polar@#6 and #6\@@%
+ \fi%
+ \edef\xarcradius{\the\pgf@x}%
+ \edef\yarcradius{\the\pgf@y}%
+ %
+ % Get the start and end angles of the arc...
+ %
+ \pgfmathsetmacro\s{#4}%
+ \pgfmathsetmacro\e{#5}%
+ %
+ % ...and also with rounding.
+ %
+ \pgfmathmod@{\s}{360}%
+ \ifdim\pgfmathresult pt<0pt\relax%
+ \pgfmathadd@{\pgfmathresult}{360}%
+ \fi%
+ \let\ss\pgfmathresult%
+ \pgfmathmod@{\e}{360}%
+ \ifdim\pgfmathresult pt<0pt\relax%
+ \pgfmathadd@{\pgfmathresult}{360}%
+ \fi%
+ \let\ee\pgfmathresult%
+ %
+ % Hackery for when arc straddles zero.
+ %
+ \ifdim\ee pt<\ss pt\relax%
+ \pgfmathadd@{\x}{180}%
+ \pgfmathmod@{\pgfmathresult}{360}%
+ \let\x\pgfmathresult%
+ \fi%
+ \def\m{360}% Measure of nearness.
+ \pgfmathadd@{\s}{\e}%
+ \pgfmathdivide@{\pgfmathresult}{2}%
+ \let\n\pgfmathresult% The best estimate (default to middle of arc).
+ \pgfmathloop%
+ \pgfmathadd@{\s}{\e}%
+ \pgfmathdivide@{\pgfmathresult}{2}%
+ \let\p\pgfmathresult%
+ \ifdim\p pt=\s pt\relax%
+ \else%
+ \pgfmathanglebetweenpoints{#2}{%
+ \pgfpointadd{#3}{%
+ \pgf@x\xarcradius\relax%
+ \pgfmathcos@{\p}%
+ \pgf@x\pgfmathresult\pgf@x%
+ \pgf@y\yarcradius\relax%
+ \pgfmathsin@{\p}%
+ \pgf@y\pgfmathresult\pgf@y%
+ }%
+ }%
+ %
+ % Hackery for when arc straddles zero.
+ %
+ \ifdim\ee pt<\ss pt\relax%
+ \pgfmathadd@{\pgfmathresult}{180}%
+ \pgfmathmod@{\pgfmathresult}{360}%
+ \fi%
+ \let\q\pgfmathresult%
+ %
+ % More hackery...
+ %
+ \ifdim\x pt>335pt\relax%
+ \ifdim\q pt<45pt\relax%
+ \pgfmathadd@{\q}{360}%
+ \let\q\pgfmathresult%
+ \fi%
+ \fi%
+ \ifdim\x pt=\q pt% Found it!
+ \pgfmathbreakloop% Breaks after current iteration is complete.
+ \else
+ \ifdim\x pt<\q pt\relax%
+ \let\e\p%
+ \else%
+ \let\s\p%
+ \fi%
+ \fi%
+ \pgfmathsubtract@{\x}{\q}%
+ \pgfmathabs@{\pgfmathresult}%
+ %
+ % Save the estimate if it is better than any previous estimate.
+ %
+ \ifdim\pgfmathresult pt<\m pt\relax%
+ \let\m\pgfmathresult%
+ \let\n\p%
+ \fi%
+ \repeatpgfmathloop%
+ \pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}%
+ }%
}
% \pgfmathangleonellipse
@@ -513,58 +480,63 @@
% #2 - the radii of the ellipse.
%
\def\pgfmathangleonellipse#1#2{%
- \begingroup%
- \pgfmath@in@{and }{#2}%
- \ifpgfmath@in@%
- \pgf@polar@#2\@@%
- \else%
- \pgf@polar@#2 and #2\@@%
- \fi%
- \pgf@xa\pgf@x%
- \pgf@ya\pgf@y%
- \pgf@process{#1}%
- \ifdim\pgf@x=0pt\relax%
- \pgfutil@tempdima1pt\relax%
- \else%
- \pgfutil@tempdima\pgf@x%
- \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}%
- \pgfutil@tempdima\pgfmathresult pt\relax%
- \fi%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima1pt\relax%
- \else%
- \pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}%
- \pgfutil@tempdima\pgfmathresult\pgfutil@tempdima%
- \pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}%
- \fi%
- %
- \pgfutil@tempdima\pgfmathresult pt\relax%
- \ifdim\pgfutil@tempdima<0pt\relax%
- \advance\pgfutil@tempdima360pt\relax%
- \fi%
- \ifdim\pgf@x<0pt\relax%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima180pt\relax%
- \else%
- \ifdim\pgf@y<0pt\relax%
- \advance\pgfutil@tempdima180pt\relax%
- \else%
- \advance\pgfutil@tempdima-180pt\relax%
- \fi%
- \fi%
- \else%
- \ifdim\pgf@x=0pt\relax%
- \ifdim\pgf@y<0pt\relax%
- \pgfutil@tempdima270pt\relax%
- \else%
- \pgfutil@tempdima90pt\relax%
- \fi%
- \else%
- \ifdim\pgf@y=0pt\relax%
- \pgfutil@tempdima0pt\relax%
- \fi%
- \fi%
- \fi%
- \pgfmath@returnone\pgfutil@tempdima%
- \endgroup%
+ \begingroup%
+ \pgfmath@in@{and }{#2}%
+ \ifpgfmath@in@%
+ \pgf@polar@#2\@@%
+ \else%
+ \pgf@polar@#2 and #2\@@%
+ \fi%
+ \pgf@xa\pgf@x%
+ \pgf@ya\pgf@y%
+ \pgf@process{#1}%
+ \ifdim\pgf@x=0pt\relax%
+ \pgfutil@tempdima1pt\relax%
+ \else%
+ \pgfutil@tempdima\pgf@x%
+ \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}%
+ \pgfutil@tempdima\pgfmathresult pt\relax%
+ \fi%
+ \ifdim\pgf@y=0pt\relax%
+ \pgfutil@tempdima1pt\relax%
+ \else%
+ \pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}%
+ \pgfutil@tempdima\pgfmathresult\pgfutil@tempdima%
+ \pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}%
+ \fi%
+ %
+ \pgfutil@tempdima\pgfmathresult pt\relax%
+ \ifdim\pgfutil@tempdima<0pt\relax%
+ \advance\pgfutil@tempdima360pt\relax%
+ \fi%
+ \ifdim\pgf@x<0pt\relax%
+ \ifdim\pgf@y=0pt\relax%
+ \pgfutil@tempdima180pt\relax%
+ \else%
+ \ifdim\pgf@y<0pt\relax%
+ \advance\pgfutil@tempdima180pt\relax%
+ \else%
+ \advance\pgfutil@tempdima-180pt\relax%
+ \fi%
+ \fi%
+ \else%
+ \ifdim\pgf@x=0pt\relax%
+ \ifdim\pgf@y<0pt\relax%
+ \pgfutil@tempdima270pt\relax%
+ \else%
+ \pgfutil@tempdima90pt\relax%
+ \fi%
+ \else%
+ \ifdim\pgf@y=0pt\relax%
+ \pgfutil@tempdima0pt\relax%
+ \fi%
+ \fi%
+ \fi%
+ \pgfmath@returnone\pgfutil@tempdima%
+ \endgroup%
}
+
+
+% Local Variables:
+% tab-width: 2
+% End:
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
index 722856f3628..727af976f8d 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
@@ -10,7 +10,28 @@
% This file contains methods for basic floating point arithmetics, rounding
% to arbitrary precision and number pretty printing.
%
-% Version 1.0 2008/09/17
+
+
+\pgfkeys{
+ % The bug 3430171 (wrong minus sign spacing in pgfmathprintnumber)
+ % has been fixed in 2.10 CVS. Since it changes the spacing, its
+ % effects can be undone with this compatibility switch.
+ /pgf/compat/number printer/.is choice,
+ /pgf/compat/number printer/2.10/.code={%
+ \def\pgfmathprintnumber@begingroup{\bgroup}%
+ \def\pgfmathprintnumber@endgroup{\egroup}%
+ },
+ % I do not know the version number of the next release at this
+ % time. Please be so kind and KEEP THIS NAME INTACT. Add an alias
+ % if needed.
+ /pgf/compat/number printer/next after 2.10/.code={%
+ \def\pgfmathprintnumber@begingroup{\begingroup}%
+ \def\pgfmathprintnumber@endgroup{\endgroup}%
+ },
+ % activate the fix by default.
+ /pgf/compat/number printer/next after 2.10,%
+}
+
\global\newif\ifpgfmathfloatcomparison
\newif\ifpgfmathfloatroundhasperiod
@@ -34,6 +55,13 @@
% can be changed with options.
\def\pgfmathfloat@round@precision{2}
+% I introduced this to acces the "original" precision in case a
+% formatted changes it locally... in this case, the formatter may
+% overwrite \pgfmathfloat@round@precision@orig to provide the original
+% one.
+% The default implementation here does nothing:
+\def\pgfmathfloat@round@precision@orig{\pgfmathfloat@round@precision}%
+
\gdef\pgfmathfloat@glob@TMP{}
@@ -472,7 +500,7 @@
\pgfkeysgetvalue{/pgf/number format/set decimal separator}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP
\pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK
\pgfkeysgetvalue{/pgf/number format/set thousands separator}\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP
- \c@pgf@counta=#4\relax
+ \c@pgf@counta=#4\relax % it is the exponent here.
\ifnum#2=0
\c@pgf@counta=0
\fi
@@ -511,20 +539,30 @@
\else
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
\fi
+ \ifpgfmathprintnumber@thousand@sep@in@fractional
+ \let\pgfmathresultfractional\pgfutil@empty%
+ \pgfmathprintnumber@thousand@sep@in@fractional#2MMMM\@@
+ \else
+ \def\pgfmathresultfractional{#2}%
+ \fi
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}%
- \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP #2}%
- \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }%
+ \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP}%
+ \toks3=\expandafter{\pgfmathresultfractional}%
+ \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 \the\toks3 }%
\endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}%
+
+% assigns \pgfmathresult such that it contains the formatted result.
+% It assumes that none of the following tokens contains a period.
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod{%
\ifx\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP\pgfutil@empty
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
\else
- \ifnum\c@pgf@counta<0\relax
+ \ifnum\c@pgf@counta<0\relax % exponent of the number in this context
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
\else
@@ -561,7 +599,7 @@
\fi
\fi
\fi
- \ifnum\c@pgf@counta>0
+ \ifnum\c@pgf@counta>0 % \c@pgf@counta = N MOD 3 in this context
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits\pgfmathfloat@loc@TMPb
}%
@@ -573,7 +611,8 @@
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits#1#2{%
- \ifcase\c@pgf@counta
+ \ifcase\c@pgf@counta % = N MOD 3 in this context
+ % does not happen per construction
\or
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
@@ -585,7 +624,7 @@
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird%
}%
\fi
- \ifnum\c@pgf@countb>0\relax
+ \ifnum\c@pgf@countb>0\relax % \c@pgf@countb = N DIV 3 in this context
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
@@ -625,6 +664,32 @@
\fi
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
+
+% \pgfmathprintnumber@thousand@sep@in@fractional 01234525MMMM\@@
+% ->
+% 012<sep>345<sep>25
+\def\pgfmathprintnumber@thousand@sep@in@fractional#1#2#3#4{%
+ \if#4M%
+ % Ok, no further separator
+ \def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional@finish#1#2#3#4}%
+ \else
+ \begingroup
+ \toks0=\expandafter{\pgfmathresultfractional}%
+ \toks1={#1#2#3}%
+ \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
+ \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }%
+ \endgroup
+ \let\pgfmathresultfractional=\pgfmathfloat@glob@TMP
+ \def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional#4}%
+ \fi
+ \pgfmathprint@next
+}%
+\def\pgfmathprintnumber@thousand@sep@in@fractional@finish#1M{%
+ \expandafter\def\expandafter\pgfmathresultfractional\expandafter{\pgfmathresultfractional #1}%
+ \pgfmathprintnumber@thousand@sep@in@fractional@finish@
+}%
+\def\pgfmathprintnumber@thousand@sep@in@fractional@finish@#1\@@{}%
+
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall#1{%
\def\pgfmathfloat@loc@TMPb{#1}%
\let\pgfmathfloat@loc@TMPc=\pgfutil@empty
@@ -662,7 +727,7 @@
% The default style to display fixed point numbers.
%
-% It does not apply numerics, but it is responsable to typeset the
+% It does not apply numerics, but it is responsable for typesetting the
% rounded number.
% It can access the \ifpgfmathfloatroundhasperiod boolean.
%
@@ -753,21 +818,23 @@
% #1: the part before the exponent code
% #2: the part for the exponent code.
\def\pgfmathfloatrounddisplaystyle@shared@impl@#1#2{%
- {\toks0={#1}%
+ \pgfmathprintnumber@begingroup
+ \toks0={#1}%
\toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }%
- }%
+ \pgfmathprintnumber@endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}%
% Same as \pgfmathfloatrounddisplaystyle@shared@impl@, but it also
% inserts the '@dec sep mark' at the end.
\def\pgfmathfloatrounddisplaystyle@shared@impl@@#1#2{%
- {\toks0={#1}%
+ \pgfmathprintnumber@begingroup
+ \toks0={#1}%
\toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}%
\pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK
\toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }%
- }%
+ \pgfmathprintnumber@endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}
@@ -782,10 +849,11 @@
}
\def\pgfmathfloatrounddisplaystyle@e#1#2e#3\relax{%
\ifnum#3<0\relax
- {\count0=#3\relax
+ \pgfmathprintnumber@begingroup
+ \count0=#3\relax
\multiply\count0 by-1
\xdef\pgfmathfloat@glob@TMP{e{-}\the\count0}%
- }%
+ \pgfmathprintnumber@endgroup%
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\else
\def\pgfmathresult{e{+}#3}%
@@ -795,10 +863,11 @@
}
\def\pgfmathfloatrounddisplaystyle@E#1#2e#3\relax{%
\ifnum#3<0\relax
- {\count0=#3\relax
+ \pgfmathprintnumber@begingroup
+ \count0=#3\relax
\multiply\count0 by-1
\xdef\pgfmathfloat@glob@TMP{E{-}\the\count0}%
- }%
+ \pgfmathprintnumber@endgroup%
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\else
\def\pgfmathresult{E{+}#3}%
@@ -841,6 +910,14 @@
\long\def\pgfmathfloatfrac@verbatim#1#2{#1/#2}%
+\let\pgfmathround@@orig=\pgfmathround@
+
+% 2 = compatible
+% 0 = no
+% 1 = yes
+\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}%
+
+\newif\ifpgfmathprintnumber@thousand@sep@in@fractional
\pgfkeys{%
/pgf/number format/.is family,
/pgf/number format,
@@ -848,6 +925,22 @@
sci/.code= \pgfmath@set@number@printer{pgfmathprintnumber@SCI},
std/.code= {\pgfmath@set@number@printer{pgfmathprintnumber@STD}\pgfmathprintnumber@STD@setparam{#1}},
std/.default=,%
+ relative round mode/.is choice,
+ relative round mode/fixed/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{1}},
+ relative round mode/mantissa/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{0}},
+ relative round mode/compatible/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}},
+ % relative={<exponent base 10>}
+ relative/.code= {%
+ \pgfmath@set@number@printer{pgfmathprintnumber@RELATIVE}%
+ \pgfmathround@@orig{#1}%
+ \expandafter\pgfmathfloattoint@@\pgfmathresult\relax
+ \let\pgfmathprintnumber@RELATIVE@param=\pgfmathresult
+ },%
+ relative/.value required,
+ relative*/.style={/pgf/number format/relative={#1},/pgf/number format/relative round mode=fixed},
+ every relative/.style=std,
+ relative style/.style={/pgf/number format/every relative/.append style={#1}},
+ fixed relative/.code= \pgfmath@set@number@printer{pgfmathprintnumber@FIXED@RELATIVE},
int detect/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@DETECT},
int trunc/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@TRUNC},
frac/.code= \pgfmath@set@number@printer{pgfmathprintnumber@frac},%
@@ -880,11 +973,13 @@
sci precision=,
fixed default/.code= {\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT},
set decimal separator/.initial=,
- dec sep/.style={/pgf/number format/set decimal separator=#1},
+ dec sep/.style={/pgf/number format/set decimal separator={#1}},
@dec sep mark/.initial=,
@sci exponent mark/.initial=,
set thousands separator/.initial=,
- 1000 sep/.style={/pgf/number format/set thousands separator=#1},
+ 1000 sep in fractionals/.is if=pgfmathprintnumber@thousand@sep@in@fractional,
+ 1000 sep in fractionals/.default=true,
+ 1000 sep/.style={/pgf/number format/set thousands separator={#1}},
min exponent for 1000 sep/.initial=0,
use period/.style= {/pgf/number format/set decimal separator={.},/pgf/number format/set thousands separator={{{,}}}},
use comma/.style= {/pgf/number format/set decimal separator={{{,}}},/pgf/number format/set thousands separator={.}},
@@ -946,7 +1041,7 @@
\ifx\pgfmathfloat@loc@TMPb\pgfutil@empty
% DEFAULT for lower and upper bound.
