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Diffstat (limited to 'Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex')
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diff --git a/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex b/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex deleted file mode 100644 index e5d1be605c1..00000000000 --- a/Master/texmf-dist/tex/generic/pgf/math/pgfmathoperations.code.tex +++ /dev/null @@ -1,781 +0,0 @@ -% Copyright 2007 by Mark Wibrow -% -% This file may be distributed and/or modified -% -% 1. under the LaTeX Project Public License and/or -% 2. under the GNU Public License. -% -% See the file doc/generic/pgf/licenses/LICENSE for more details. - -% This file defines the mathematical functions and operators. -% -% Version 0.0 08/03/2007 - -% This file defines the mathematical functions and operators. -% -% Adding/redefining extra operators/functions: -% -% Each operator/function XXX has two forms: -% -% -% \pgfmathXXX#1... a public version which evaluates any -% arguments passed to it and passes the -% results on to... -% -% \pgfmathXXX@#1... a non-public version which performs -% required calculation on arguments which -% must have already been evaluated (i.e. -% *without* dimensions). -% -% If a function XXX is to be included in the parser, it is -% recommended, for consistency, that where possible, the -% pgfmathparser file should define the macro \pgfmath@parseXXX. -% The parser should (ideally) then call \pgfmathXXX@. -% -% It is recommend that the pgfmath versions of the pgf dimension -% and count registers be used, i.e., \pgfmath@x for \pgfmath@x, -% \c@pgfmath@counta for c@pgfmath@counta, and so on. These are currently -% \let to their pgf equivalents, but it may be necessary to change -% this. -% -% It is also recommened that all calculations (where necessary) -% take place within a TeX group. \pgfmath@returnone#1 makes and -% expanded version of #1 global and stores this in \pgfmathresult -% after the group is ended. -% - -\input pgfmathtrig.code.tex% Load the trig. stuff. -\input pgfmathrnd.code.tex% Load the random stuff. - - -% \pgfmathadd -% -% Add #1 and #2. -% -\def\pgfmathadd#1#2{% - \pgfmathparse{#1}\edef\pgfmath@adda{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@addb{\pgfmathresult}% - \pgfmathadd@{\pgfmath@adda}{\pgfmath@addb}} -\def\pgfmathadd@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \advance\pgfmath@x by\pgfmath@y% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathsubtract -% -% Subtract #2 from #1. -% -\def\pgfmathsubtract#1#2{% - \pgfmathparse{#1}\edef\pgfmath@subtracta{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@subtractb{\pgfmathresult}% - \pgfmathsubtract@{\pgfmath@subtracta}{\pgfmath@subtractb}} - -\def\pgfmathsubtract@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \advance\pgfmath@x by-\pgfmath@y% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathmultiply -% -% Multiply #1 by #2. -% -\def\pgfmathmultiply#1#2{% - \pgfmathparse{#1}\edef\pgfmath@multiplya{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@multiplyb{\pgfmathresult}% - \pgfmathmultiply@{\pgfmath@multiplya}{\pgfmath@multiplyb}} -\def\pgfmathmultiply@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@x#2\pgfmath@x% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathdivide -% -% Divide #1 by #2. -% -\def\pgfmathdivide#1#2{% - \pgfmathparse{#1}\edef\pgfmath@dividea{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@divideb{\pgfmathresult}% - \pgfmathdivide@{\pgfmath@dividea}{\pgfmath@divideb}} -\def\pgfmathdivide@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - % If #2 is an integer use TeX arithmatic. - \expandafter\pgfmath@xa#2pt\relax% - \afterassignment\pgfmath@xa% - \expandafter\c@pgfmath@counta\the\pgfmath@xa\relax% - \ifdim\pgfmath@xa=0pt\relax% - \ifnum\c@pgfmath@counta=0\relax% - \pgfmath@error{Division by zero.}{}% - \fi% - \divide\pgfmath@x\c@pgfmath@counta% - \else% - \pgfmathreciprocal@{#2}% - \pgfmath@x=\pgfmathresult\pgfmath@x% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathgreaterthan -% -% 1.0 if #1 > #2. Otherwise 0.0 -% -\def\pgfmathgreaterthan#1#2{% - \pgfmathparse{#1}\edef\pgfmath@greaterthana{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@greaterthanb{\pgfmathresult}% - \pgfmathgreaterthan@{\pgfmath@greaterthana}{\pgfmath@greaterthanb}} -\def\pgfmathgreaterthan@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \advance\pgfmath@x-\pgfmath@y% - \ifdim\pgfmath@x>0pt\relax% - \pgfmath@x1pt\relax% - \else% - \pgfmath@x0pt\relax% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathlessthan -% -% 1.0 if #1< #2. Otherwise 0.0 -% -\def\pgfmathlessthan#1#2{% - \pgfmathparse{#1}\edef\pgfmath@lessthana{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@lessthanb{\pgfmathresult}% - \pgfmathlessthan@{\pgfmath@lessthana}{\pgfmath@lessthanb}} -\def\pgfmathlessthan@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \advance\pgfmath@x-\pgfmath@y\relax% - \ifdim\pgfmath@x<0pt\relax% - \pgfmath@x1pt\relax% - \else% - \pgfmath@x0pt\relax% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathequalto -% -% 1.0 if #1 = #2. Otherwise 0.0 -% -\def\pgfmathequalto#1#2{% - \pgfmathparse{#1}\edef\pgfmath@equaltoa{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@equaltob{\pgfmathresult}% - \pgfmathadd@{\pgfmath@equaltoa}{\pgfmath@equaltob}} -\def\pgfmathequalto@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \advance\pgfmath@x-\pgfmath@y% - \ifdim\pgfmath@x=0pt\relax% - \pgfmath@x1pt\relax% - \else% - \pgfmath@x0pt\relax% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathreciprocal -% -% 1 / #1 -% -\def\pgfmathreciprocal#1{% - \pgfmathparse{#1}% - \pgfmathreciprocal@{\pgfmathresult}} -\def\pgfmathreciprocal@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \ifdim\pgfmath@x=0pt\relax% - \pgfmath@error{Division by zero.}{}% - \fi% - \edef\pgfmath@reciprocaltemp{\pgfmath@tonumber{\pgfmath@x}}% - \expandafter\pgfmathreciprocal@@\pgfmath@reciprocaltemp00000\pgfmath@} -\def\pgfmathreciprocal@@#1.