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-% 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 trigonometric functions/operations.
-%
-% Much of this file is based on ideas and code (particularly
-% \pgfcoremath.code.tex) due to Till Tantau
-%
-% Version 0.0 08/03/2007
-
-% \pgfmathpi
-%
-\def\pgfmathpi{\edef\pgfmathresult{\pgfmath@pi}}
-\def\pgfmath@pi{3.14159}
-
-% \pgfmathradians
-%
-% Convert #1 from radians to degrees (accurate to 1 deg).
-%
-\def\pgfmathradians#1{%
- \pgfmathparse{#1}%
- \pgfmathradians@{\pgfmathresult}}
-\def\pgfmathradians@#1{%
- \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.
-%
-\def\pgfmathdeg#1{%
- \pgfmathparse{#1}%
- \pgfmathdeg@{\pgfmathresult}}
-\def\pgfmathdeg@#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.
-%
-\def\pgfmathrad#1{%
- \pgfmathparse{#1}%
- \pgfmathrad@{\pgfmathresult}}
-\def\pgfmathrad@#1{%
- \begingroup%
- \expandafter\pgfmath@x#1pt\relax%
- \pgfmath@x3.14159\pgfmath@x%
- \divide\pgfmath@x180\relax%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}%
-
-% \pgfmathsin
-%
-% Calculate the sine of #1 (in degrees).
-%
-\def\pgfmathsin#1{%
- \pgfmathparse{#1}%
- \pgfmathsin@{\pgfmathresult}}
-\def\pgfmathsin@#1{%
- % Let #1 = a.b
- % Then sin(#1) \approx (1-b)*cos(a) + b*cos(a+1)
- %
- \begingroup%
- \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
-}
-
-% \pgfmathcos
-%
-% Calculate the cosine of #1 (in degrees).
-%
-\def\pgfmathcos#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathcos@\expandafter{\pgfmathresult}}
-\def\pgfmathcos@#1{%
- % Let x = a.b
- % Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
- %
- \begingroup%
- \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
-%
-% Calculate the sin and cosine of #1 (in degrees).
-%
-\def\pgfmathsincos#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathcos@\expandafter{\pgfmathresult}}
-\def\pgfmathsincos@#1{%
- \pgfmathsin@{#1}\edef\pgfmathresulty{\pgfmathresult}%
- \pgfmathcos@{#1}\edef\pgfmathresultx{\pgfmathresult}%
-}
-% \pgfmathtan
-%
-% Calculate the cotangent of #1 (in degrees).
-%
-\def\pgfmathtan#1{%
- \pgfmathparse{#1}%
- \pgfmathtan@{\pgfmathresult}}
-\def\pgfmathtan@#1{%
- \begingroup%
- \pgfmathcos@{#1}%
- \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
- \edef\pgfmath@tantemp{\pgfmathresult}%
- \pgfmathsin@{#1}%
- \pgfmath@x\pgfmathresult pt\relax%
- \pgfmath@x\pgfmath@tantemp\pgfmath@x%
- % Adjust to 4 decimal places. This gets rid of some annoyingly tiny errors.
- \afterassignment\pgfmath@x%
- \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
- \ifdim\pgfmath@x<.0001pt\relax%
- \pgfmath@x0pt\relax%
- \fi%
- \advance\pgfmath@x\c@pgfmath@counta pt%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-
-% \pgfmathasin
-%
-% The asin of #1
-%
-\def\pgfmathasin#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathasin@\expandafter{\pgfmathresult}}
-\def\pgfmathasin@#1{%
- \begingroup%
- \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@asin@\the\c@pgfmath@counta\endcsname pt\relax%
- \ifdim\pgfmath@xa<0pt\relax%
- \pgfmath@x-\pgfmath@x%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathacos
-%
-% The acos of #1
-%
-\def\pgfmathacos#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathacos@\expandafter{\pgfmathresult}}
-\def\pgfmathacos@#1{%
- \begingroup%
- \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%
- \fi%
- \pgfmath@returnone\pgfmath@x%
- \endgroup%
-}
-
-% \pgfmathasin
-%
-% The atan of #1
-%
-\def\pgfmathatan#1{%
- \pgfmathparse{#1}%
- \expandafter\pgfmathatan@\expandafter{\pgfmathresult}}
-\def\pgfmathatan@#1{%
- \begingroup%
- \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%
-}
-
-
-\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}
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-
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-% Oh No! Some really loooooong tables.
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