\def\pgfmathprintnumber@STD@getlowerbound{%
- \c@pgf@counta=\pgfmathfloat@round@precision\relax
+ \c@pgf@counta=\pgfmathfloat@round@precision@orig\relax
\divide\c@pgf@counta by-2\relax
}%
\def\pgfmathprintnumber@STD@upperbound{4}%
@@ -992,6 +1087,114 @@
\fi
}
+\def\pgfmathprintnumber@RELATIVE#1{%
+ % parse the input:
+ \pgfmathfloatparsenumber{#1}%
+ \pgfmathfloat@to@FMeE@style\pgfmathresult
+ \expandafter\pgfmathprintnumber@RELATIVE@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn{%
+ \immediate\write16{! Package pgf warning: the use of /pgf/number format/relative is discouraged (buggy). Please use 'relative*' instead or type \string\pgfkeys{/pgf/number format/relative round mode=fixed} into your preamble.}%
+ \global\let\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn=\relax
+}
+
+\def\pgfmathprintnumber@RELATIVE@issci#1#2e#3\relax{%
+ \begingroup
+ % format X / 10^{relative}:
+ \c@pgf@counta=#3\relax
+ \advance\c@pgf@counta by-\pgfmathprintnumber@RELATIVE@param\relax
+ \pgfmathfloatcreate{#1}{#2}{\the\c@pgf@counta}%
+ % OK, round it to the desired precision:
+ \if0\pgfmathprintnumber@RELATIVE@choice@roundtofixed
+ % relative round mode=mantissa
+ \def\b@round@fixed{0}%
+ \else
+ \if1\pgfmathprintnumber@RELATIVE@choice@roundtofixed
+ % relative round mode=fixed
+ \def\b@round@fixed{1}%
+ \else
+ \pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn
+ % relative round mode=compatible
+ \ifnum\c@pgf@counta>0
+ % hm. for positive exponents, we should round the
+ % mantissa rather than only the fractional part.
+ \def\b@round@fixed{0}%
+ \else
+ % negative exponent -> round fixed representation:
+ \def\b@round@fixed{1}%
+ \fi
+ \fi
+ \fi
+ \if1\b@round@fixed
+ % round fixed representation:
+ \pgfmathfloattofixed\pgfmathresult
+ \expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
+ \pgfmathfloatparsenumber{\pgfmathresult}%
+ \pgfmathfloatroundhasperiodtrue% make sure the code below works:
+ \else
+ % round the mantissa:
+ \expandafter\pgfmathfloatround\expandafter{\pgfmathresult}%
+ \fi
+ % Now, compute result * 10^{relative} and format the result:
+ \pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+ \ifnum\pgfmathfloat@a@S=0
+ \pgfmathfloat@a@E=\pgfmathfloat@a@S % avoid 0 * 10^8
+ \else
+ \advance\pgfmathfloat@a@E by+\pgfmathprintnumber@RELATIVE@param\relax
+ \fi
+ \edef\pgfmathresultX{%
+ \the\pgfmathfloat@a@S
+ \the\pgfmathfloat@a@Mtok
+ \ifpgfmathfloatroundhasperiod\else.0\fi
+ e\the\pgfmathfloat@a@E}%
+ % call another formatter for the result (but avoid rounding inside of it):
+ \pgfqkeys{/pgf/number format}{/pgf/number format/every relative,
+ fixed zerofill=false,% useless here!
+ sci zerofill=false}%
+ \ifx\pgfmathprintnumber@issci\pgfmathprintnumber@RELATIVE@issci
+ \pgfmath@error{The '/pgf/number format/every relative' style should set a valid display style}%
+ \fi
+ \let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision
+ \def\pgfmathfloat@round@precision{9999}%
+ \expandafter\pgfmathprintnumber@issci\pgfmathresultX\relax%
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup
+}
+
+\def\pgfmathprintnumber@FIXED@RELATIVE#1{%
+ % parse the input:
+ \pgfmathfloatparsenumber{#1}%
+ \pgfmathfloat@to@FMeE@style\pgfmathresult
+ \expandafter\pgfmathprintnumber@FIXED@RELATIVE@issci\pgfmathresult\relax
+}
+
+\def\pgfmathprintnumber@FIXED@RELATIVE@issci#1#2e#3\relax{%
+ \begingroup
+ \pgfmathfloatcreate{#1}{#2}{#3}%
+ % we want the first <precision> digits - not the first
+ % <precision>+1 digits:
+ \c@pgf@counta=\pgfmathfloat@round@precision\relax
+ \advance\c@pgf@counta by-1
+ \edef\pgfmathfloat@round@precision{\the\c@pgf@counta}%
+ \pgfmathfloatround{\pgfmathresult}%
+ \pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+ \ifnum\pgfmathfloat@a@S=0
+ \pgfmathfloat@a@E=\pgfmathfloat@a@S % avoid 0 * 10^8
+ \fi
+ \edef\pgfmathresultX{%
+ \the\pgfmathfloat@a@S
+ \the\pgfmathfloat@a@Mtok
+ \ifpgfmathfloatroundhasperiod\else.0\fi
+ e\the\pgfmathfloat@a@E}%
+ \let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision
+ \pgfmathfloat@usezerofill@fixedfalse
+ \def\pgfmathfloat@round@precision{9999}% typeset all remaining digits!
+ \expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresultX\relax%
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup
+}
+
\def\pgfmathprintnumber@frac#1{%
% parse the input:
\pgfmathfloatparsenumber{#1}%
@@ -1048,7 +1251,7 @@
% The numerator and denominator is always a number (not empty)
\def\pgfmathfloatgetfrac#1{%
\pgfutil@ifundefined{pgfmathfloatmultiply@}{%
- \PackageError{tikz}{Sorry, the number format 'frac' requires '\string\usetikzlibrary{fpu}' (and, optionally, \string\usepackage{fp}) in order to work correctly}{}%
+ \pgfmath@PackageError{Sorry, the number format 'frac' requires '\string\usetikzlibrary{fpu}' (and, optionally, \string\usepackage{fp}) in order to work correctly}%
\edef\pgfmathresult{{#1}{0}{1}}%
}{%
\pgfmathfloatgetfrac@{#1}%
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex
index a4e510d4dc8..581cdaade5f 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex
@@ -301,3 +301,31 @@
\def\pgfmathsetbasenumberlength#1{\def\pgfmath@basenumberlength{#1}}
\pgfmathsetbasenumberlength{1}%
+
+% \pgfmathtodigitlist\marg{macro}\marg{number}}
+%
+% This command converts \meta{number} into a comma-separated
+% list of digits and stores the result in \meta{macro}.
+% The \marg{number} is \emph{not} parsed before processing.
+%
+\def\pgfmathtodigitlist#1#2{%
+ \def\pgfmath@temp{#1}%
+ \let\pgfmath@digitlist=\pgfutil@empty%
+ \edef\pgfmath@@tmp{#2}%
+ \expandafter\pgfmath@todigitlist\pgfmath@@tmp @%
+}
+\def\pgfmath@base@atchar{@}
+\def\pgfmath@todigitlist#1{%
+ \def\pgfmath@digit{#1}%
+ \ifx\pgfmath@digit\pgfmath@base@atchar%
+ \expandafter\let\pgfmath@temp=\pgfmath@digitlist%
+ \else%
+ \ifx\pgfmath@digitlist\pgfutil@empty%
+ \edef\pgfmath@digitlist{#1}%
+ \else%
+ \edef\pgfmath@digitlist{\pgfmath@digitlist,#1}%
+ \fi%
+ \expandafter\pgfmath@todigitlist%
+ \fi%
+}
+
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 ca741fa7adc..99f8ccbb2c0 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
@@ -121,9 +121,24 @@
\divide\c@pgfmath@counta by\c@pgfmath@countb%
\pgfmath@ya=\c@pgfmath@counta\pgfmath@y%
\advance\pgfmath@x by-\pgfmath@ya%
- \expandafter\expandafter\expandafter\def%
- \expandafter\expandafter\expandafter\pgfmathresult
- \expandafter\expandafter\expandafter{\expandafter\pgfmathresult\the\c@pgfmath@counta}%
+ \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%
@@ -131,6 +146,46 @@
\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}%
+}%
+
+{
+\catcode`\p=12
+\catcode`\t=12
+\gdef\Pgf@geT@NO@TRAILING@ZERO#1.#2pt{%
+ #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\@@}
@@ -451,32 +506,33 @@
% exp function.
%
\pgfmathdeclarefunction{exp}{1}{%
- \begingroup%
- \pgfmath@xc=#1pt\relax%
- \ifdim\pgfmath@xc<-9pt%
- \pgfmath@x=1sp\relax%
- \else%
- \ifdim\pgfmath@xc<0pt%
- \pgfmath@xc=-\pgfmath@xc%
- \fi%
- \pgfmath@x=1pt\relax%
- \pgfmath@xa=1pt\relax%
- \pgfmath@xb=\pgfmath@x%
+ \begingroup
+ \pgfmath@xc=#1pt\relax
+ \pgfmath@yc=#1pt\relax
+ \ifdim\pgfmath@xc<-9pt
+ \pgfmath@x=1sp\relax
+ \else
+ \ifdim\pgfmath@xc<0pt
+ \pgfmath@xc=-\pgfmath@xc
+ \fi
+ \pgfmath@x=1pt\relax
+ \pgfmath@xa=1pt\relax
+ \pgfmath@xb=\pgfmath@x
\pgfmathloop%
- \divide\pgfmath@xa by\pgfmathcounter%
+ \divide\pgfmath@xa by\pgfmathcounter
\pgfmath@xa=\pgfmath@tonumber\pgfmath@xc\pgfmath@xa%
- \advance\pgfmath@x by\pgfmath@xa%
- \ifdim\pgfmath@x=\pgfmath@xb%
- \else%
- \pgfmath@xb=\pgfmath@x%
+ \advance\pgfmath@x by\pgfmath@xa
+ \ifdim\pgfmath@x=\pgfmath@xb
+ \else
+ \pgfmath@xb=\pgfmath@x
\repeatpgfmathloop%
- \ifdim#1pt<0pt%
+ \ifdim\pgfmath@yc<0pt
\pgfmathreciprocal@{\pgfmath@tonumber\pgfmath@x}%
- \pgfmath@x=\pgfmathresult pt\relax%
- \fi%
- \fi%
+ \pgfmath@x=\pgfmathresult pt\relax
+ \fi
+ \fi
\pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \endgroup
}
% sqrt function.
@@ -664,34 +720,42 @@
\begingroup%
\pgfmath@xa=#1pt%
\pgfmath@xb=#2pt%
- \afterassignment\pgfmath@x%
- \expandafter\c@pgfmath@counta\the\pgfmath@xb\relax%
- \ifnum\c@pgfmath@counta<0\relax%
- \c@pgfmath@counta=-\c@pgfmath@counta%
- \pgfmathreciprocal@{#1}%
- \pgfmath@xa=\pgfmathresult pt\relax%
- \fi
- \ifdim\pgfmath@x=0pt\relax%
- \pgfmath@x=1pt\relax%
- \pgfmathloop%
- \ifnum\c@pgfmath@counta>0\relax%
- \ifodd\c@pgfmath@counta%
- \pgfmath@x=\pgfmath@tonumber{\pgfmath@x}\pgfmath@xa%
- \fi
- \ifnum\c@pgfmath@counta>1\relax%
- \pgfmath@xa=\pgfmath@tonumber{\pgfmath@xa}\pgfmath@xa%
- \fi%
- \divide\c@pgfmath@counta by2\relax%
- \repeatpgfmathloop%
- \else%
- \pgfmathln@{#1}%
- \pgfmath@x=\pgfmathresult pt\relax%
- \pgfmath@x=\pgfmath@tonumber{\pgfmath@xb}\pgfmath@x%
- \pgfmathexp@{\pgfmath@tonumber{\pgfmath@x}}%
- \pgfmath@x=\pgfmathresult pt\relax%
- \fi%
- \pgfmath@returnone\pgf@x%
- \endgroup%
+ \ifdim\pgfmath@xa=0pt\relax%
+ \ifdim\pgfmath@xb=0pt\relax%
+ \pgfmath@x=1pt\relax%
+ \else%
+ \pgfmath@x=0pt\relax%
+ \fi%
+ \else%
+ \afterassignment\pgfmath@x%
+ \expandafter\c@pgfmath@counta\the\pgfmath@xb\relax%
+ \ifnum\c@pgfmath@counta<0\relax%
+ \c@pgfmath@counta=-\c@pgfmath@counta%
+ \pgfmathreciprocal@{#1}%
+ \pgfmath@xa=\pgfmathresult pt\relax%
+ \fi
+ \ifdim\pgfmath@x=0pt\relax%
+ \pgfmath@x=1pt\relax%
+ \pgfmathloop%
+ \ifnum\c@pgfmath@counta>0\relax%
+ \ifodd\c@pgfmath@counta%
+ \pgfmath@x=\pgfmath@tonumber{\pgfmath@x}\pgfmath@xa%
+ \fi
+ \ifnum\c@pgfmath@counta>1\relax%
+ \pgfmath@xa=\pgfmath@tonumber{\pgfmath@xa}\pgfmath@xa%
+ \fi%
+ \divide\c@pgfmath@counta by2\relax%
+ \repeatpgfmathloop%
+ \else%
+ \pgfmathln@{#1}%
+ \pgfmath@x=\pgfmathresult pt\relax%
+ \pgfmath@x=\pgfmath@tonumber{\pgfmath@xb}\pgfmath@x%
+ \pgfmathexp@{\pgfmath@tonumber{\pgfmath@x}}%
+ \pgfmath@x=\pgfmathresult pt\relax%
+ \fi%
+ \fi
+ \pgfmath@returnone\pgf@x%
+ \endgroup%
}
% factorial function.
@@ -711,3 +775,7 @@
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
+
+% Local Variables:
+% coding: undecided-unix
+% End:
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex
index a493b6c6b62..55ef700c14d 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex
@@ -238,3 +238,10 @@
\input pgfmathfunctions.base.code.tex
\input pgfmathfunctions.round.code.tex
\input pgfmathfunctions.misc.code.tex
+\input pgfmathfunctions.integerarithmetics.code.tex
+
+
+
+% Local Variables:
+% tab-width: 2
+% End:
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex
new file mode 100644
index 00000000000..f11704c94c2
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex
@@ -0,0 +1,124 @@
+% 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.
+
+% Macros contributed by Alain Matthes and adapted by CJ
+\pgfmathdeclarefunction{gcd}{2}{%
+ \begingroup
+ \pgfmathcontinuelooptrue
+ \pgfmath@xa=#1pt
+ \pgfmath@xb=#2pt
+ \ifdim\pgfmath@xa=0pt
+ \pgfmathcontinueloopfalse
+ \pgfmath@xa=\pgfmath@xb
+ \fi
+ \ifdim\pgfmath@xb=0pt
+ \pgfmathcontinueloopfalse
+ \pgfmath@xb=\pgfmath@xa
+ \fi
+ \ifdim\pgfmath@xa<0pt
+ \pgfmath@xa=-\pgfmath@xa
+ \fi
+ \ifdim\pgfmath@xb<0pt
+ \pgfmath@xb=-\pgfmath@xb
+ \fi
+ \loop
+ \ifpgfmathcontinueloop
+ \ifdim\pgfmath@xa=\pgfmath@xb
+ \pgfmathcontinueloopfalse
+ \else
+ \ifdim\pgfmath@xa>\pgfmath@xb
+ \advance\pgfmath@xa by-\pgfmath@xb
+ \else
+ \advance\pgfmath@xb by-\pgfmath@xa
+ \fi
+ \fi
+ \repeat
+ \pgfmathparse{int(\pgfmath@xa)}%
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup}
+
+\newif\ifpgfmath@isprime@unknown
+\newif\ifpgfmath@isprime
+
+\pgfmathdeclarefunction{isprime}{1}{%
+ \begingroup
+ \pgfmath@isprime@unknowntrue
+ \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}%
+ \ifcase\c@pgfmath@counta\relax
+ % |#1| = 0
+ \pgfmath@isprimefalse
+ \pgfmath@isprime@unknownfalse
+ \or
+ % |#1| = 1
+ \pgfmath@isprimefalse
+ \pgfmath@isprime@unknownfalse
+ \or
+ % |#1| = 2
+ \pgfmath@isprimetrue
+ \pgfmath@isprime@unknownfalse
+ \or
+ % |#1| = 3
+ \pgfmath@isprimetrue
+ \pgfmath@isprime@unknownfalse
+ \else
+ % |#1| > 3
+ \ifodd\c@pgfmath@counta\relax
+ \else
+ \pgfmath@isprimefalse
+ \pgfmath@isprime@unknownfalse
+ \fi
+ \fi
+ \ifpgfmath@isprime@unknown
+ \c@pgfmath@countd=3
+ \pgfmath@isprimetrue
+ \pgfmathloop
+ \c@pgfmath@countb=\c@pgfmath@counta
+ \divide\c@pgfmath@countb by\c@pgfmath@countd
+ \ifnum\c@pgfmath@countb>\c@pgfmath@countd
+ \pgfmath@isprime@unknowntrue
+ \else
+ \pgfmath@isprime@unknownfalse
+ \fi
+ \multiply\c@pgfmath@countb by\c@pgfmath@countd
+ \ifnum\c@pgfmath@countb=\c@pgfmath@counta
+ \global\pgfmath@isprimefalse
+ \pgfmath@isprime@unknownfalse
+ \fi
+ \ifpgfmath@isprime@unknown\advance\c@pgfmath@countd by 2
+ \repeatpgfmathloop
+ \fi
+ \ifpgfmath@isprime
+ \def\pgfmathresult{1}%
+ \else
+ \def\pgfmathresult{0}%
+ \fi
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup}
+
+\pgfmathdeclarefunction{isodd}{1}{%
+ \begingroup
+ \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}%
+ \ifodd\c@pgfmath@counta
+ \def\pgfmathresult{1}%
+ \else
+ \def\pgfmathresult{0}%
+ \fi
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup}
+
+\pgfmathdeclarefunction{iseven}{1}{%
+ \begingroup
+ \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}%
+ \ifodd\c@pgfmath@counta
+ \def\pgfmathresult{0}%
+ \else
+ \def\pgfmathresult{1}%
+ \fi
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup}
+
+\endinput \ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex
index 65460e4b3cc..e00786d7a37 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex
@@ -160,6 +160,9 @@
\def\pgfmath@scientific@@@#1#2#3#4#5#6\pgfmath@{%
\edef\pgfmath@sci@mantissaB{#1#2#3#4#5}%
\c@pgfmath@counta\pgfmath@sci@exponent\relax%
+ \ifnum\c@pgfmath@counta<-4\relax%
+ \pgfmath@x0pt\relax%
+ \else%
\c@pgfmath@countb\c@pgfmath@counta%
\ifnum\c@pgfmath@counta<0\relax%
\c@pgfmath@counta-\c@pgfmath@counta%
@@ -191,7 +194,7 @@
\advance\c@pgfmath@countc100000\relax%
\edef\pgfmath@sci@result{\pgfmath@sci@sign\the\c@pgfmath@counta.\expandafter\pgfmath@gobbleone\the\c@pgfmath@countc pt}%
\pgfmath@x\pgfmath@sci@result\relax%
- \fi%
+ \fi\fi%
\pgfmath@returnone\pgfmath@x%
\endgroup}
@@ -263,6 +266,24 @@
\pgfmath@smuggleone\pgfmathresult\endgroup%
}
+% dim function: return dimension of an array
+% dim({1,2,3}) return 3
+% dim({{1,2,3},{4,5,6}}) return 2
+\pgfmathdeclarefunction{dim}{1}{%
+ \begingroup
+ \pgfmath@count=0\relax
+ \expandafter\pgfmath@dim@i\pgfutil@firstofone#1\pgfmath@token@stop
+ \edef\pgfmathresult{\the\pgfmath@count}%
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup}
+
+\def\pgfmath@dim@i#1{%
+ \ifx\pgfmath@token@stop#1%
+ \else
+ \advance\pgfmath@count by 1\relax
+ \expandafter\pgfmath@dim@i
+ \fi}
+
% max function.