#2#3#4#5#6#7\pgfmath@{% - \c@pgfmath@counta#2#3#4#5#6\relax% - % If the number is an integer, use TeX arithmatic. - \ifnum\c@pgfmath@counta=0\relax% - \pgfmath@x1pt\relax% - \divide\pgfmath@x#1\relax% - \else% - \c@pgfmath@counta#1#2#3#4#5#6\relax% - \c@pgfmath@countb1000000000\relax% - \divide\c@pgfmath@countb\c@pgfmath@counta% - \c@pgfmath@counta\c@pgfmath@countb% - \divide\c@pgfmath@counta10000\relax% - \pgfmath@x\c@pgfmath@counta pt\relax% - \multiply\c@pgfmath@counta-10000\relax% - \advance\c@pgfmath@countb\c@pgfmath@counta% - \pgfmath@y\c@pgfmath@countb pt\relax% - \pgfmath@y.1\pgfmath@y% Yes! This way is more accurate. Go figure... - \pgfmath@y.1\pgfmath@y% - \pgfmath@y.1\pgfmath@y% - \pgfmath@y.1\pgfmath@y% - \advance\pgfmath@x\pgfmath@y% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup -} - - -% \pgfmathabs -% -% Calculate |#1| -% -\def\pgfmathabs#1{% - \pgfmathparse{#1}% - \pgfmathabsolute@{\pgfmathresult}} -\def\pgfmathabs@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \ifdim\pgfmath@x<0pt\relax% - \pgfmath@x=-\pgfmath@x% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathmod -% -% Calculate #1 mod #2. -% -\def\pgfmathmod#1#2{% - \pgfmathparse{#1}\edef\pgfmath@moda{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@modb{\pgfmathresult}% - \pgfmathmod@{\pgfmath@mod@a}{\pgfmath@modb}% -} -\def\pgfmathmod@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \pgfmath@xa\pgfmath@x% - \expandafter\pgfmath@xb#2pt\relax% - \c@pgfmath@counta=\pgfmath@xa% - \c@pgfmath@countb=\pgfmath@xb% - \divide\c@pgfmath@counta\c@pgfmath@countb% - \multiply\pgfmath@xb\c@pgfmath@counta% - \advance\pgfmath@x-\pgfmath@xb% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathsqrt -% -% Square-root of #1. -% -% -\def\pgfmathsqrt#1{% - \pgfmathparse{#1}% - \pgfmathsqrt{\pgfmathresult}} -\def\pgfmathsqrt@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \ifdim\pgfmath@x>9999pt\relax% - \def\pgfmath@zeros{0}% - \def\pgfmath@targetiterations{3}% - \else% - \ifdim\pgfmath@x>999pt\relax% - \def\pgfmath@zeros{}% - \def\pgfmath@targetiterations{2}% - \else% - \ifdim\pgfmath@x>99pt\relax% - \def\pgfmath@zeros{0}% - \def\pgfmath@targetiterations{2}% - \else% - \ifdim\pgfmath@x>9pt\relax% - \def\pgfmath@zeros{}% - \def\pgfmath@targetiterations{1}% - \else% - \ifdim\pgfmath@x<0pt\relax% - \pgfmath@error{Cannot calculate the square-root of the negative number `#1'}{}% - \else% - \def\pgfmath@zeros{0}% - \def\pgfmath@targetiterations{1}% - \fi\fi\fi\fi\fi% - \edef\pgfmath@temp{\pgfmath@zeros\pgfmath@tonumber{\pgfmath@x}}% - \expandafter\pgfmath@sqrt@\pgfmath@temp\pgfmath@% -} -\def\pgfmath@sqrt@#1.#2\pgfmath@{\pgfmath@@sqrt@#1#2\pgfmath@empty\pgfmath@empty\pgfmath@} - -\def\pgfmath@@sqrt@#1#2{% - \c@pgfmath@countb#1#2\relax% - \ifnum\c@pgfmath@countb>35\relax% - \ifnum\c@pgfmath@countb>63\relax% - \ifnum\c@pgfmath@countb>80\relax% - \c@pgfmath@counta9\relax% - \else% - \c@pgfmath@counta8\relax% - \fi% - \else% - \ifnum\c@pgfmath@countb>48\relax% - \c@pgfmath@counta7\relax% - \else% - \c@pgfmath@counta6\relax% - \fi% - \fi% - \else% - \ifnum\c@pgfmath@countb>15\relax% - \ifnum\c@pgfmath@countb>24\relax% - \c@pgfmath@counta5\relax% - \else% - \c@pgfmath@counta4\relax% - \fi% - \else% - \ifnum\c@pgfmath@countb>3\relax% - \ifnum\c@pgfmath@countb>8\relax% - \c@pgfmath@counta3\relax% - \else% - \c@pgfmath@counta2\relax% - \fi% - \else% - \ifnum\c@pgfmath@countb>0\relax% - \c@pgfmath@counta1\relax% - \else% - \c@pgfmath@counta0\relax% - \fi% - \fi% - \fi% - \fi% - \edef\pgfmath@root{\the\c@pgfmath@counta}% - \edef\pgfmath@rootspecial{\the\c@pgfmath@counta}% - \multiply\c@pgfmath@counta-\c@pgfmath@counta\relax% - \advance\c@pgfmath@counta#1#2\relax% - \edef\pgfmath@remainder{\the\c@pgfmath@counta}% - \pgfmath@@@sqrt@% -} - -\def\pgfmath@@@sqrt@#1#2{% - \ifx\pgfmath@empty#1% - \edef\pgfmath@remainder{\pgfmath@remainder00}% - \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}% - \else% - \ifx\pgfmath@empty#2% - \edef\pgfmath@remainder{\pgfmath@remainder#10}% - \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}% - \else% - \edef\pgfmath@remainder{\pgfmath@remainder#1#2}% - \def\pgfmath@tokens{}% - \fi\fi% - \c@pgfmath@counta\pgfmath@rootspecial\relax% - \multiply\c@pgfmath@counta20\relax% - \c@pgfmath@countb\c@pgfmath@counta% - \multiply\c@pgfmath@countb6\relax% - \advance\c@pgfmath@countb36\relax% - \c@pgfmath@countc\c@pgfmath@counta\relax% - \multiply\c@pgfmath@countc2\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \advance\c@pgfmath@countb-\c@pgfmath@countc% - \advance\c@pgfmath@countb-20\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \advance\c@pgfmath@countb-\c@pgfmath@countc% - \advance\c@pgfmath@countb-12\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \advance\c@pgfmath@countb-\c@pgfmath@counta% - \advance\c@pgfmath@countb-3\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \def\pgfmath@digit{0}% - \else% - \def\pgfmath@digit{1}% - \fi% - \else% - \advance\c@pgfmath@countb\c@pgfmath@counta% - \advance\c@pgfmath@countb5\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \def\pgfmath@digit{2}% - \else% - \def\pgfmath@digit{3}% - \fi% - \fi% - \else% - \advance\c@pgfmath@countb\c@pgfmath@counta% - \advance\c@pgfmath@countb9\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \def\pgfmath@digit{4}% - \else% - \def\pgfmath@digit{5}% - \fi% - \fi% - \else% - \advance\c@pgfmath@countb\c@pgfmath@countc% - \advance\c@pgfmath@countb28\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \advance\c@pgfmath@countb-\c@pgfmath@counta% - \advance\c@pgfmath@countb-15\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \def\pgfmath@digit{6}% - \else% - \def\pgfmath@digit{7}% - \fi% - \else% - \advance\c@pgfmath@countb\c@pgfmath@counta% - \advance\c@pgfmath@countb17\relax% - \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% - \def\pgfmath@digit{8}% - \else% - \def\pgfmath@digit{9}% - \fi% - \fi% - \fi% - \edef\pgfmath@rootspecial{\pgfmath@rootspecial\pgfmath@digit}% - \advance\c@pgfmath@counta\pgfmath@digit\relax% - \multiply\c@pgfmath@counta-\pgfmath@digit\relax% - \advance\c@pgfmath@counta\pgfmath@remainder\relax% - \edef\pgfmath@remainder{\the\c@pgfmath@counta}% - \c@pgfmath@counta\pgfmath@targetiterations\relax% - \advance\c@pgfmath@counta-1\relax% - \edef\pgfmath@targetiterations{\the\c@pgfmath@counta}% - \ifnum\c@pgfmath@counta=0\relax% - \edef\pgfmath@root{\pgfmath@root.