%
@@ -287,7 +308,7 @@
% For compatability with old code.
\def\pgfmathmax#1#2{%
- \pgfmathparse{getargs(#1,#2)}%
+ \pgfmathparse{#1,#2}%
\expandafter\pgfmathmax@\expandafter{\pgfmathresult}%
}
@@ -314,7 +335,7 @@
% For compatability with old code.
\def\pgfmathmin#1#2{%
- \pgfmathparse{getargs(#1,#2)}%
+ \pgfmathparse{#1,#2}%
\expandafter\pgfmathmin@\expandafter{\pgfmathresult}%
}
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex
index 6b60eb7ec16..02726731357 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex
@@ -24,36 +24,36 @@
% Convert #1 from radians to degrees (accurate to 1 deg).
%
\pgfmathdeclarefunction{radians}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}%
% \pgfmathdeg
%
% Convert #1 from radians to degrees.
%
-\pgfmathdeclarefunction{deg}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+\pgfmathdeclarefunction{deg}{1}{%
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}%
% \pgfmathrad
%
% Convert #1 from degrees to radians.
%
-\pgfmathdeclarefunction{rad}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@x3.14159\pgfmath@x%
- \divide\pgfmath@x180\relax%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+\pgfmathdeclarefunction{rad}{1}{%
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \pgfmath@x3.14159\pgfmath@x%
+ \divide\pgfmath@x180\relax%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}%
% \pgfmathsin
@@ -61,40 +61,41 @@
% Calculate the sine of #1 (in degrees).
%
\pgfmathdeclarefunction{sin}{1}{%
- % Let #1 = a.b
- % Then sin(#1) \approx (1-b)*sin(a) + b*sin(a+1)
- %
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \advance\pgfmath@x-90pt\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@
- \divide\c@pgfmath@counta360\relax%
- \multiply\c@pgfmath@counta-360\relax%
- \advance\pgfmath@x\c@pgfmath@counta pt\relax%
- \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
- \ifdim\pgfmath@x<180pt\relax%
- \else
- \pgfmath@x-\pgfmath@x%
- \advance\pgfmath@x360pt\relax%
- \fi%
- % Now 0 <= x < 179. So split x into integer and decimal...
- %
- \afterassignment\pgfmath@xa%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
- %
- % ...if #1 is an integer, don't do anything fancy.
- \ifdim\pgfmath@xa=0pt%
- \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax%
- \else%
- \pgfmath@x-\pgfmath@xa%
- \advance\pgfmath@x1pt\relax%
- \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
- \advance\c@pgfmath@counta1\relax%
- \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup
+ % Let #1 = a.b
+ % Then sin(#1) \approx (1-b)*sin(a) + b*sin(a+1)
+ %
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \advance\pgfmath@x-90pt\relax%
+ \afterassignment\pgfmath@gobbletilpgfmath@
+ \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@
+ \divide\c@pgfmath@counta360\relax%
+ \multiply\c@pgfmath@counta-360\relax%
+ \advance\pgfmath@x\c@pgfmath@counta pt\relax%
+ \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
+ \ifdim\pgfmath@x<180pt\relax%
+ \else
+ \pgfmath@x-\pgfmath@x%
+ \advance\pgfmath@x360pt\relax%
+ \fi%
+ % Now 0 <= x < 179. So split x into integer and decimal...
+ %
+ \afterassignment\pgfmath@xa%
+ \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+ %
+ % ...if #1 is an integer, don't do anything fancy.
+ \ifdim\pgfmath@xa=0pt%
+ \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax%
+ \else%
+ \pgfmath@x-\pgfmath@xa%
+ \advance\pgfmath@x1pt\relax%
+ \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
+ \advance\c@pgfmath@counta1\relax%
+ \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
+ \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup
}
% \pgfmathcos
@@ -102,40 +103,40 @@
% Calculate the cosine of #1 (in degrees).
%
\pgfmathdeclarefunction{cos}{1}{%
- % Let x = a.b
- % Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
- %
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \divide\c@pgfmath@counta360\relax%
- \multiply\c@pgfmath@counta-360\relax%
- \advance\pgfmath@x\c@pgfmath@counta pt\relax%
- \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
- \ifdim\pgfmath@x<180pt\relax%
- \else%
- \pgfmath@x-\pgfmath@x%
- \advance\pgfmath@x360pt\relax%
- \fi%
- % Now 0 <= x < 179. So split x into integer and decimal...
- %
- \afterassignment\pgfmath@xa%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
- %
- % ...if #1 is an integer, don't do anything fancy.
- \ifdim\pgfmath@xa=0pt%
- \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt%
- \else%
- \pgfmath@x-\pgfmath@xa%
- \advance\pgfmath@x1pt\relax%
- \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
- \advance\c@pgfmath@counta1\relax%
- \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
- \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ % Let x = a.b
+ % Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
+ %
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \afterassignment\pgfmath@gobbletilpgfmath@%
+ \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
+ \divide\c@pgfmath@counta360\relax%
+ \multiply\c@pgfmath@counta-360\relax%
+ \advance\pgfmath@x\c@pgfmath@counta pt\relax%
+ \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
+ \ifdim\pgfmath@x<180pt\relax%
+ \else%
+ \pgfmath@x-\pgfmath@x%
+ \advance\pgfmath@x360pt\relax%
+ \fi%
+ % Now 0 <= x < 179. So split x into integer and decimal...
+ %
+ \afterassignment\pgfmath@xa%
+ \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
+ %
+ % ...if #1 is an integer, don't do anything fancy.
+ \ifdim\pgfmath@xa=0pt%
+ \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt%
+ \else%
+ \pgfmath@x-\pgfmath@xa%
+ \advance\pgfmath@x1pt\relax%
+ \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
+ \advance\c@pgfmath@counta1\relax%
+ \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
+ \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
% \pgfmathsincos
@@ -143,12 +144,12 @@
% Calculate the sin and cosine of #1 (in degrees).
%
\def\pgfmathsincos#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathsincos@\expandafter{\pgfmathresult}}
+ \pgfmathparse{#1}%
+ \expandafter\pgfmathsincos@\expandafter{\pgfmathresult}}
\def\pgfmathsincos@#1{%
- \edef\pgfmath@temparg{#1}%
- \pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}%
- \pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}%
+ \edef\pgfmath@temparg{#1}%
+ \pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}%
+ \pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}%
}
% \pgfmathtan
@@ -156,25 +157,25 @@
% Calculate the tangent of #1 (in degrees).
%
\pgfmathdeclarefunction{tan}{1}{%
- \begingroup%
- \edef\pgfmath@temparg{#1}%
- \pgfmathcos@{\pgfmath@temparg}%
- \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
- \edef\pgfmath@tantemp{\pgfmathresult}%
- \pgfmathsin@{\pgfmath@temparg}%
- \pgfmath@x\pgfmathresult pt\relax%
- \pgfmath@x\pgfmath@tantemp\pgfmath@x%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \begingroup%
+ \edef\pgfmath@temparg{#1}%
+ \pgfmathcos@{\pgfmath@temparg}%
+ \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
+ \edef\pgfmath@tantemp{\pgfmathresult}%
+ \pgfmathsin@{\pgfmath@temparg}%
+ \pgfmath@x\pgfmathresult pt\relax%
+ \pgfmath@x\pgfmath@tantemp\pgfmath@x%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
% \pgfmathcosec
%
% Calculate the cosec of #1 (in degrees).
%
-\pgfmathdeclarefunction{cosec}{1}{%
- \expandafter\pgfmathsin@\expandafter{#1}%
- \pgfmathreciprocal@{\pgfmathresult}%
+\pgfmathdeclarefunction{cosec}{1}{%
+ \expandafter\pgfmathsin@\expandafter{#1}%
+ \pgfmathreciprocal@{\pgfmathresult}%
}
% \pgfmathsec
@@ -182,1282 +183,1338 @@
% Calculate the sec of #1 (in degrees).
%
\pgfmathdeclarefunction{sec}{1}{%
- \expandafter\pgfmathcos@\expandafter{#1}%
- \pgfmathreciprocal@{\pgfmathresult}%
+ \expandafter\pgfmathcos@\expandafter{#1}%
+ \pgfmathreciprocal@{\pgfmathresult}%
}
% \pgfmathcot
%
% Calculate the cotangent of #1 (in degrees).
%
-\pgfmathdeclarefunction{cot}{1}{%
- \begingroup%
- \edef\pgfmath@temparg{#1}%
- \pgfmathsin@{\pgfmath@temparg}%
- \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
- \edef\pgfmath@tantemp{\pgfmathresult}%
- \pgfmathcos@{\pgfmath@temparg}%
- \pgfmath@x\pgfmathresult pt\relax%
- \pgfmath@x\pgfmath@tantemp\pgfmath@x%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+\pgfmathdeclarefunction{cot}{1}{%
+ \begingroup%
+ \edef\pgfmath@temparg{#1}%
+ \pgfmathsin@{\pgfmath@temparg}%
+ \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
+ \edef\pgfmath@tantemp{\pgfmathresult}%
+ \pgfmathcos@{\pgfmath@temparg}%
+ \pgfmath@x\pgfmathresult pt\relax%
+ \pgfmath@x\pgfmath@tantemp\pgfmath@x%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
+\def\pgfmath@multiply@thousand#1.#2#3#4#5\relax{%
+ \edef\pgfmathresult{#1#2#3#4.#5}%
+}%
+
% \pgfmathasin
%
% The asin of #1
%
\pgfmathdeclarefunction{asin}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@xa\pgfmath@x%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@x1000\pgfmath@x%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \pgfmath@x-\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
- \advance\pgfmath@x90pt\relax%
- \ifdim\pgfmath@xa<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \begingroup%
+ \pgfmath@x=#1pt %
+ \pgfmath@xa\pgfmath@x%
+ \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
+ % compute lossless '*1000' operation:
+ \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
+ \pgfmath@x=\pgfmathresult pt %
+ \ifdim\pgfmath@x<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \fi%
+ \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}%
+ \pgfmath@x=-\pgfmath@x
+ \advance\pgfmath@x90pt\relax%
+ \ifdim\pgfmath@xa<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
+}
+
+% Defines \pgfmath@x to be the result of the table lookup for value
+% '#1' in table '#2'
+%
+% #1: a value for which lookup should be performed
+% #2: the table's prefix name
+% #3: the table's size
+\def\pgfmath@table@lookup#1#2#3{%
+ \pgfmath@x=#1\relax
+ \expandafter\pgfmath@table@lookup@\the\pgfmath@x\relax{#2}{#3}%
}
+\def\pgfmath@table@lookup@#1.#2\relax#3#4{%
+ \edef\pgf@temp{\Pgf@geT#2}% strip 'pt' suffix.
+ %
+ % prepare constant interpolant (i.e. the value at node '#1'):
+ \pgfmath@x=\csname #3#1\endcsname pt %
+ %
+ \c@pgfmath@countc=#1 %
+ \advance\c@pgfmath@countc by1 %
+ \ifnum\c@pgfmath@countc<#4 %
+ % Ah - we have enough elements in the table.
+ %
+ % perform linear interpolation:
+ \pgfmath@ya=\csname #3\the\c@pgfmath@countc\endcsname pt %
+ \advance\pgfmath@ya by-\pgfmath@x %
+ \advance\pgfmath@x by0.\pgf@temp\pgfmath@ya
+ \fi
+}%
% \pgfmathacos
%
% The acos of #1
-%
+%
\pgfmathdeclarefunction{acos}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@xa\pgfmath@x%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@x1000\pgfmath@x%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \expandafter\pgfmath@x\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
- \ifdim\pgfmath@xa<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \advance\pgfmath@x by180pt\relax%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \begingroup%
+ \pgfmath@x#1pt\relax%
+ \pgfmath@xa\pgfmath@x%
+ \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
+ % compute lossless '*1000' operation:
+ \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
+ \pgfmath@x=\pgfmathresult pt %
+ \ifdim\pgfmath@x<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \fi%
+ \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}%
+ \ifdim\pgfmath@xa<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \advance\pgfmath@x by180pt\relax%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
\pgfmathdeclarefunction{atan}{1}{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@xa\pgfmath@x%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@xb\pgfmath@x%
- \ifdim\pgfmath@x>1pt\relax%
- \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
- \pgfmathreciprocal@{\pgfmath@temp}%
- \pgfmath@x\pgfmathresult pt\relax%
- \fi%
- \pgfmath@x1000\pgfmath@x%
- \afterassignment\pgfmath@gobbletilpgfmath@%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
- \ifdim\pgfmath@xb>1pt\relax%
- \expandafter\pgfmath@x\expandafter-\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
- \advance\pgfmath@x90pt%
- \else%
- \expandafter\pgfmath@x\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
- \fi%
- \ifdim\pgfmath@xa<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ \begingroup%
+ \expandafter\pgfmath@x#1pt\relax%
+ \pgfmath@xa\pgfmath@x%
+ \ifdim\pgfmath@x<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \fi%
+ \pgfmath@xb\pgfmath@x%
+ \ifdim\pgfmath@x>1pt\relax%
+ \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
+ \pgfmathreciprocal@{\pgfmath@temp}%
+ \pgfmath@x\pgfmathresult pt\relax%
+ \fi%
+ % compute lossless '*1000' operation:
+ \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
+ \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
+ \pgfmath@x=\pgfmathresult pt %
+ \pgfmath@table@lookup{\pgfmath@x}{pgfmath@atan@}{1001}%xxx
+ \ifdim\pgfmath@xb>1pt\relax%
+ \pgfmath@x=-\pgfmath@x%
+ \advance\pgfmath@x90pt%
+ \fi%
+ \ifdim\pgfmath@xa<0pt\relax%
+ \pgfmath@x-\pgfmath@x%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
\pgfmathdeclarefunction{atan2}{2}{%
- \begingroup%
- \pgfmath@x=#1pt\relax%
- \ifdim\pgfmath@x<0pt\relax%
- \pgfmath@x=-\pgfmath@x%
- \fi%
- \ifdim\pgfmath@x<0.001pt\relax%
- \ifdim#2pt<0pt\relax%
- \pgfmath@x=-90pt\relax%
- \else%
- \ifdim#2pt>0pt\relax%
- \pgfmath@x=90pt\relax%
- \else%
- \pgfmath@x=0pt\relax%
- \fi%
- \fi%
- \else%
- \pgfmathdivide@{#2}{#1}%
- \expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
- \pgfmath@x=\pgfmathresult pt\relax%
- \ifdim#2pt<0pt\relax%
- \ifdim#1pt<0pt\relax%
- \advance\pgfmath@x by-180pt\relax%
- \fi%
- \else%
- \ifdim#1pt<0pt\relax%
- \advance\pgfmath@x by180pt\relax%
- \fi%
- \fi%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
+ % Note: first parameter is y (!), second is x (!)
+ \begingroup%
+ \pgfmath@y=#1pt\relax%
+ \ifdim\pgfmath@y<0pt\relax%
+ \pgfmath@y=-\pgfmath@y%
+ \fi%
+ \ifdim\pgfmath@y<0.001pt\relax%
+ \ifdim#2pt<0pt\relax%
+ \pgfmath@x=-180pt\relax%
+ \else%
+ \ifdim#2pt>0pt\relax%
+ \pgfmath@x=0pt\relax%
+ \else%
+ \ifdim#1pt<0pt%
+ \pgfmath@x=-90pt\relax%
+ \else%
+ \pgfmath@x=90pt\relax%
+ \fi%
+ \fi%
+ \fi%
+ \else%
+ \pgfmathabs@{#1}\let\pgfmath@tempa\pgfmathresult%
+ \pgfmathabs@{#2}\let\pgfmath@tempb\pgfmathresult%
+ \ifdim\pgfmath@tempa pt>\pgfmath@tempb pt%
+ \pgfmathdivide@{#2}{\pgfmath@tempa}%
+ \expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
+ \pgfmath@x=90pt%
+ \advance\pgfmath@x by-\pgfmathresult pt\relax%
+ \else%
+ \pgfmathdivide@{\pgfmath@tempa}{#2}%
+ \expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
+ \pgfmath@x=\pgfmathresult pt\relax%
+ \ifdim#2pt<0pt%
+ \advance\pgfmath@x by180pt\relax%
+ \fi%
+ \fi%
+ \ifdim#1pt<0pt\relax%
+ \pgfmath@x=-\pgfmath@x%
+ \fi%
+ \fi%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
}
+% This is needed since \pgfmathatan2 is not a legal macro name
+\expandafter\let\expandafter\pgfmathatantwo\csname pgfmathatan2\endcsname
+\expandafter\let\expandafter\pgfmathatantwo@\csname pgfmathatan2@\endcsname
+
\def\pgfmath@def#1#2#3{\expandafter\def\csname pgfmath@#1@#2\endcsname{#3}}
-\pgfmath@def{cos}{0}{1.00000} \pgfmath@def{cos}{1}{0.99985}
-\pgfmath@def{cos}{2}{0.99939} \pgfmath@def{cos}{3}{0.99863}
-\pgfmath@def{cos}{4}{0.99756} \pgfmath@def{cos}{5}{0.99619}
-\pgfmath@def{cos}{6}{0.99452} \pgfmath@def{cos}{7}{0.99255}
-\pgfmath@def{cos}{8}{0.99027} \pgfmath@def{cos}{9}{0.98769}
-\pgfmath@def{cos}{10}{0.98481} \pgfmath@def{cos}{11}{0.98163}
-\pgfmath@def{cos}{12}{0.97815} \pgfmath@def{cos}{13}{0.97437}
-\pgfmath@def{cos}{14}{0.97030} \pgfmath@def{cos}{15}{0.96593}
-\pgfmath@def{cos}{16}{0.96126} \pgfmath@def{cos}{17}{0.95630}
-\pgfmath@def{cos}{18}{0.95106} \pgfmath@def{cos}{19}{0.94552}
-\pgfmath@def{cos}{20}{0.93969} \pgfmath@def{cos}{21}{0.93358}
-\pgfmath@def{cos}{22}{0.92718} \pgfmath@def{cos}{23}{0.92050}
-\pgfmath@def{cos}{24}{0.91355} \pgfmath@def{cos}{25}{0.90631}
-\pgfmath@def{cos}{26}{0.89879} \pgfmath@def{cos}{27}{0.89101}
-\pgfmath@def{cos}{28}{0.88295} \pgfmath@def{cos}{29}{0.87462}
-\pgfmath@def{cos}{30}{0.86603} \pgfmath@def{cos}{31}{0.85717}
-\pgfmath@def{cos}{32}{0.84805} \pgfmath@def{cos}{33}{0.83867}
-\pgfmath@def{cos}{34}{0.82904} \pgfmath@def{cos}{35}{0.81915}
-\pgfmath@def{cos}{36}{0.80902} \pgfmath@def{cos}{37}{0.79864}
-\pgfmath@def{cos}{38}{0.78801} \pgfmath@def{cos}{39}{0.77715}
-\pgfmath@def{cos}{40}{0.76604} \pgfmath@def{cos}{41}{0.75471}
-\pgfmath@def{cos}{42}{0.74314} \pgfmath@def{cos}{43}{0.73135}
-\pgfmath@def{cos}{44}{0.71934} \pgfmath@def{cos}{45}{0.70711}
-\pgfmath@def{cos}{46}{0.69466} \pgfmath@def{cos}{47}{0.68200}
-\pgfmath@def{cos}{48}{0.66913} \pgfmath@def{cos}{49}{0.65606}
-\pgfmath@def{cos}{50}{0.64279} \pgfmath@def{cos}{51}{0.62932}
-\pgfmath@def{cos}{52}{0.61566} \pgfmath@def{cos}{53}{0.60182}
-\pgfmath@def{cos}{54}{0.58779} \pgfmath@def{cos}{55}{0.57358}
-\pgfmath@def{cos}{56}{0.55919} \pgfmath@def{cos}{57}{0.54464}
-\pgfmath@def{cos}{58}{0.52992} \pgfmath@def{cos}{59}{0.51504}
-\pgfmath@def{cos}{60}{0.50000} \pgfmath@def{cos}{61}{0.48481}
-\pgfmath@def{cos}{62}{0.46947} \pgfmath@def{cos}{63}{0.45399}
-\pgfmath@def{cos}{64}{0.43837} \pgfmath@def{cos}{65}{0.42262}
-\pgfmath@def{cos}{66}{0.40674} \pgfmath@def{cos}{67}{0.39073}
-\pgfmath@def{cos}{68}{0.37461} \pgfmath@def{cos}{69}{0.35837}
-\pgfmath@def{cos}{70}{0.34202} \pgfmath@def{cos}{71}{0.32557}
-\pgfmath@def{cos}{72}{0.30902} \pgfmath@def{cos}{73}{0.29237}
-\pgfmath@def{cos}{74}{0.27564} \pgfmath@def{cos}{75}{0.25882}
-\pgfmath@def{cos}{76}{0.24192} \pgfmath@def{cos}{77}{0.22495}
-\pgfmath@def{cos}{78}{0.20791} \pgfmath@def{cos}{79}{0.19081}
-\pgfmath@def{cos}{80}{0.17365} \pgfmath@def{cos}{81}{0.15643}
-\pgfmath@def{cos}{82}{0.13917} \pgfmath@def{cos}{83}{0.12187}
-\pgfmath@def{cos}{84}{0.10453} \pgfmath@def{cos}{85}{0.08716}
-\pgfmath@def{cos}{86}{0.06976} \pgfmath@def{cos}{87}{0.05234}
-\pgfmath@def{cos}{88}{0.03490} \pgfmath@def{cos}{89}{0.01745}
-\pgfmath@def{cos}{90}{0.00000} \pgfmath@def{cos}{91}{-0.01745}
-\pgfmath@def{cos}{92}{-0.03490} \pgfmath@def{cos}{93}{-0.05234}
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+\pgfmath@def{cosfrac}{94}{0.72862} \pgfmath@def{cosfrac}{95}{0.72499}
+\pgfmath@def{cosfrac}{96}{0.72138} \pgfmath@def{cosfrac}{97}{0.71779}
+\pgfmath@def{cosfrac}{98}{0.71421} \pgfmath@def{cosfrac}{99}{0.71065}
+\pgfmath@def{cosfrac}{100}{0.70710}
% Oh No! Some really loooooong tables.
-\pgfmath@def{atan}{0}{0.00000} \pgfmath@def{atan}{1}{0.05729}
-\pgfmath@def{atan}{2}{0.11459} \pgfmath@def{atan}{3}{0.17188}
-\pgfmath@def{atan}{4}{0.22918} \pgfmath@def{atan}{5}{0.28647}
-\pgfmath@def{atan}{6}{0.34377} \pgfmath@def{atan}{7}{0.40106}
-\pgfmath@def{atan}{8}{0.45835} \pgfmath@def{atan}{9}{0.51564}
-\pgfmath@def{atan}{10}{0.57293} \pgfmath@def{atan}{11}{0.63022}
-\pgfmath@def{atan}{12}{0.68751} \pgfmath@def{atan}{13}{0.74480}
-\pgfmath@def{atan}{14}{0.80208} \pgfmath@def{atan}{15}{0.85937}
-\pgfmath@def{atan}{16}{0.91665} \pgfmath@def{atan}{17}{0.97393}
-\pgfmath@def{atan}{18}{1.03121} \pgfmath@def{atan}{19}{1.08848}
-\pgfmath@def{atan}{20}{1.14576} \pgfmath@def{atan}{21}{1.20303}
-\pgfmath@def{atan}{22}{1.26030} \pgfmath@def{atan}{23}{1.31757}
-\pgfmath@def{atan}{24}{1.37483} \pgfmath@def{atan}{25}{1.43209}
-\pgfmath@def{atan}{26}{1.48935} \pgfmath@def{atan}{27}{1.54661}
-\pgfmath@def{atan}{28}{1.60386} \pgfmath@def{atan}{29}{1.66111}
-\pgfmath@def{atan}{30}{1.71835} \pgfmath@def{atan}{31}{1.77560}
-\pgfmath@def{atan}{32}{1.83284} \pgfmath@def{atan}{33}{1.89007}
-\pgfmath@def{atan}{34}{1.94730} \pgfmath@def{atan}{35}{2.00453}
-\pgfmath@def{atan}{36}{2.06175} \pgfmath@def{atan}{37}{2.11897}
-\pgfmath@def{atan}{38}{2.17619} \pgfmath@def{atan}{39}{2.23340}
-\pgfmath@def{atan}{40}{2.29061} \pgfmath@def{atan}{41}{2.34781}
-\pgfmath@def{atan}{42}{2.40500} \pgfmath@def{atan}{43}{2.46220}
-\pgfmath@def{atan}{44}{2.51938} \pgfmath@def{atan}{45}{2.57657}
-\pgfmath@def{atan}{46}{2.63374} \pgfmath@def{atan}{47}{2.69092}
-\pgfmath@def{atan}{48}{2.74808} \pgfmath@def{atan}{49}{2.80524}
-\pgfmath@def{atan}{50}{2.86240} \pgfmath@def{atan}{51}{2.91955}
-\pgfmath@def{atan}{52}{2.97669} \pgfmath@def{atan}{53}{3.03383}
-\pgfmath@def{atan}{54}{3.09097} \pgfmath@def{atan}{55}{3.14809}
-\pgfmath@def{atan}{56}{3.20521} \pgfmath@def{atan}{57}{3.26232}
-\pgfmath@def{atan}{58}{3.31943} \pgfmath@def{atan}{59}{3.37653}
-\pgfmath@def{atan}{60}{3.43363} \pgfmath@def{atan}{61}{3.49071}
-\pgfmath@def{atan}{62}{3.54779} \pgfmath@def{atan}{63}{3.60487}
-\pgfmath@def{atan}{64}{3.66193} \pgfmath@def{atan}{65}{3.71899}
-\pgfmath@def{atan}{66}{3.77604} \pgfmath@def{atan}{67}{3.83308}
-\pgfmath@def{atan}{68}{3.89012} \pgfmath@def{atan}{69}{3.94715}
-\pgfmath@def{atan}{70}{4.00417} \pgfmath@def{atan}{71}{4.06118}
-\pgfmath@def{atan}{72}{4.11819} \pgfmath@def{atan}{73}{4.17518}
-\pgfmath@def{atan}{74}{4.23217} \pgfmath@def{atan}{75}{4.28915}
-\pgfmath@def{atan}{76}{4.34612} \pgfmath@def{atan}{77}{4.40308}
-\pgfmath@def{atan}{78}{4.46004} \pgfmath@def{atan}{79}{4.51698}
-\pgfmath@def{atan}{80}{4.57392} \pgfmath@def{atan}{81}{4.63084}
-\pgfmath@def{atan}{82}{4.68776} \pgfmath@def{atan}{83}{4.74467}
-\pgfmath@def{atan}{84}{4.80157} \pgfmath@def{atan}{85}{4.85846}
-\pgfmath@def{atan}{86}{4.91534} \pgfmath@def{atan}{87}{4.97221}
-\pgfmath@def{atan}{88}{5.02907} \pgfmath@def{atan}{89}{5.08592}
-\pgfmath@def{atan}{90}{5.14276} \pgfmath@def{atan}{91}{5.19959}
-\pgfmath@def{atan}{92}{5.25641} \pgfmath@def{atan}{93}{5.31322}
-\pgfmath@def{atan}{94}{5.37002} \pgfmath@def{atan}{95}{5.42681}
-\pgfmath@def{atan}{96}{5.48359} \pgfmath@def{atan}{97}{5.54035}
-\pgfmath@def{atan}{98}{5.59711} \pgfmath@def{atan}{99}{5.65385}
-\pgfmath@def{atan}{100}{5.71059} \pgfmath@def{atan}{101}{5.76731}
-\pgfmath@def{atan}{102}{5.82402} \pgfmath@def{atan}{103}{5.88072}
-\pgfmath@def{atan}{104}{5.93741} \pgfmath@def{atan}{105}{5.99409}
-\pgfmath@def{atan}{106}{6.05075} \pgfmath@def{atan}{107}{6.10741}
-\pgfmath@def{atan}{108}{6.16405} \pgfmath@def{atan}{109}{6.22068}
-\pgfmath@def{atan}{110}{6.27729} \pgfmath@def{atan}{111}{6.33390}
-\pgfmath@def{atan}{112}{6.39049} \pgfmath@def{atan}{113}{6.44707}
-\pgfmath@def{atan}{114}{6.50364} \pgfmath@def{atan}{115}{6.56019}
-\pgfmath@def{atan}{116}{6.61673} \pgfmath@def{atan}{117}{6.67326}
-\pgfmath@def{atan}{118}{6.72978} \pgfmath@def{atan}{119}{6.78628}
-\pgfmath@def{atan}{120}{6.84277} \pgfmath@def{atan}{121}{6.89924}
-\pgfmath@def{atan}{122}{6.95571} \pgfmath@def{atan}{123}{7.01216}
-\pgfmath@def{atan}{124}{7.06859} \pgfmath@def{atan}{125}{7.12501}
-\pgfmath@def{atan}{126}{7.18142} \pgfmath@def{atan}{127}{7.23781}
-\pgfmath@def{atan}{128}{7.29419} \pgfmath@def{atan}{129}{7.35056}
-\pgfmath@def{atan}{130}{7.40691} \pgfmath@def{atan}{131}{7.46324}
-\pgfmath@def{atan}{132}{7.51957} \pgfmath@def{atan}{133}{7.57587}
-\pgfmath@def{atan}{134}{7.63217} \pgfmath@def{atan}{135}{7.68844}
-\pgfmath@def{atan}{136}{7.74471} \pgfmath@def{atan}{137}{7.80095}
-\pgfmath@def{atan}{138}{7.85719} \pgfmath@def{atan}{139}{7.91340}
-\pgfmath@def{atan}{140}{7.96961} \pgfmath@def{atan}{141}{8.02579}
-\pgfmath@def{atan}{142}{8.08196} \pgfmath@def{atan}{143}{8.13812}
-\pgfmath@def{atan}{144}{8.19426} \pgfmath@def{atan}{145}{8.25038}
-\pgfmath@def{atan}{146}{8.30649} \pgfmath@def{atan}{147}{8.36258}
-\pgfmath@def{atan}{148}{8.41866} \pgfmath@def{atan}{149}{8.47472}
-\pgfmath@def{atan}{150}{8.53076} \pgfmath@def{atan}{151}{8.58679}
-\pgfmath@def{atan}{152}{8.64280} \pgfmath@def{atan}{153}{8.69879}
-\pgfmath@def{atan}{154}{8.75477} \pgfmath@def{atan}{155}{8.81073}
-\pgfmath@def{atan}{156}{8.86667} \pgfmath@def{atan}{157}{8.92260}
-\pgfmath@def{atan}{158}{8.97851} \pgfmath@def{atan}{159}{9.03440}
-\pgfmath@def{atan}{160}{9.09027} \pgfmath@def{atan}{161}{9.14613}
-\pgfmath@def{atan}{162}{9.20197} \pgfmath@def{atan}{163}{9.25779}
-\pgfmath@def{atan}{164}{9.31359} \pgfmath@def{atan}{165}{9.36938}
-\pgfmath@def{atan}{166}{9.42515} \pgfmath@def{atan}{167}{9.48090}
-\pgfmath@def{atan}{168}{9.53663} \pgfmath@def{atan}{169}{9.59235}
-\pgfmath@def{atan}{170}{9.64804} \pgfmath@def{atan}{171}{9.70372}
-\pgfmath@def{atan}{172}{9.75938} \pgfmath@def{atan}{173}{9.81502}
-\pgfmath@def{atan}{174}{9.87064} \pgfmath@def{atan}{175}{9.92624}
-\pgfmath@def{atan}{176}{9.98182} \pgfmath@def{atan}{177}{10.03739}
-\pgfmath@def{atan}{178}{10.09294} \pgfmath@def{atan}{179}{10.14846}
-\pgfmath@def{atan}{180}{10.20397} \pgfmath@def{atan}{181}{10.25946}
-\pgfmath@def{atan}{182}{10.31493} \pgfmath@def{atan}{183}{10.37037}
-\pgfmath@def{atan}{184}{10.42580} \pgfmath@def{atan}{185}{10.48121}
-\pgfmath@def{atan}{186}{10.53660} \pgfmath@def{atan}{187}{10.59197}
-\pgfmath@def{atan}{188}{10.64732} \pgfmath@def{atan}{189}{10.70265}
-\pgfmath@def{atan}{190}{10.75796} \pgfmath@def{atan}{191}{10.81325}
-\pgfmath@def{atan}{192}{10.86852} \pgfmath@def{atan}{193}{10.92377}
-\pgfmath@def{atan}{194}{10.97900} \pgfmath@def{atan}{195}{11.03420}
-\pgfmath@def{atan}{196}{11.08939} \pgfmath@def{atan}{197}{11.14456}
-\pgfmath@def{atan}{198}{11.19970} \pgfmath@def{atan}{199}{11.25483}
-\pgfmath@def{atan}{200}{11.30993} \pgfmath@def{atan}{201}{11.36501}
-\pgfmath@def{atan}{202}{11.42007} \pgfmath@def{atan}{203}{11.47511}
-\pgfmath@def{atan}{204}{11.53013} \pgfmath@def{atan}{205}{11.58512}
-\pgfmath@def{atan}{206}{11.64010} \pgfmath@def{atan}{207}{11.69505}
-\pgfmath@def{atan}{208}{11.74998} \pgfmath@def{atan}{209}{11.80489}
-\pgfmath@def{atan}{210}{11.85977} \pgfmath@def{atan}{211}{11.91464}
-\pgfmath@def{atan}{212}{11.96948} \pgfmath@def{atan}{213}{12.02430}
-\pgfmath@def{atan}{214}{12.07910} \pgfmath@def{atan}{215}{12.13388}
-\pgfmath@def{atan}{216}{12.18863} \pgfmath@def{atan}{217}{12.24336}