\pgfmath@digit}% - \else% - \edef\pgfmath@root{\pgfmath@root\pgfmath@digit}% - \fi% - \ifnum\c@pgfmath@counta=-4\relax% - \let\pgfmath@next\pgfmath@sqrt@end% - \else% - \let\pgfmath@next\pgfmath@@@sqrt@% - \fi% - \expandafter\pgfmath@next\pgfmath@tokens% -} - -\def\pgfmath@sqrt@end#1\pgfmath@{% - \edef\pgfmathresult{\pgfmath@root}% - \pgfmath@smuggleone\pgfmathresult% - \endgroup} - -% \pgfmathpow -% -% Calculates #1 ^ #2 -% -% #2 is expected to be an integer. -% -\def\pgfmathpow#1#2{% - \pgfmathparse{#1}\edef\pgfmath@powera{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@powerb{\pgfmathresult}% - \pgfmathpow@{\pgfmath@powera}{\pgfmath@powerb}} -\def\pgfmathpow@#1#2{% - \begingroup% - \expandafter\pgfmath@xa#1pt\relax% - \afterassignment\pgfmath@gobbletilpgfmath@% - \expandafter\c@pgfmath@counta#2\relax\pgfmath@ - % If #2 is negative, take the reciprocal of #1 - % and the absolute value of #2, and carry on. - % - \ifnum\c@pgfmath@counta<0\relax% - \c@pgfmath@counta-\c@pgfmath@counta% - \pgfmathreciprocal@{#1}% - \pgfmath@xa\pgfmathresult pt\relax% - \fi% - \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 by 2\relax% - \repeatpgfmathloop% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - - -% \pgfmathround -% -% Half-up rounding. -% -\def\pgfmathround#1{% - \pgfmathparse{#1}% - \pgfmathround@{\pgfmathresult}} -\def\pgfmathround@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \afterassignment\pgfmath@xa% - \expandafter\c@pgfmath@counta\the\pgfmath@x\relax% - \pgfmath@xb\pgfmath@x% - \ifdim\pgfmath@xb<0pt\relax% - \ifdim\pgfmath@xa<0.5pt\relax% - \else% - \advance\c@pgfmath@counta-1\relax% - \fi% - \else% - \ifdim\pgfmath@xa<0.5pt\relax% - \else% - \advance\c@pgfmath@counta1\relax% - \fi% - \fi% - \pgfmath@returnone\c@pgfmath@counta% - \endgroup% -}% - -% \pgfmathfloor -% -% Floor function. -% -\def\pgfmathfloor#1{% - \pgfmathparse{#1}% - \expandafter\pgfmathfloor@\expandafter{\pgfmathresult}} -\def\pgfmathfloor@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \afterassignment\pgfmath@gobbletilpgfmath@% - \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% - \pgfmath@x\c@pgfmath@counta pt\relax% - \pgfmath@returnone\pgfmath@x% - \endgroup -}% - -% \pgfmathceil -% -% Ceiling function. -% -\def\pgfmathceil#1{% - \pgfmathparse{#1}% - \expandafter\pgfmathceil@\expandafter{\pgfmathresult}} -\def\pgfmathceil@#1{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \afterassignment\pgfmath@gobbletilpgfmath@% - \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% - \pgfmath@y\pgfmath@x% - \advance\pgfmath@y-\c@pgfmath@counta pt\relax% - \pgfmath@x\c@pgfmath@counta pt\relax% - \ifdim\pgfmath@y>0pt\relax% - \advance\pgfmath@x1pt\relax% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -}% - -% \pgfmathexp -% -% A Maclaurens