-\pgfmath@def{atan}{218}{12.29807} \pgfmath@def{atan}{219}{12.35275}
-\pgfmath@def{atan}{220}{12.40741} \pgfmath@def{atan}{221}{12.46205}
-\pgfmath@def{atan}{222}{12.51667} \pgfmath@def{atan}{223}{12.57126}
-\pgfmath@def{atan}{224}{12.62583} \pgfmath@def{atan}{225}{12.68038}
-\pgfmath@def{atan}{226}{12.73490} \pgfmath@def{atan}{227}{12.78940}
-\pgfmath@def{atan}{228}{12.84388} \pgfmath@def{atan}{229}{12.89833}
-\pgfmath@def{atan}{230}{12.95276} \pgfmath@def{atan}{231}{13.00717}
-\pgfmath@def{atan}{232}{13.06155} \pgfmath@def{atan}{233}{13.11590}
-\pgfmath@def{atan}{234}{13.17024} \pgfmath@def{atan}{235}{13.22455}
-\pgfmath@def{atan}{236}{13.27883} \pgfmath@def{atan}{237}{13.33309}
-\pgfmath@def{atan}{238}{13.38733} \pgfmath@def{atan}{239}{13.44154}
-\pgfmath@def{atan}{240}{13.49573} \pgfmath@def{atan}{241}{13.54989}
-\pgfmath@def{atan}{242}{13.60403} \pgfmath@def{atan}{243}{13.65814}
-\pgfmath@def{atan}{244}{13.71223} \pgfmath@def{atan}{245}{13.76630}
-\pgfmath@def{atan}{246}{13.82034} \pgfmath@def{atan}{247}{13.87435}
-\pgfmath@def{atan}{248}{13.92834} \pgfmath@def{atan}{249}{13.98230}
-\pgfmath@def{atan}{250}{14.03624} \pgfmath@def{atan}{251}{14.09015}
-\pgfmath@def{atan}{252}{14.14404} \pgfmath@def{atan}{253}{14.19790}
-\pgfmath@def{atan}{254}{14.25174} \pgfmath@def{atan}{255}{14.30555}
-\pgfmath@def{atan}{256}{14.35933} \pgfmath@def{atan}{257}{14.41309}
-\pgfmath@def{atan}{258}{14.46682} \pgfmath@def{atan}{259}{14.52053}
-\pgfmath@def{atan}{260}{14.57421} \pgfmath@def{atan}{261}{14.62787}
-\pgfmath@def{atan}{262}{14.68149} \pgfmath@def{atan}{263}{14.73510}
-\pgfmath@def{atan}{264}{14.78867} \pgfmath@def{atan}{265}{14.84222}
-\pgfmath@def{atan}{266}{14.89575} \pgfmath@def{atan}{267}{14.94924}
-\pgfmath@def{atan}{268}{15.00271} \pgfmath@def{atan}{269}{15.05615}
-\pgfmath@def{atan}{270}{15.10957} \pgfmath@def{atan}{271}{15.16296}
-\pgfmath@def{atan}{272}{15.21632} \pgfmath@def{atan}{273}{15.26966}
-\pgfmath@def{atan}{274}{15.32297} \pgfmath@def{atan}{275}{15.37625}
-\pgfmath@def{atan}{276}{15.42950} \pgfmath@def{atan}{277}{15.48273}
-\pgfmath@def{atan}{278}{15.53593} \pgfmath@def{atan}{279}{15.58910}
-\pgfmath@def{atan}{280}{15.64224} \pgfmath@def{atan}{281}{15.69536}
-\pgfmath@def{atan}{282}{15.74845} \pgfmath@def{atan}{283}{15.80151}
-\pgfmath@def{atan}{284}{15.85454} \pgfmath@def{atan}{285}{15.90755}
-\pgfmath@def{atan}{286}{15.96052} \pgfmath@def{atan}{287}{16.01347}
-\pgfmath@def{atan}{288}{16.06640} \pgfmath@def{atan}{289}{16.11929}
-\pgfmath@def{atan}{290}{16.17215} \pgfmath@def{atan}{291}{16.22499}
-\pgfmath@def{atan}{292}{16.27780} \pgfmath@def{atan}{293}{16.33058}
-\pgfmath@def{atan}{294}{16.38333} \pgfmath@def{atan}{295}{16.43605}
-\pgfmath@def{atan}{296}{16.48875} \pgfmath@def{atan}{297}{16.54142}
-\pgfmath@def{atan}{298}{16.59405} \pgfmath@def{atan}{299}{16.64666}
-\pgfmath@def{atan}{300}{16.69924} \pgfmath@def{atan}{301}{16.75179}
-\pgfmath@def{atan}{302}{16.80431} \pgfmath@def{atan}{303}{16.85680}
-\pgfmath@def{atan}{304}{16.90927} \pgfmath@def{atan}{305}{16.96170}
-\pgfmath@def{atan}{306}{17.01411} \pgfmath@def{atan}{307}{17.06648}
-\pgfmath@def{atan}{308}{17.11883} \pgfmath@def{atan}{309}{17.17114}
-\pgfmath@def{atan}{310}{17.22343} \pgfmath@def{atan}{311}{17.27569}
-\pgfmath@def{atan}{312}{17.32792} \pgfmath@def{atan}{313}{17.38012}
-\pgfmath@def{atan}{314}{17.43228} \pgfmath@def{atan}{315}{17.48442}
-\pgfmath@def{atan}{316}{17.53653} \pgfmath@def{atan}{317}{17.58861}
-\pgfmath@def{atan}{318}{17.64066} \pgfmath@def{atan}{319}{17.69268}
-\pgfmath@def{atan}{320}{17.74467} \pgfmath@def{atan}{321}{17.79663}
-\pgfmath@def{atan}{322}{17.84855} \pgfmath@def{atan}{323}{17.90045}
-\pgfmath@def{atan}{324}{17.95232} \pgfmath@def{atan}{325}{18.00416}
-\pgfmath@def{atan}{326}{18.05596} \pgfmath@def{atan}{327}{18.10774}
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-\pgfmath@def{atan}{330}{18.26289} \pgfmath@def{atan}{331}{18.31454}
-\pgfmath@def{atan}{332}{18.36616} \pgfmath@def{atan}{333}{18.41775}
-\pgfmath@def{atan}{334}{18.46931} \pgfmath@def{atan}{335}{18.52084}
-\pgfmath@def{atan}{336}{18.57234} \pgfmath@def{atan}{337}{18.62381}
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-\pgfmath@def{atan}{340}{18.77803} \pgfmath@def{atan}{341}{18.82937}
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-\pgfmath@def{atan}{382}{20.90685} \pgfmath@def{atan}{383}{20.95684}
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-\pgfmath@def{atan}{420}{22.78240} \pgfmath@def{atan}{421}{22.83109}
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+\pgfmath@def{acos}{998}{3.62430} \pgfmath@def{acos}{999}{2.56255}
+\pgfmath@def{acos}{1000}{0.00000}
+
+
+
+% Local Variables:
+% tab-width: 2
+% End:
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex
new file mode 100644
index 00000000000..d8837897558
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathode.code.tex
@@ -0,0 +1,178 @@
+% Copyright 2011 by Christophe Jorssen
+%
+% 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.
+\def\pgfmathode@stopadd{\pgfmathode@stopadd}
+
+\def\pgfmathode@addindextofunc[#1]#2{%
+ \begingroup
+ \gdef\pgfmathode@func{}%
+ \pgfmathode@addindextofunc@i[#1]#2\pgfmathode@stopadd}
+
+\def\pgfmathode@addindextofunc@i[#1]#2#3{%
+ \ifx#1#2
+ \expandafter\gdef\expandafter\pgfmathode@func\expandafter{%
+ \pgfmathode@func #2[\pgfmathode@timeindex]}%
+ \else
+ \expandafter\gdef\expandafter\pgfmathode@func\expandafter{%
+ \pgfmathode@func #2}%
+ \fi
+ \ifx#3\pgfmathode@stopadd
+ \expandafter\gdef\expandafter\pgfmathode@func\expandafter{%
+ \expandafter{\pgfmathode@func}}%
+ \let\next\endgroup
+ \else
+ \def\next{\pgfmathode@addindextofunc@i[#1]#3}%
+ \fi
+ \next}
+
+%**********************************************************************
+% Know limitation: fk cannot be a time function. Should be possible to
+% use \Sol[0] as time in the set of equations.
+%**********************************************************************
+
+% Numerically solve a differential system with 1st order Runge-Kutta
+% (Euler method)
+% dq1/dt = f1(t,q1,q2,...,qN)
+% dq2/dt = f2(t,q1,q2,...,qN)
+% ...
+% dqN/dt = fN(t,q1,q2,...,qN)
+%
+% #1: A pgf array where the solution will be stored.
+% At the end:
+% #1 -> {{t(0),q1(t(0)),q2(t(0)),...,qN(t(0))},
+% {t(1),q1(t(1)),q2(t(1)),...,qN(t(1))},
+% ...
+% {t(Nstep),q1(t(Nstep)),q2(t(Nstep)),...,qN(t(Nstep))}}
+% #2: A pgf array with f1,f2,...,fN
+% {f1}
+% #3: A pgf array with initial conditions.
+% {t(0),q1(t(0)),q2(t(0)),...,qN(t(0))}
+% #4: t(Nstep)
+% #5: Nstep (number of steps)
+%
+% * First order example: dq/dt = -q + 5 with IC=(t=0,q(0)=0)
+% \pgfmathodeRKI{\Sol}{{-\Sol[1]+5}}{{0,0}}{3.5}{100}
+% * Second order example: {dq1/dt=q2, dq2/dt=-q2/2-sin(q1)} (damped
+% pendulum)
+% \pgfmathodeRKI{\Sol}{{\Sol[2],-\Sol[2]/2-sin(deg(\Sol[1]))}}%
+% {{0,-1,5}}{15}{50}
+
+\def\pgfmathode@generic@init@RK{%
+ \begingroup
+ % Sol array (#1) first element is given by the set of initial
+ % conditions (#3). We need to enclose it in brace so that is a now
+ % a "matrix" array.
+ \gdef#1{{#3}}%
+ % The set of rhs {f1(t,q1,q2,...,qN),...,fN(t,q1,q2,...,qN)} is
+ % given in terms of #1[0],#1[1],...,#1[N]. We need to transform to
+ % #1[\pgfmathode@timeindex][0],...,#1[\pgfmathode@timeindex][N], that is
+ % add [\pgfmathode@timeindex] after every occurence of #1 in #2.
+ % No need to brace #2 since it is already surounded by braces. The
+ % result is stored in \pgfmathode@func
+ \pgfmathode@addindextofunc[#1]#2%
+ % Set time step. Actually the number of time steps is #5-1, so we
+ % divide by (#5-1)+1 = #5.
+ \pgfmathsetmacro\pgfmathode@Sol@t{#1[0][0]}%
+ \pgfmathsetmacro\pgfmathode@Deltat{(#4-\pgfmathode@Sol@t)/#5}%
+ % Compute the order of the system: it is equal to the number of IC
+ % minus one (time).
+ \pgfmathsetmacro\pgfmathode@dimfunc{dim(#3)-1}%
+ \pgfmathsetmacro\pgfmathode@numstep{#5-1}}
+
+\def\pgfmathodeRKI#1#2#3#4#5{%
+ \pgfmathode@generic@init@RK
+ % Start the time loop for Runge-Kutta 1st order
+ \foreach \pgfmathode@timeindex in {0,...,\pgfmathode@numstep} {%
+ \message{Step \pgfmathode@timeindex...}%
+ % Start the function loop
+ \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
+ % The RKI algorithm
+ % qk[t(i)] = Deltat*fk(t(i-1),q1(t(i-1)),...qN(t(i-1))) +
+ % qk[t(i-1)]
+ % Note: this part can be really slow due to array managment in
+ % pgfmath.
+ % TODO: find a better way (at least inside this loop)
+ \pgfmathparse{%
+ \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+
+ #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}%
+ % Store the result in a helper macro
+ \expandafter\xdef\csname pgfmathode@Sol@\pgfmathode@funcindex
+ \endcsname{\pgfmathresult}%
+ }
+ % Store step i
+ \pgfmathparse{\pgfmathode@Sol@t+\pgfmathode@Deltat}%
+ \xdef\pgfmathode@Sol@t{\pgfmathresult}%
+ \xdef\pgfmathode@temp{}%
+ \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
+ \ifx\pgfmathode@temp\pgfutil@empty
+ \xdef\pgfmathode@temp{%
+ \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}%
+ \else
+ \xdef\pgfmathode@temp{%
+ \pgfmathode@temp,
+ \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}%
+ \fi}
+ \xdef#1{%
+ {\expandafter\pgfutil@firstofone#1,%
+ {\pgfmathode@Sol@t,\pgfmathode@temp}}}%
+ }
+ \endgroup}
+
+% RKIV: far from working yet!
+\def\pgfmathodeRKIV#1#2#3#4#5{%
+ \pgfmathode@generic@init@RK
+ % Start the time loop for Runge-Kutta 4th order
+ \foreach \pgfmathode@timeindex in {0,...,\pgfmathode@numstep} {%
+ \message{Step \pgfmathode@timeindex...}%
+ % Start the function loop
+ \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
+ % The RKIV algorithm
+ % qk[t(i)] = qk[t(i-1)] +
+ % (1/6) * (j1k + 2j2k + 2j3k + j4k)
+ % where j1k = fk(t(i-1),q1(t(i-1)),...qN(t(i-1))) * Deltat
+ % j2k = fk(t(i-1)+.5*Deltat,
+ % q1(t(i-1))+.5*j11,...qN(t(i-1))+.5*j1N) * Deltat
+ % j3k = fk(t(i-1)+.5*Deltat,
+ % q1(t(i-1))+.5*j21,...qN(t(i-1))+.5*j2N) * Deltat
+ % j4k = fk(t(i-1)+Deltat,
+ % q1(t(i-1))+j31,...qN(t(i-1))+j3N) * Deltat
+ %
+ % Compute j1k
+ \pgfmathparse{%
+ \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+
+ #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}%
+ \expandafter\xdef\csname pgfmathode@RKIV@1@\pgfmathode@funcindex
+ \endcsname{\pgfmathresult}%
+ % Compute j2k
+ \pgfmathparse{%
+ \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+
+ #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}%
+ \expandafter\xdef\csname pgfmathode@RKIV@1@\pgfmathode@funcindex
+ \endcsname{\pgfmathresult}%
+ }
+ % Store step i
+ \pgfmathparse{\pgfmathode@Sol@t+\pgfmathode@Deltat}%
+ \xdef\pgfmathode@Sol@t{\pgfmathresult}%
+ \xdef\pgfmathode@temp{}%
+ \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {%
+ \ifx\pgfmathode@temp\pgfutil@empty
+ \xdef\pgfmathode@temp{%
+ \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}%
+ \else
+ \xdef\pgfmathode@temp{%
+ \pgfmathode@temp,
+ \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}%
+ \fi}
+ \xdef#1{%
+ {\expandafter\pgfutil@firstofone#1,%
+ {\pgfmathode@Sol@t,\pgfmathode@temp}}}%
+ }
+ \endgroup}
+
+
+\endinput \ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
index 81f6545897e..71843fb2499 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
@@ -7,83 +7,92 @@
\newif\ifpgfmath@quickparse
\newif\ifpgfmathfloat
\newif\ifpgfmathunitsdeclared
+\newif\ifpgfmathmathunitsdeclared
\newif\ifpgfmathignoreunitscale
\def\pgfmathprint#1{\pgfmathparse{#1}\pgfmathresult}
\def\pgfmathparse{%
- \begingroup%
- \pgfmath@catcodes%
- \pgfmath@quickparsefalse%
- \ifpgfmathfloat%
- \let\pgfmath@parse@next=\pgfmathfloatparsenumber%
- \else%
- \let\pgfmath@parse@next=\pgfmathparse@%
- \fi%
- \pgfmath@parse@next}
+ \begingroup
+ \pgfmath@catcodes
+ \pgfmath@quickparsefalse
+ % Test for the fpu library
+ \ifpgfmathfloat
+ \let\pgfmath@parse@next=\pgfmathfloatparsenumber
+ \else
+ \let\pgfmath@parse@next=\pgfmathparse@
+ \fi
+ \pgfmath@parse@next}
\def\pgfmath@catcodes{% Maybe unecessary.
- \catcode`\==12%
- \catcode`\,=12%
- \catcode`\|=12%
- \catcode`\&=12%
+ \catcode`\==12%
+ \catcode`\,=12%
+ \catcode`\|=12%
+ \catcode`\&=12%
}
\def\pgfmathqparse{%
- \begingroup%
- \pgfmath@catcodes%
- \pgfmath@quickparsetrue%
- \pgfmathparse@}
-
+ \begingroup
+ \pgfmath@catcodes
+ \pgfmath@quickparsetrue
+ \pgfmathparse@}
+
\def\pgfmathparse@#1{%
- % Stuff for calc compatiability.
- \let\real=\pgfmath@calc@real%
- \let\minof=\pgfmath@calc@minof%
- \let\maxof=\pgfmath@calc@maxof%
- \let\ratio=\pgfmath@calc@ratio%
- \let\widthof=\pgfmath@calc@widthof%
- \let\heightof=\pgfmath@calc@heightof%
- \let\depthof=\pgfmath@calc@depthof%
- % Restore font.
- \pgfmath@selectfont%
+ % We are inside a group (opened in |\pgfmathparse| or
+ % |\pgfmathqparse|).
+ % Stuff for calc compatiability.
+ \let\real=\pgfmath@calc@real
+ \let\minof=\pgfmath@calc@minof
+ \let\maxof=\pgfmath@calc@maxof
+ \let\ratio=\pgfmath@calc@ratio
+ \let\widthof=\pgfmath@calc@widthof
+ \let\heightof=\pgfmath@calc@heightof
+ \let\depthof=\pgfmath@calc@depthof
+ % Restore font (defined in pgfmathutil.code.tex)
+ \pgfmath@selectfont
% Expand expression so any reamining CSs are registers
- % or box dimensions (i.e., \wd, \ht, \dp).
+ % or box dimensions (i.e. |\wd|, |\ht|, |\dp|).
\edef\pgfmath@expression{#1}%
- % No units yet.
- \global\pgfmathunitsdeclaredfalse%
+ % No (math) units yet.
+ \global\pgfmathunitsdeclaredfalse
+ \global\pgfmathmathunitsdeclaredfalse
% Set up stack.
\pgfmath@stack@operation={{}{}{}}%
- \pgfmath@stack@operand={{}{}{}}%
- \let\pgfmath@stack@operation@top=\pgfmath@stack@empty%
- \let\pgfmath@stack@operand@top=\pgfmath@stack@empty%
- % An expression always begins with an operand.
- \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmath@expression}%
- \expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped @@@@\pgfmath@parse@stop%
-}%
+ \pgfmath@stack@operand={{}{}{}}%
+ \let\pgfmath@stack@operation@top=\pgfmath@stack@empty
+ \let\pgfmath@stack@operand@top=\pgfmath@stack@empty
+ % An expression always begins with an operand.
+ \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmath@expression}%
+ % |\pgfmath@bgroup@stripped| is the result of
+ % |\pgfmath@bgroup@strip|
+ \expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped @@@@\pgfmath@parse@stop%
+}
\def\pgfmath@parse@end#1\pgfmath@parse@stop{%
- \pgfmathpostparse%
- \pgfmath@smuggleone\pgfmathresult%
- \endgroup%
- \ignorespaces}%
+ \pgfmathpostparse
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup
+ \ignorespaces}
-\let\pgfmathpostparse=\relax%
+\let\pgfmathpostparse=\relax
% For compatiability with older version.
%
\def\pgfmathscaleresult{%
- \ifpgfmathunitsdeclared%
- \else%
- \ifpgfmathignoreunitscale%
- \else%
- \afterassignment\pgfmath@gobbletilpgfmath@%
+ \ifpgfmathunitsdeclared
+ \else
+ \ifpgfmathignoreunitscale
+ \else
+ \afterassignment\pgfmath@gobbletilpgfmath@%
\pgfmath@x\pgfmathresultunitscale pt\relax\pgfmath@%
\expandafter\pgfmath@x\pgfmathresult\pgfmath@x%
\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}%
- \fi%
- \fi%
+ \fi
+ \fi
}
+
\def\pgfmathsetresultunitscale#1{\def\pgfmathresultunitscale{#1}}
+
\def\pgfmathresultunitscale{1}
% Stuff for compatability with the calc package.
@@ -116,19 +125,29 @@
\edef\pgfmath@char@hash{\the\pgfmath@toks}
\def\pgfmath@tokens@make#1#2{%
- \def\pgfmath@prefix{#1}%
- \expandafter\pgfmath@tokens@@make#2{}}
-
+ % Defines for each token or balenced text in |#2| a control sequence
+ % |\pgfmath@token@<#1>@\string<one token from #2>| and stores |#2|
+ % in it.
+ \def\pgfmath@prefix{#1}%
+ % Note the empty group |{}| at the end that ends the loop in
+ % |\pgfmath@token@@make|.
+ \expandafter\pgfmath@tokens@@make#2{}}
+
\def\pgfmath@tokens@@make#1{%
- \def\pgfmath@token{#1}%
- \ifx\pgfmath@token\pgfmath@empty%
- \else%
- \pgfmath@namedef{pgfmath@token@\pgfmath@prefix @\string#1}{#1}%
- \expandafter\pgfmath@tokens@@make%
- \fi}
+ \def\pgfmath@token{#1}%
+ \ifx\pgfmath@token\pgfmath@empty
+ % End of loop: all tokens or balanced texts were parsed.
+ \else
+ \pgfmath@namedef{pgfmath@token@\pgfmath@prefix @\string#1}{#1}%
+ \expandafter\pgfmath@tokens@@make%
+ \fi}
\pgfmath@tokens@make{box}{\wd\ht\dp}
+\ifx\dimexpr\@undefined\else % needed for classic tex
+ \pgfmath@tokens@make{dimexpr}{\dimexpr\glueexpr}
+\fi
\pgfmath@tokens@make{unit}{{bp}{cc}{cm}{dd}{em}{ex}{in}{mm}{pc}{pt}{sp}}
+\pgfmath@tokens@make{mathunit}{{mu}}
\pgfmath@tokens@make{numeric}{.0123456789}
\pgfmath@tokens@make{number}{0123456789}
\pgfmath@tokens@make{functional}{_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNPQRSTUVWXYZ}
@@ -145,39 +164,42 @@
\pgfmath@namedef{pgfmath@base@0B}{2}
% Determine if a register is a count or a dimension/skip register.
-%
\newif\ifpgfmath@dimen@
\def\pgfmath@dimen@#1{%
- \begingroup%
- \afterassignment\pgfmath@dimen@@%
- #1=0.0pt\relax\pgfmath@}
+ \begingroup
+ \afterassignment\pgfmath@dimen@@%
+ #1=0.0pt\relax\pgfmath@}
\def\pgfmath@dimen@@#1#2\pgfmath@{%
- \endgroup%
- \ifx#1.%
- \pgfmath@dimen@false%
- \else%
- \pgfmath@dimen@true%
- \fi}
+ \endgroup
+ \ifx#1.%
+ \pgfmath@dimen@false
+ \else
+ \pgfmath@dimen@true
+ \fi}
\def\pgfmath@parse@ifbgroup#1#2{%
- \let\pgfmath@parse@bgroup@after=#1%
- \let\pgfmath@parse@nobgroup@after=#2%
- \futurelet\pgfmath@token@let%
- \pgfmath@parse@@ifbgroup}
-
+ \let\pgfmath@parse@bgroup@after=#1%
+ \let\pgfmath@parse@nobgroup@after=#2%
+ \futurelet\pgfmath@token@let%
+ \pgfmath@parse@@ifbgroup}
+
\def\pgfmath@parse@@ifbgroup{%
- \ifx\pgfmath@token@let\bgroup%
- \let\pgfmath@parse@next=\pgfmath@parse@@@ifbgroup%
- \else%
- \ifx\pgfmath@token@let\pgfmath@sptoken%
- \let\pgfmath@parse@next=\pgfmath@parse@@@@ifbgroup%
- \else%
- \let\pgfmath@parse@next=\pgfmath@parse@nobgroup@after%
- \fi%
- \fi%
- \pgfmath@parse@next}
-
-\def\pgfmath@parse@@@ifbgroup#1{\pgfmath@parse@bgroup@after\pgfmath@bgroup#1\pgfmath@egroup}
+ \ifx\pgfmath@token@let\bgroup
+ \let\pgfmath@parse@next=\pgfmath@parse@@@ifbgroup
+ \else
+ % |\pgfmath@sptoken| defined in \file{pgfmathutil.code.tex}.
+ \ifx\pgfmath@token@let\pgfmath@sptoken
+ \let\pgfmath@parse@next=\pgfmath@parse@@@@ifbgroup
+ \else
+ \let\pgfmath@parse@next=\pgfmath@parse@nobgroup@after
+ \fi
+ \fi
+ \pgfmath@parse@next}
+
+% I (CJ) *think* it replaces |{| and |}| by |\pgfmath@bgroup| and
+% |\pgfmath@egroup|?
+\def\pgfmath@parse@@@ifbgroup#1{%
+ \pgfmath@parse@bgroup@after\pgfmath@bgroup#1\pgfmath@egroup}
{
\def\:{\pgfmath@parse@@@@ifbgroup}
@@ -185,81 +207,96 @@
}
% Parse an operand.
-%
-\def\pgfmath@parse@operand{\expandafter\pgfmath@parse@@operand\pgfmath@token@next}%
-
-\def\pgfmath@parse@@operand{\pgfmath@parse@ifbgroup{\pgfmath@parse@@operand}{\pgfmath@parse@@operand@}}
-
+\def\pgfmath@parse@operand{%
+ \expandafter\pgfmath@parse@@operand\pgfmath@token@next}
+
+% This is the entry point for the parser. It is called at the end of
+% |\pgfmathparse@| with the following syntax
+% |\expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped
+% @@@@\pgfmath@parse@stop|.
+% Note: we are inside a group.
+\def\pgfmath@parse@@operand{%
+ \pgfmath@parse@ifbgroup{\pgfmath@parse@@operand}{\pgfmath@parse@@operand@}}
+
+% An operand is
+% * |+| (unary plus),
+% * |-| (unary minus),
+% * a prefix operator
\def\pgfmath@parse@@operand@#1{%
- \def\pgfmath@token{#1}%
- \ifx\pgfmath@token\pgfmath@char@plus% Ignore.
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \else%
- \ifx\pgfmath@token\pgfmath@char@minus%
- \pgfmath@stack@push@operation{neg}% Unary minus.
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \else%
- \expandafter\ifx\csname pgfmath@operation@\expandafter\string\pgfmath@token @prefix\endcsname\pgfmath@token%
- \let\pgfmath@parse@next=\pgfmath@parse@prefix@operator%
- \else%
- \ifpgfmath@quickparse%
- \let\pgfmath@parse@next=\pgfmath@qparse@operand%
- \else%
- \let\pgfmath@number=\pgfmath@empty%
- \expandafter\ifx\csname pgfmath@token@functional@\string#1\endcsname\relax%
- \let\pgfmath@base=\pgfmath@empty%
- \let\pgfmath@token@next=\pgfmath@token%
- \if#10% Check for octal prefix.
- \def\pgfmath@base{8}%
- \fi%
- \let\pgfmath@parse@next=\pgfmath@parse@number%
- \else%
- \let\pgfmath@function=\pgfmath@token%
- \let\pgfmath@parse@next=\pgfmath@parse@function%
- \fi%
- \fi%
- \fi%
- \fi%
- \fi%
- \pgfmath@parse@next%
+ \def\pgfmath@token{#1}%
+ \ifx\pgfmath@token\pgfmath@char@plus
+ % Unary (prefix) plus
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand%
+ \else
+ \ifx\pgfmath@token\pgfmath@char@minus
+ % Unary (prefix) minus
+ \pgfmath@stack@push@operation{neg}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand
+ \else
+ % See |\pgfmathdeclareoperator| (below). Note that |+| and |-|
+ % that are also declared as operators have been tested before so
+ % they should never be parsed as binary (infix) operator at this stage.
+ \expandafter\ifx\csname pgfmath@operation@\expandafter\string\pgfmath@token @prefix\endcsname\pgfmath@token
+ \let\pgfmath@parse@next=\pgfmath@parse@prefix@operator
+ \else
+ \ifpgfmath@quickparse
+ \let\pgfmath@parse@next=\pgfmath@qparse@operand
+ \else
+ \let\pgfmath@number=\pgfmath@empty
+ \expandafter\ifx\csname pgfmath@token@functional@\string#1\endcsname\relax%
+ \let\pgfmath@base=\pgfmath@empty%
+ \let\pgfmath@token@next=\pgfmath@token%
+ \if#10% Check for octal prefix.
+ \def\pgfmath@base{8}%
+ \fi%
+ \let\pgfmath@parse@next=\pgfmath@parse@number%
+ \else%
+ \let\pgfmath@function=\pgfmath@token%
+ \let\pgfmath@parse@next=\pgfmath@parse@function%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+ \pgfmath@parse@next%
}
% Parse prefix operators.
%
\def\pgfmath@parse@prefix@operator{%
- \ifx\pgfmath@token\pgfmath@char@quote% Quote character.
- \let\pgfmath@parse@next=\pgfmath@parse@operand@quote%
- \else%
- \ifx\pgfmath@token\pgfmath@char@exclamation% Prefix !.
- \pgfmath@stack@push@operation{not}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \else% Anything else, just push and hope.
- \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@token}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \fi%
- \fi%
- \pgfmath@parse@next%
+ \ifx\pgfmath@token\pgfmath@char@quote% Quote character.
+ \let\pgfmath@parse@next=\pgfmath@parse@operand@quote%
+ \else%
+ \ifx\pgfmath@token\pgfmath@char@exclamation% Prefix !.
+ \pgfmath@stack@push@operation{not}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand%
+ \else% Anything else, just push and hope.
+ \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@token}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand%
+ \fi%
+ \fi%
+ \pgfmath@parse@next%
}%
% Quote part of an expression.
%
\def\pgfmath@parse@operand@quote#1"{%
- \def\pgfmathresult{#1}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \pgfmath@parse@@operator%
+ \def\pgfmathresult{#1}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \pgfmath@parse@@operator%
}
% Quick operand parsing. Should always have units.
% No functions, base conversion, quoting or scientific notation
% are permitted.
\def\pgfmath@qparse@operand{%
- \afterassignment\pgfmath@qparse@@operand%
- \pgfmath@dimen\pgfmath@token}
+ \afterassignment\pgfmath@qparse@@operand%
+ \pgfmath@dimen\pgfmath@token}
\def\pgfmath@qparse@@operand{%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \pgfmath@parse@@operator%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \pgfmath@parse@@operator%
}
% Parse a number, which can take the form:
@@ -274,337 +311,414 @@
%
\def\pgfmath@parse@number{\pgfmath@parse@ifbgroup{\pgfmath@parse@number}{\pgfmath@parse@number@}}
\def\pgfmath@parse@number@#1{%
- \let\pgfmath@token=\pgfmath@token@next%
- \def\pgfmath@token@next{#1}%
- \pgfmath@parse@@number}
+ \let\pgfmath@token=\pgfmath@token@next%
+ \def\pgfmath@token@next{#1}%
+ \pgfmath@parse@@number}
\def\pgfmath@parse@@number{%
- \ifx\pgfmath@token\pgfmath@egroup@token%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmath@number}%
- \let\pgfmath@parse@next=\pgfmath@parse@@@operator%
- \else%
- \expandafter\ifcat\pgfmath@token\relax% A CS?
- \expandafter\ifx\csname pgfmath@token@box@\expandafter\string\pgfmath@token\endcsname\relax%
- % So, is the CS is a dimension or a count register?
- \expandafter\pgfmath@dimen@\pgfmath@token%
- \ifpgfmath@dimen@% A dimension register.
- \global\pgfmathunitsdeclaredtrue%
- \pgfmath@dimen=\pgfmath@number\pgfmath@token%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@operator%
- \else% A count register.
- \pgfmath@count=\pgfmath@token%
- \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}%
- \expandafter\ifcat\pgfmath@token@next\relax%
- % A CS following a count register should be \wd, \ht or \dp.
- \let\pgfmath@parse@next=\pgfmath@parse@number%
- \else%
- \let\pgfmathresult=\pgfmath@number%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@operator%
- \fi%
- \fi%
- \else%
- % This should be a box specification, for example, 0.5\wd\mybox.
- \global\pgfmathunitsdeclaredtrue%
- \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operator%
- \fi%
- \else%
- \expandafter\ifx\csname pgfmath@token@numeric@\expandafter\string\pgfmath@token\endcsname\relax%
- % It isn't numeric (i.e., 012345679.), so it might be units...
- \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
- % ...or the exponent characters...
- \expandafter\ifx\csname pgfmath@token@exponent@\pgfmath@token\endcsname\relax%
- % ...or a base prefix...
- \expandafter\ifx\csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname\relax%
- % ...none of the above...
- \ifx\pgfmath@base\pgfmath@empty%
- \let\pgfmathresult=\pgfmath@number%
- \else%
- \ifx\pgfmath@number\pgfmath@char@zero%
- \let\pgfmathresult=\pgfmath@number%
- \else%
- % Convert from octal.
- \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{8}{10}%
- \fi%
- \fi%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@@@operator%
- \else%
- % ...here, it is a base prefix 0x, 0X, 0b or 0B
- \expandafter\let\expandafter\pgfmath@base\expandafter=%
- \csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname%
- \let\pgfmath@parse@next=\pgfmath@parse@base%
- \fi%
- \else% ... and here, it is the exponent characters.
- \let\pgfmath@parse@next=\pgfmath@parse@exponent%
- \fi%
- \else% ...but here it is units.