expansion for e^#1. -% 0 <= #1 < ln(16384). -% -\def\pgfmathexp#1{% - \pgfmathparse{#1}% - \expandafter\pgfmathexp@\expandafter{\pgfmathresult}} -\def\pgfmathexp@#1{% - \begingroup% - \pgfmath@x1pt\relax% - \pgfmath@xa1pt\relax% - \pgfmath@xb\pgfmath@x% - \pgfmathloop% - \pgfmath@xc\pgfmathcounter pt\relax% - \c@pgfmath@counta\pgfmath@xc% - \divide\c@pgfmath@counta65536\relax% - \pgfmath@xc1pt\relax% - \divide\pgfmath@xc\c@pgfmath@counta% - \pgfmath@xa\pgfmath@tonumber{\pgfmath@xc}\pgfmath@xa% - \expandafter\pgfmath@xa#1\pgfmath@xa% - \advance\pgfmath@x\pgfmath@xa% - \ifdim\pgfmath@x=\pgfmath@xb% - \else% - \pgfmath@xb\pgfmath@x% - \repeatpgfmathloop% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - - - -% \pgfmathvectorlength -% -% Calcluate the Eulidean length of a 2D vector. -% -% This based on polynomial approximation co-efficents -% contributed by Rouben Rostamian. -% -% #1 - the x component of the vector. -% #2 - the y component of the vector. -% -% P(x) = c0 + x^2 * (c1 + x^2 * (c2 + x^2 * ( c3 + c4 * x^2))) -\def\pgfmath@cE{-0.01019} -\def\pgfmath@cD{0.04453} -\def\pgfmath@cC{-0.11951} -\def\pgfmath@cB{0.49936} -\def\pgfmath@cA{1.00001} - -\def\pgfmathveclen#1#2{% - \pgfmathparse{#1}\edef\pgfmath@vecx{\pgfmathresult}% - \pgfmathparse{#2}\edef\pgfmath@vecy{\pgfmathresult}% - \pgfmathveclen@{\pgfmath@vecx}{\pgfmath@vecy}% -} -\def\pgfmathveclen@#1#2{% - \begingroup% - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \pgfmath@xa\pgfmath@x% - \ifdim\pgfmath@xa=0pt\relax% - \pgfmath@xa\pgfmath@y% - \fi% - \ifdim\pgfmath@xa=0pt\relax% - \else% - \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi% - \ifdim\pgfmath@y<0pt\relax\pgfmath@y-\pgfmath@y\fi% - \ifdim\pgfmath@x>\pgfmath@y% - \pgfmath@xa\pgfmath@x% - \pgfmath@x\pgfmath@y% - \pgfmath@y\pgfmath@xa% - \fi% - % We use a scaling factor to reduce errors. - \ifdim\pgfmath@y>10000pt\relax% - \c@pgfmath@counta1500\relax% - \else% - \ifdim\pgfmath@y>1000pt\relax% - \c@pgfmath@counta150\relax% - \else% - \ifdim\pgfmath@y>100pt\relax% - \c@pgfmath@counta50\relax% - \else% - \c@pgfmath@counta1\relax% - \fi% - \fi% - \fi% - \divide\pgfmath@x by\c@pgfmath@counta\relax% - \divide\pgfmath@y by\c@pgfmath@counta\relax% - \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}% - \pgfmath@x=\pgfmathresult\pgfmath@x% - \pgfmath@xa=\pgfmath@tonumber{\pgfmath@x}\pgfmath@x% - \edef\pgfmath@xsq{\pgfmath@tonumber{\pgfmath@xa}}% - \pgfmath@x=\pgfmath@cE\pgfmath@xa% - \advance\pgfmath@x by\pgfmath@cD pt\relax% - \pgfmath@x=\pgfmath@xsq\pgfmath@x% - \advance\pgfmath@x by\pgfmath@cC pt\relax% - \pgfmath@x=\pgfmath@xsq\pgfmath@x% - \advance\pgfmath@x by\pgfmath@cB pt\relax% - \pgfmath@x=\pgfmath@xsq\pgfmath@x% - \advance\pgfmath@x by\pgfmath@cA pt\relax% - \ifdim\pgfmath@y<0pt\relax% - \pgfmath@y=-\pgfmath@y% - \fi% - \pgfmath@x=\pgfmath@tonumber{\pgfmath@y}\pgfmath@x% - % Invert the scaling factor. - \multiply\pgfmath@x by\c@pgfmath@counta\relax% - \fi% - \pgfmath@returnone\pgfmath@x% - \endgroup% -} - -% \pgfmathmax -% -% Return the maximum of #1 or #2 -% -\def\pgfmathmax#1#2{% - \pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}% - \pgfmathparse@{#2}\edef\pgfmath@secondoperand{\pgfmathresult}% - \pgfmathmax@{\pgfmath@firstoperand}{\pgfmath@secondoperand}} -\def\pgfmathmax@#1#2{% - \begingroup - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \ifdim\pgfmath@x>\pgfmath@y% - \pgfmath@returnone\pgfmath@x% - \else% - \pgfmath@returnone\pgfmath@y% - \fi% - \endgroup} - -% \pgfmathmax -% -% Return the minimim of #1 or #2 -% -\def\pgfmathmin#1#2{% - \pgfmathparse@{#1}\edef\pgfmath@firstoperand{\pgfmathresult}% - \pgfmathparse@{#2}\edef\pgfmath@secondoperand{\pgfmathresult}% - \pgfmathmin@{\pgfmath@firstoperand}{\pgfmath@secondoperand}} -\def\pgfmathmin@#1#2{% - \begingroup - \expandafter\pgfmath@x#1pt\relax% - \expandafter\pgfmath@y#2pt\relax% - \ifdim\pgfmath@x<\pgfmath@y% - \pgfmath@returnone\pgfmath@x% - \else% - \pgfmath@returnone\pgfmath@y% - \fi% - \endgroup% -} - -% \pgfmathscientific -% -% Return the value of #1e#2 -% -% e.g. \pgfmathscientific{1.23456789123}{4} -% -% defines \pgfmathresult as 12345.67891 -% -% NB This arguments *are not parsed*, as the long mantissa would be lost. -% -\def\pgfmathscientific#1#2{% - \begingroup% - \edef\pgfmath@sci@exponent{#2}% - \pgfmath@x#1pt\relax% - \ifdim\pgfmath@x<0pt\relax% - \pgfmath@x-\pgfmath@x% - \edef\pgfmath@sci@sign{-}% - \edef\pgfmath@temp{\pgfmath@gobbleone#1}% - \else% - \edef\pgfmath@sci@sign{+}% - \edef\pgfmath@temp{#1}% - \fi% - \expandafter\pgfmath@scientific@@\pgfmath@temp00000000000\pgfmath@} - -\def\pgfmath@scientific@@#1.#2#3#4#5#6{% - \edef\pgfmath@sci@int{#1}% - \edef\pgfmath@sci@mantissaA{#2#3#4#5#6}% - \pgfmath@scientific@@@} - -\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% - \c@pgfmath@countb\c@pgfmath@counta% - \ifnum\c@pgfmath@counta<0\relax% - \c@pgfmath@counta-\c@pgfmath@counta% - \fi% - \pgfmathpow@{10}{\the\c@pgfmath@counta}% - \afterassignment\pgfmath@gobbletilpgfmath@ - \c@pgfmath@countc\pgfmathresult\relax\pgfmath@ - \edef\pgfmath@sci@factor{\the\c@pgfmath@countc}% - \ifnum\c@pgfmath@countb<0\relax% - % xE-y: easy... - \pgfmath@x\pgfmath@sci@int.\pgfmath@sci@mantissaA pt\relax% - \divide\pgfmath@x\pgfmath@sci@factor\relax% - \else% - % xE+y: - % Must do this way so as not lose digits in a long mantissa. Sigh... - \c@pgfmath@counta\pgfmath@sci@int% - \c@pgfmath@countb\pgfmath@sci@mantissaA% - \multiply\c@pgfmath@counta\pgfmath@sci@factor\relax% - \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% - \c@pgfmath@countc\c@pgfmath@countb% - \divide\c@pgfmath@countb100000\relax% - \advance\c@pgfmath@counta\c@pgfmath@countb% - \multiply\c@pgfmath@countb100000\relax% - \advance\c@pgfmath@countc-\c@pgfmath@countb% - \c@pgfmath@countb\pgfmath@sci@mantissaB\relax% - \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% - \divide\c@pgfmath@countb100000\relax% - \advance\c@pgfmath@countc\c@pgfmath@countb% - \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% - \pgfmath@returnone\pgfmath@x% - \endgroup}
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