- \global\pgfmathunitsdeclaredtrue%
- \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next\relax%
- \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operator%
- \fi%
- \else% It is numeric.
- \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfmath@number%
- \expandafter\expandafter\expandafter{\expandafter\pgfmath@number\pgfmath@token}%
- \ifx\pgfmath@token\pgfmath@char@period%
- \let\pgfmath@base=\pgfmath@empty%
- \fi%
- \let\pgfmath@parse@next=\pgfmath@parse@number%
- \fi%
- \fi%
- \fi%
- \pgfmath@parse@next%
+ \ifx\pgfmath@token\pgfmath@egroup@token%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmath@number}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@@operator%
+ \else%
+ \expandafter\ifcat\pgfmath@token\relax% A CS?
+ \expandafter\ifx\csname pgfmath@token@dimexpr@\expandafter\string\pgfmath@token\endcsname\relax%
+ \expandafter\ifx\pgfmath@token\numexpr%
+ \let\pgfmath@parse@next=\pgfmath@parse@numexpr%
+ \else%
+ \expandafter\ifx\pgfmath@token\muexpr%
+ \let\pgfmath@parse@next=\pgfmath@parse@muexpr%
+ \else%
+ \expandafter\ifx\csname pgfmath@token@box@\expandafter\string\pgfmath@token\endcsname\relax%
+ % So, is the CS is a dimension or a count register?
+ \expandafter\pgfmath@dimen@\pgfmath@token%
+ \ifpgfmath@dimen@% A dimension register.
+ \global\pgfmathunitsdeclaredtrue%
+ \pgfmath@dimen=\pgfmath@number\pgfmath@token%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \else% A count register.
+ \pgfmath@count=\pgfmath@token%
+ \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}%
+ \expandafter\ifcat\pgfmath@token@next\relax%
+ % A CS following a count register should be \wd, \ht or \dp.
+ \let\pgfmath@parse@next=\pgfmath@parse@number%
+ \else%
+ \let\pgfmathresult=\pgfmath@number%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \fi%
+ \fi%
+ \else%
+ % This should be a box specification, for example, 0.5\wd\mybox.
+ \global\pgfmathunitsdeclaredtrue%
+ \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operator%
+ \fi%
+ \fi%
+ \fi%
+ \else%
+ \global\pgfmathunitsdeclaredtrue%
+ \let\pgfmath@parse@next=\pgfmath@parse@dimexpr%
+ \fi%
+ \else%
+ \expandafter\ifx\csname pgfmath@token@numeric@\expandafter\string\pgfmath@token\endcsname\relax%
+ % It isn't numeric (i.e., 012345679.), so it might be units...
+ \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
+ % ...or the exponent characters...
+ \expandafter\ifx\csname pgfmath@token@exponent@\pgfmath@token\endcsname\relax%
+ % ...or a base prefix...
+ \expandafter\ifx\csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname\relax%
+ % ...or a math unit...
+ \expandafter\ifx\csname pgfmath@token@mathunit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
+ % ...none of the above...
+ \ifx\pgfmath@base\pgfmath@empty%
+ \let\pgfmathresult=\pgfmath@number%
+ \else%
+ \ifx\pgfmath@number\pgfmath@char@zero%
+ \let\pgfmathresult=\pgfmath@number%
+ \else%
+ % Convert from octal.
+ \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{8}{10}%
+ \fi%
+ \fi%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@@operator%
+ \else%
+ % ...here, it is a math unit (mu). Treat it as a pt.
+ \global\pgfmathunitsdeclaredtrue%
+ \global\pgfmathmathunitsdeclaredtrue%
+ \pgfmath@dimen=\pgfmath@number pt\relax%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operator%
+ \fi%
+ \else%
+ % ...here, it is a base prefix 0x, 0X, 0b or 0B
+ \expandafter\let\expandafter\pgfmath@base\expandafter=%
+ \csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname%
+ \let\pgfmath@parse@next=\pgfmath@parse@base%
+ \fi%
+ \else% ... and here, it is the exponent characters.
+ \let\pgfmath@parse@next=\pgfmath@parse@exponent%
+ \fi%
+ \else% ...but here it is units.
+ \global\pgfmathunitsdeclaredtrue%
+ \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next\relax%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operator%
+ \fi%
+ \else% It is numeric.
+ \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfmath@number%
+ \expandafter\expandafter\expandafter{\expandafter\pgfmath@number\pgfmath@token}%
+ \ifx\pgfmath@token\pgfmath@char@period%
+ \let\pgfmath@base=\pgfmath@empty%
+ \fi%
+ \let\pgfmath@parse@next=\pgfmath@parse@number%
+ \fi%
+ \fi%
+ \fi%
+ \pgfmath@parse@next%
+}
+
+
+% Parse a \dimexpr
+\def\pgfmath@parse@dimexpr{%
+ \afterassignment\pgfmath@parse@dimexpr@%
+ \expandafter\expandafter\expandafter\pgfmath@dimen\expandafter\pgfmath@token\pgfmath@token@next%
+}
+\def\pgfmath@parse@dimexpr@{%
+ \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \pgfmath@parse@@operator%
+}
+
+
+% Parse a \muexpr
+\def\pgfmath@parse@muexpr{%
+ \begingroup%
+ \afterassignment\pgfmath@parse@muexpr@%
+ \expandafter\expandafter\expandafter\muskip\expandafter\expandafter\expandafter0\expandafter\pgfmath@token\expandafter\pgfmath@token@next%
+}
+\def\pgfmath@parse@muexpr@{%
+ \expandafter\endgroup%
+ \expandafter\edef\expandafter\pgfmathresult\expandafter{\expandafter\pgfMATH@STRIPMU\the\muskip0}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \pgfmath@parse@@operator%
+}
+
+{
+\catcode`\m=12
+\catcode`\u=12
+\gdef\pgfMATH@STRIPMU#1mu{#1}
+}
+
+
+% Parse a \numexpr
+\def\pgfmath@parse@numexpr{%
+ \afterassignment\pgfmath@parse@numexpr@%
+ \expandafter\expandafter\expandafter\pgfmath@count\expandafter\pgfmath@token\pgfmath@token@next%
+}
+\def\pgfmath@parse@numexpr@#1{%
+ \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}%
+ \def\pgfmath@token@next{#1}%
+ \expandafter\ifcat\pgfmath@token@next\relax%
+ % A CS following a count register should be \wd, \ht or \dp.
+ \let\pgfmath@parse@next=\pgfmath@parse@number%
+ \else%
+ \let\pgfmathresult=\pgfmath@number%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \fi%
+ \pgfmath@parse@next%
}
+
% Parse the exponent of a number.
%
% REMARK: this method will be overwritten by the FPU library. Please
% keep changes consistent...
\def\pgfmath@parse@exponent{%
- \afterassignment\pgfmath@parse@@exponent%
- \pgfmath@count\pgfmath@token@next}
+ \afterassignment\pgfmath@parse@@exponent%
+ \pgfmath@count\pgfmath@token@next}
\def\pgfmath@parse@@exponent{%
- \pgfmathscientific{\pgfmath@number}{\the\pgfmath@count}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \pgfmath@parse@@operator%
+ \pgfmathscientific{\pgfmath@number}{\the\pgfmath@count}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \pgfmath@parse@@operator%
}
% Parse binary or hexadecimal numbers (octal numbers done elsehwere).
%
\def\pgfmath@parse@base{%
- \ifnum\pgfmath@base=2\relax%
- \let\pgfmath@parse@next=\pgfmath@parse@binary%
- \else%
- \ifnum\pgfmath@base=16\relax%
- \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal%
- \else%
- \pgfmath@error{Unexpected numerical base `\pgfmath@base'}{}%
- \def\pgfmathresult{0}%
- \let\pgfmath@parse@next=\pgfmath@parse@end%
- \fi%
- \fi%
- \let\pgfmath@number=\pgfmath@empty%
- \expandafter\pgfmath@parse@next\pgfmath@token@next%
+ \ifnum\pgfmath@base=2\relax%
+ \let\pgfmath@parse@next=\pgfmath@parse@binary%
+ \else%
+ \ifnum\pgfmath@base=16\relax%
+ \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal%
+ \else%
+ \pgfmath@error{Unexpected numerical base `\pgfmath@base'}{}%
+ \def\pgfmathresult{0}%
+ \let\pgfmath@parse@next=\pgfmath@parse@end%
+ \fi%
+ \fi%
+ \let\pgfmath@number=\pgfmath@empty%
+ \expandafter\pgfmath@parse@next\pgfmath@token@next%
}
-
+
\def\pgfmath@parse@binary#1{%
- \expandafter\ifx\csname pgfmath@token@binary@#1\endcsname\relax%
- \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{2}{10}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \def\pgfmath@token@next{#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@operator%
- \else%
- \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@binary%
- \fi%
- \pgfmath@parse@next%
+ \expandafter\ifx\csname pgfmath@token@binary@#1\endcsname\relax%
+ \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{2}{10}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \def\pgfmath@token@next{#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \else%
+ \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@binary%
+ \fi%
+ \pgfmath@parse@next%
}
\def\pgfmath@parse@hexadecimal#1{%
- \expandafter\ifx\csname pgfmath@token@hexadecimal@#1\endcsname\relax%
- \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{16}{10}%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \def\pgfmath@token@next{#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@operator%
- \else%
- \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal%
- \fi%
- \pgfmath@parse@next%
+ \expandafter\ifx\csname pgfmath@token@hexadecimal@#1\endcsname\relax%
+ \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{16}{10}%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \def\pgfmath@token@next{#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \else%
+ \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal%
+ \fi%
+ \pgfmath@parse@next%
}
-
+
% Parse a function.
%
\def\pgfmath@parse@function{\pgfmath@parse@ifbgroup{\pgfmath@parse@function}{\pgfmath@parse@@function}}
\def\pgfmath@parse@function@{\futurelet\pgfmath@token@let\pgfmath@parse@@function}
\def\pgfmath@parse@@function{%
- \ifx\pgfmath@token@let\pgfmath@sptoken%
- \let\pgfmath@token=\pgfmath@empty%
- \let\pgfmath@parse@next=\pgfmath@parse@@@@function%
- \else%
- \let\pgfmath@parse@next=\pgfmath@parse@@@function%
- \fi%
- \pgfmath@parse@next}
+ \ifx\pgfmath@token@let\pgfmath@sptoken%
+ \let\pgfmath@token=\pgfmath@empty%
+ \let\pgfmath@parse@next=\pgfmath@parse@@@@function%
+ \else%
+ \let\pgfmath@parse@next=\pgfmath@parse@@@function%
+ \fi%
+ \pgfmath@parse@next}
\def\pgfmath@parse@@@function#1{%
- \expandafter\ifx\csname pgfmath@token@functional@\expandafter\string#1\endcsname\relax%
- \expandafter\ifx\csname pgfmath@token@number@\expandafter\string#1\endcsname\relax%
- \def\pgfmath@token{#1}% Not from A-Z, a-z, 0-9, or _.
- \let\pgfmath@parse@next=\pgfmath@parse@@@@function%
- \else% It is from 0-9.
- \expandafter\def\expandafter\pgfmath@function\expandafter{\pgfmath@function#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@function@%
- \fi%
- \else% It is from from A-Z, a-z, or _.
- \edef\pgfmath@function{\pgfmath@function#1}%
- \let\pgfmath@parse@next=\pgfmath@parse@function@%
- \fi%
- \pgfmath@parse@next}
+ \expandafter\ifx\csname pgfmath@token@functional@\expandafter\string#1\endcsname\relax%
+ \expandafter\ifx\csname pgfmath@token@number@\expandafter\string#1\endcsname\relax%
+ \def\pgfmath@token{#1}% Not from A-Z, a-z, 0-9, or _.
+ \let\pgfmath@parse@next=\pgfmath@parse@@@@function%
+ \else% It is from 0-9.
+ \expandafter\def\expandafter\pgfmath@function\expandafter{\pgfmath@function#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@function@%
+ \fi%
+ \else% It is from from A-Z, a-z, or _.
+ \edef\pgfmath@function{\pgfmath@function#1}%
+ \let\pgfmath@parse@next=\pgfmath@parse@function@%
+ \fi%
+ \pgfmath@parse@next}
\def\pgfmath@parse@@@@function{%
- \expandafter\ifx\csname pgfmath@function@\pgfmath@function\endcsname\relax%
- \pgfmath@error{Unknown function `\pgfmath@function'}{}%
- \def\pgfmathresult{0}%
- \let\pgfmath@parse@next=\pgfmath@parse@end%
- \else%
- \expandafter\ifnum\csname pgfmath@operation@\pgfmath@function @arity\endcsname=0\relax%
- % Functions with zero arity are called directly.
- \csname pgfmath\pgfmath@function @\endcsname%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operator%
- \else% Otherwise, they are pushed onto the operator stack
- \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@function}%
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \fi%
- \fi%
- \expandafter\pgfmath@parse@next\pgfmath@token}
+ \expandafter\ifx\csname pgfmath@function@\pgfmath@function\endcsname\relax%
+ \pgfmath@error{Unknown function `\pgfmath@function'}{}%
+ \def\pgfmathresult{0}%
+ \let\pgfmath@parse@next=\pgfmath@parse@end%
+ \else%
+ \expandafter\ifnum\csname pgfmath@operation@\pgfmath@function @arity\endcsname=0\relax%
+ % Functions with zero arity are called directly.
+ \csname pgfmath\pgfmath@function @\endcsname%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operator%
+ \else% Otherwise, they are pushed onto the operator stack
+ \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@function}%
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand%
+ \fi%
+ \fi%
+ \expandafter\pgfmath@parse@next\pgfmath@token}
% Parse an operator.
%
\def\pgfmath@parse@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@operator}{\pgfmath@parse@operator@}}%
\def\pgfmath@parse@operator@#1{% Get one token.
- \let\pgfmath@token=\pgfmath@token@next%
- \def\pgfmath@token@next{#1}%
- \pgfmath@parse@@@operator}
+ \let\pgfmath@token=\pgfmath@token@next%
+ \def\pgfmath@token@next{#1}%
+ \pgfmath@parse@@@operator}
\def\pgfmath@parse@@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@@operator}{\pgfmath@parse@@operator@}}%
\def\pgfmath@parse@@operator@#1{% Get first token...
- \def\pgfmath@token{#1}%
- \pgfmath@parse@ifbgroup{\pgfmath@parse@@operator@@}{\pgfmath@parse@@operator@@}}%
+ \def\pgfmath@token{#1}%
+ \pgfmath@parse@ifbgroup{\pgfmath@parse@@operator@@}{\pgfmath@parse@@operator@@}}%
\def\pgfmath@parse@@operator@@#1{% ...and second token.
- \def\pgfmath@token@next{#1}%
- \pgfmath@parse@@@operator}
+ \def\pgfmath@token@next{#1}%
+ \pgfmath@parse@@@operator}
\def\pgfmath@parse@@@operator{%
- \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
- % Not a double character operator.
- \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\endcsname\relax%
- % Not a single character operator.
- \pgfmath@error{Unknown operator `\pgfmath@token' or `\pgfmath@token\pgfmath@token@next'}{}%
- \def\pgfmathresult{0}%
- \let\pgfmath@parse@next=\pgfmath@parse@end%
- \else%
- \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}%
- \ifx\pgfmath@token\pgfmath@text@@%
- \let\pgfmath@parse@next=\pgfmath@parse@end%
- \else%
- \expandafter\ifx\csname pgfmath@operation@\pgfmath@token @postfix\endcsname\pgfmath@token%
- % Postfix operators are followed by an operator.
- \ifx\pgfmath@token@next\pgfmath@char@leftbracket% Except [.
- \let\pgfmath@parse@next=\pgfmath@parse@operand%
- \else%
- \let\pgfmath@parse@next=\pgfmath@parse@operator%
- \fi%
- \else%
- % Any other operator is followed by an operand.
- \let\pgfmath@parse@next=\pgfmath@parse@operand%
- \fi%
- \fi%
- \fi%
- \else%
- % A double character operator...
- \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
- \pgfmath@token\expandafter\expandafter\expandafter%
- {\expandafter\pgfmath@token\pgfmath@token@next}%
- \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}%
- % ...is always followed by an operand.
- \let\pgfmath@parse@next=\pgfmath@parse@@operand%
- \fi%
- \pgfmath@parse@next%
+ \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
+ % Not a double character operator.
+ \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\endcsname\relax%
+ % Not a single character operator.
+ \pgfmath@error{Unknown operator `\pgfmath@token' or `\pgfmath@token\pgfmath@token@next'}{}%
+ \def\pgfmathresult{0}%
+ \let\pgfmath@parse@next=\pgfmath@parse@end%
+ \else%
+ \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}%
+ \ifx\pgfmath@token\pgfmath@text@@%
+ \let\pgfmath@parse@next=\pgfmath@parse@end%
+ \else%
+ \expandafter\ifx\csname pgfmath@operation@\pgfmath@token @postfix\endcsname\pgfmath@token%
+ % Postfix operators are followed by an operator.
+ \ifx\pgfmath@token@next\pgfmath@char@leftbracket% Except [.
+ \let\pgfmath@parse@next=\pgfmath@parse@operand%
+ \else%
+ \let\pgfmath@parse@next=\pgfmath@parse@operator%
+ \fi%
+ \else%
+ % Any other operator is followed by an operand.
+ \let\pgfmath@parse@next=\pgfmath@parse@operand%
+ \fi%
+ \fi%
+ \fi%
+ \else%
+ % A double character operator...
+ \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
+ \pgfmath@token\expandafter\expandafter\expandafter%
+ {\expandafter\pgfmath@token\pgfmath@token@next}%
+ \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}%
+ % ...is always followed by an operand.
+ \let\pgfmath@parse@next=\pgfmath@parse@@operand%
+ \fi%
+ \pgfmath@parse@next%
}
% Process an operation.
%
\def\pgfmath@operation@process#1{%
- \def\pgfmath@operator{#1}%
- \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty%
- \else%
- \pgfmath@operation@@process%
- \fi%
- \expandafter\ifx\csname pgfmath@token@specials@#1\endcsname\relax%
- \pgfmath@stack@push@operation{#1}%
- \fi%
+ \def\pgfmath@operator{#1}%
+ \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty%
+ \else%
+ \pgfmath@operation@@process%
+ \fi%
+ \expandafter\ifx\csname pgfmath@token@specials@#1\endcsname\relax%
+ \pgfmath@stack@push@operation{#1}%
+ \fi%
}
% Process the operation stack.
%
\def\pgfmath@operation@@process{%
- \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty%
- \let\pgfmath@parse@next=\relax%
- \else%
- \ifnum\csname pgfmath@operation@\pgfmath@operator @precedence\endcsname>%
- \csname pgfmath@operation@\pgfmath@stack@operation@top @precedence\endcsname\relax%
- % If the precedence of the scanned operator is greater than the
- % precedence of the operator at the top of the stack, do nothing.
- \let\pgfmath@parse@next=\relax%
- \else%
- \let\pgfmath@stack@operation@last=\pgfmath@stack@operation@top%
- \expandafter\ifx\csname pgfmath@operator@\pgfmath@stack@operation@top\endcsname\relax%
- \pgfmath@function@@@process%
- \else%
- \pgfmath@operator@@@process%
- \fi%
- \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
- \expandafter\ifx\csname pgfmath@token@group@\pgfmath@stack@operation@last\pgfmath@operator\endcsname\relax%
- \let\pgfmath@parse@next=\pgfmath@operation@@process%
- \else%
- \let\pgfmath@parse@next=\relax%
- \fi%
- \fi%
- \fi%
- \pgfmath@parse@next%
+ \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty%
+ \let\pgfmath@parse@next=\relax%
+ \else%
+ \ifnum\csname pgfmath@operation@\pgfmath@operator @precedence\endcsname>%
+ \csname pgfmath@operation@\pgfmath@stack@operation@top @precedence\endcsname\relax%
+ % If the precedence of the scanned operator is greater than the
+ % precedence of the operator at the top of the stack, do nothing.
+ \let\pgfmath@parse@next=\relax%
+ \else%
+ \let\pgfmath@stack@operation@last=\pgfmath@stack@operation@top%
+ \expandafter\ifx\csname pgfmath@operator@\pgfmath@stack@operation@top\endcsname\relax%
+ \pgfmath@function@@@process%
+ \else%
+ \pgfmath@operator@@@process%
+ \fi%
+ \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
+ \expandafter\ifx\csname pgfmath@token@group@\pgfmath@stack@operation@last\pgfmath@operator\endcsname\relax%
+ \let\pgfmath@parse@next=\pgfmath@operation@@process%
+ \else%
+ \let\pgfmath@parse@next=\relax%
+ \fi%
+ \fi%
+ \fi%
+ \pgfmath@parse@next%
}
% Process an operator.
%
\def\pgfmath@operator@@@process{% Process an operator.
- \pgfmath@stack@pop@operation\pgfmath@@operator%
- \pgfmath@stack@pop@operand\pgfmath@operand@a%
- \ifcase\csname pgfmath@operation@\pgfmath@@operator @arity\endcsname\relax%
- % Zero arity operators (!).
- \or%
- \pgfmath@operator@@@@process{\pgfmath@operand@a}%
- \or%
- \pgfmath@stack@pop@operand\pgfmath@operand@b%
- \pgfmath@operator@@@@process{\pgfmath@operand@b}{\pgfmath@operand@a}%
- \or%
- \pgfmath@stack@pop@operand\pgfmath@operand@b%
- \expandafter\pgfmath@operator@@@@process\expandafter%
- {\expandafter\pgfmath@operand@b\expandafter}\pgfmath@operand@a%
- \else%
- % No operators with more than tenary arity.
- \fi%
+ \pgfmath@stack@pop@operation\pgfmath@@operator%
+ \pgfmath@stack@pop@operand\pgfmath@operand@a%
+ \ifcase\csname pgfmath@operation@\pgfmath@@operator @arity\endcsname\relax%
+ % Zero arity operators (!).
+ \or%
+ \pgfmath@operator@@@@process{\pgfmath@operand@a}%
+ \or%
+ \pgfmath@stack@pop@operand\pgfmath@operand@b%
+ \pgfmath@operator@@@@process{\pgfmath@operand@b}{\pgfmath@operand@a}%
+ \or%
+ \pgfmath@stack@pop@operand\pgfmath@operand@b%
+ \expandafter\pgfmath@operator@@@@process\expandafter%
+ {\expandafter\pgfmath@operand@b\expandafter}\pgfmath@operand@a%
+ \else%
+ % No operators with more than tenary arity.
+ \fi%
}
\def\pgfmath@operator@@@@process{%
- \csname pgfmath%
- \csname pgfmath@operation@\pgfmath@@operator @name\endcsname%
- @\endcsname}
+ \csname pgfmath%
+ \csname pgfmath@operation@\pgfmath@@operator @name\endcsname%
+ @\endcsname}
% Process a function.
%
\def\pgfmath@function@@@process{% Process a function.
- \ifnum\csname pgfmath@operation@\pgfmath@stack@operation@top @arity\endcsname>0\relax%
- \pgfmath@stack@pop@operation\pgfmath@@function%
- \pgfmath@stack@pop@operand\pgfmath@@operand%
- \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>1\relax%
- \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>9\relax%
- \csname pgfmath\pgfmath@@function @\endcsname{\pgfmath@@operand}%
- \else%
- \expandafter\pgfmath@function@@@@process\pgfmath@@operand%
- \fi
- \else%
- \expandafter\pgfmath@function@@@@process\expandafter{\pgfmath@@operand}%
- \fi%
- \fi%
+ \ifnum\csname pgfmath@operation@\pgfmath@stack@operation@top @arity\endcsname>0\relax%
+ \pgfmath@stack@pop@operation\pgfmath@@function%
+ \pgfmath@stack@pop@operand\pgfmath@@operand%
+ \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>1\relax%
+ \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>9\relax%
+ \csname pgfmath\pgfmath@@function @\endcsname{\pgfmath@@operand}%
+ \else%
+ \expandafter\pgfmath@function@@@@process\pgfmath@@operand%
+ \fi
+ \else%
+ \expandafter\pgfmath@function@@@@process\expandafter{\pgfmath@@operand}%
+ \fi%
+ \fi%
}
\def\pgfmath@function@@@@process{\csname pgfmath\pgfmath@@function @\endcsname}
@@ -616,32 +730,32 @@
\let\pgfmath@stack@empty=\pgfmath@empty
\def\pgfmath@stack@push#1#2{%
- \def\pgfmath@stack@top{#2}%
- \expandafter\expandafter\expandafter#1%
- \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter%
- {\expandafter\pgfmath@stack@top\expandafter}\the#1}}%
+ \def\pgfmath@stack@top{#2}%
+ \expandafter\expandafter\expandafter#1%
+ \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter%
+ {\expandafter\pgfmath@stack@top\expandafter}\the#1}}%
\def\pgfmath@stack@pop#1#2{\expandafter\pgfmath@stack@@pop\the#1\pgfmath@stack@stop{#1}{#2}}
\def\pgfmath@stack@@pop#1#2#3\pgfmath@stack@stop#4#5{\def#5{#1}#4={{#2}#3}\def\pgfmath@stack@top{#2}}
\def\pgfmath@stack@push@operation#1{%
- \pgfmath@stack@push\pgfmath@stack@operation{#1}%
- \let\pgfmath@stack@operation@top=\pgfmath@stack@top}
+ \pgfmath@stack@push\pgfmath@stack@operation{#1}%
+ \let\pgfmath@stack@operation@top=\pgfmath@stack@top}
\def\pgfmath@stack@pop@operation#1{%
- \pgfmath@stack@pop\pgfmath@stack@operation{#1}%
- \let\pgfmath@stack@operation@top=\pgfmath@stack@top}
-
+ \pgfmath@stack@pop\pgfmath@stack@operation{#1}%
+ \let\pgfmath@stack@operation@top=\pgfmath@stack@top}
+
% REMARK: This method will be overwritten by the FPU library. Please
% keep any changes consistent.
\def\pgfmath@stack@push@operand#1{%
- \pgfmath@stack@push\pgfmath@stack@operand{#1}%
- \let\pgfmath@stack@operand@top=\pgfmath@stack@top}
+ \pgfmath@stack@push\pgfmath@stack@operand{#1}%
+ \let\pgfmath@stack@operand@top=\pgfmath@stack@top}
\def\pgfmath@stack@pop@operand#1{%
- \pgfmath@stack@pop\pgfmath@stack@operand{#1}%
- \let\pgfmath@stack@operand@top=\pgfmath@stack@top}
-
+ \pgfmath@stack@pop\pgfmath@stack@operand{#1}%
+ \let\pgfmath@stack@operand@top=\pgfmath@stack@top}
+
% Declare an operator for the parser.
%
@@ -649,13 +763,20 @@
% the parser is not fully robust for arbitrary operators.
%
\def\pgfmathdeclareoperator#1#2#3#4#5{%
- \pgfmath@namedef{pgfmath@operator@\string#1}{#1}%
- \pgfmath@namedef{pgfmath@operation@\string#1@name}{#2}%
- \pgfmath@namedef{pgfmath@operation@\string#1@arity}{#3}%
- \pgfmath@namedef{pgfmath@operation@\string#1@#4}{#1}%
- \pgfmath@namedef{pgfmath@operation@\string#1@precedence}{#5}%
+ \ifx\pgfmath@operatorlist\pgfutil@empty
+ \edef\pgfmath@operatorlist{{\string#1}}%
+ \else
+ \edef\pgfmath@operatorlist{\pgfmath@operatorlist,{\string#1}}%
+ \fi
+ \pgfmath@namedef{pgfmath@operator@\string#1}{#1}%
+ \pgfmath@namedef{pgfmath@operation@\string#1@name}{#2}%
+ \pgfmath@namedef{pgfmath@operation@\string#1@arity}{#3}%
+ \pgfmath@namedef{pgfmath@operation@\string#1@#4}{#1}%
+ \pgfmath@namedef{pgfmath@operation@\string#1@precedence}{#5}%
}
+\def\pgfmath@operatorlist{}
+
\pgfmathdeclareoperator{+}{add} {2}{infix}{500}
\pgfmathdeclareoperator{-}{subtract}{2}{infix}{500}
\pgfmathdeclareoperator{*}{multiply}{2}{infix}{700}
@@ -671,7 +792,7 @@
\pgfmathdeclareoperator{<=}{notgreater}{2}{infix} {250}
\pgfmathdeclareoperator{&&}{and} {2}{infix} {200}
\pgfmathdeclareoperator{||}{or} {2}{infix} {200}
-\pgfmathdeclareoperator{!=}{notequalto}{2}{infix} {250}
+\pgfmathdeclareoperator{!=}{notequal} {2}{infix} {250}
\pgfmathdeclareoperator{!} {not} {1}{prefix}{975}
\pgfmathdeclareoperator{?} {ifthenelse}{3}{infix} {100}
\pgfmathdeclareoperator{:} {@@collect} {2}{infix}{101}
@@ -702,11 +823,11 @@
% Begin and end array access [].
%
\def\pgfmath@startindex@#1#2{%
- \expandafter\pgfmatharray@#1{#2}%
- \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmathresult}%
- \ifx\pgfmath@token@let\bgroup%
- \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmathresult}}%
- \fi}
+ \expandafter\pgfmatharray@#1{#2}%
+ \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmathresult}%
+ \ifx\pgfmath@token@let\bgroup%
+ \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmathresult}}%
+ \fi}
\def\pgfmath@endindex@{}% Never actually called.
% Begin and end array {}.
@@ -716,57 +837,63 @@
\def\pgfmath@@collect@#1#2{%
- \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
- \pgfmathresult\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter%
- {\expandafter#1\expandafter}\expandafter{#2}}%
+ \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
+ \pgfmathresult\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter%
+ {\expandafter#1\expandafter}\expandafter{#2}}%
}
% Collect items separated by ,.
%
\def\pgfmath@collect@#1#2{%
- \expandafter\def\expandafter\pgfmath@collect@original\expandafter{#1}%
- \expandafter\pgfmath@bgroup@strip\expandafter{#1}%
- \ifx\pgfmath@token@let\bgroup%
- \ifx\pgfmath@collect@original\pgfmath@bgroup@stripped%
- \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}%
- \else%
- \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}%
- \fi%
- \else%
- \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}%
- \fi%
- \expandafter\pgfmath@bgroup@strip\expandafter{#2}%
- \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
- \pgfmathresult\expandafter\expandafter\expandafter%
- {\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}}%
+ \expandafter\def\expandafter\pgfmath@collect@original\expandafter{#1}%
+ \expandafter\pgfmath@bgroup@strip\expandafter{#1}%
+ \ifx\pgfmath@token@let\bgroup%
+ \ifx\pgfmath@collect@original\pgfmath@bgroup@stripped%
+ \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}%
+ \else%
+ \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}%
+ \fi%
+ \else%
+ \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}%
+ \fi%
+ \expandafter\pgfmath@bgroup@strip\expandafter{#2}%
+ \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
+ \pgfmathresult\expandafter\expandafter\expandafter%
+ {\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}}%
}
% Strip braces from a token sequence.
%
\def\pgfmath@bgroup@strip#1{%
- \def\pgfmath@bgroup@strip@last{#1}%
- \pgfmath@bgroup@@strip{#1}\pgfmath@\pgfmath@@\pgfmath@@@}
+ \def\pgfmath@bgroup@strip@last{#1}%
+ \pgfmath@bgroup@@strip{#1}\pgfmath@\pgfmath@@\pgfmath@@@}
\def\pgfmath@bgroup@strip@#1{%
- \def\pgfmath@bgroup@strip@last{#1}%
- \pgfmath@bgroup@@strip#1\pgfmath@\pgfmath@@\pgfmath@@@}
+ \def\pgfmath@bgroup@strip@last{#1}%
+ \pgfmath@bgroup@@strip#1\pgfmath@\pgfmath@@\pgfmath@@@}
\def\pgfmath@bgroup@pgfmath@{\pgfmath@}
-\def\pgfmath@bgroup@@strip{\futurelet\pgfmath@token@let\pgfmath@bgroup@@@strip}
-\def\pgfmath@bgroup@@@strip#1#2#3\pgfmath@@@{%
- \ifx\pgfmath@token@let\bgroup%
- \def\pgfmath@bgroup@test{#2}%
- \ifx\pgfmath@bgroup@test\pgfmath@bgroup@pgfmath@%
- \def\pgfmath@next{\pgfmath@bgroup@strip@{#1}}%
- \else%
- \let\pgfmath@bgroup@stripped=\pgfmath@bgroup@strip@last%
- \let\pgfmath@next=\relax%
- \fi%
- \else%
- \pgfmath@bgroup@@@@strip#1#2#3%
- \let\pgfmath@next=\relax%
- \fi%
- \pgfmath@next%
-}
+\def\pgfmath@bgroup@@strip{%
+ \futurelet\pgfmath@token@let\pgfmath@bgroup@@@strip}
-\def\pgfmath@bgroup@@@@strip#1\pgfmath@\pgfmath@@{\def\pgfmath@bgroup@stripped{#1}}%
+\def\pgfmath@bgroup@@@strip#1#2#3\pgfmath@@@{%
+ \ifx\pgfmath@token@let\bgroup
+ \def\pgfmath@bgroup@test{#2}%
+ \ifx\pgfmath@bgroup@test\pgfmath@bgroup@pgfmath@
+ \def\pgfmath@next{\pgfmath@bgroup@strip@{#1}}%
+ \else
+ \let\pgfmath@bgroup@stripped=\pgfmath@bgroup@strip@last
+ \let\pgfmath@next=\relax
+ \fi
+ \else
+ \pgfmath@bgroup@@@@strip#1#2#3%
+ \let\pgfmath@next=\relax
+ \fi
+ \pgfmath@next}
+
+\def\pgfmath@bgroup@@@@strip#1\pgfmath@\pgfmath@@{%
+ \def\pgfmath@bgroup@stripped{#1}}
+
+% Local Variables:
+% tab-width: 2
+% End: \ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex
index 5e353007618..44d39c75b6a 100644
--- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex
@@ -80,7 +80,7 @@
\let\pgfmath@yc\pgf@yc
\let\pgfmath@tempdima\pgfutil@tempdima
-\let\pgfmath@tempdima\pgfutil@tempdima
+\let\pgfmath@tempdimb\pgfutil@tempdimb
\let\c@pgfmath@counta\c@pgf@counta
\let\c@pgfmath@countb\c@pgf@countb
@@ -177,7 +177,7 @@
\let\pgfmath@PackageWarning\PackageWarning%
\fi%
\ifx\PackageError\pgfmath@undefined
- \def\pgfmath@PackageError#1#2#3{\immediate\write-1{Package #1: Error! #2.}}%
+ \def\pgfmath@PackageError#1#2#3{\errmessage{Package #1 Error: #2.}}%
\else%
\let\pgfmath@PackageError\PackageError%
\fi%