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% Copyright 2018 by Mark Wibrow
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
\pgfkeys{/pgf/.cd,
fixed point arithmetic/.code={%
\pgfmathfp@plots@install%
\pgfmathfp@parser@install%
\let\pgfmathparse=\pgfmathfpparse%
\pgfkeys{/pgf/fixed point/.cd, #1}%
},%
fixed point/.cd,
scale results/.code={%
\pgfmathfpparse{#1}%
\let\pgfmathfpscale=\pgfmathresult%
}%
}%
\def\pgfmathfpscale{1}%
\def\pgfmathfpparse{%
\begingroup%
\let\pgfmathpostparse=\relax%
\pgfmath@catcodes%
\pgfmath@quickparsefalse%
\pgfmathfpparse@}%
\def\pgfmathfpparse@#1{%
\edef\pgfmathfp@expression{#1}%
\expandafter\pgfmathfpparse@@\pgfmathfp@expression\pgfmathfp@}%
\def\pgfmathfp@char@asterisk{*}%
\def\pgfmathfpparse@@#1#2\pgfmathfp@{%
\def\pgfmathfp@test{#1}%
\ifx\pgfmathfp@test\pgfmathfp@char@asterisk%
\edef\pgfmathfp@expression{\pgfmathfpscale#1#2}%
\else%
\edef\pgfmathfp@expression{#1#2}%
\fi%
\expandafter\pgfmathparse@\expandafter{\pgfmathfp@expression}%
% \endgroup provided by \pgfpathmarse@end
}%
% Crude handling of file plots
%
\pgfkeys{/pgf/fixed point/.cd,
scale file plot x/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscalex{\pgfmathresult*},
scale file plot y/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscaley{\pgfmathresult*},
scale file plot z/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscalez{\pgfmathresult*},
}%
\def\pgfmathfp@plots@install{%
\let\pgfmathfpplotscalex=\pgfutil@empty
\let\pgfmathfpplotscaley=\pgfutil@empty
\let\pgfmathfpplotscalez=\pgfutil@empty
\let\pgf@parsexyline=\pgfmathfp@parsexyline%
\let\pgf@parsexyzline=\pgfmathfp@parsexyzline%
}%
\def\pgfmathfp@parsexyline#1 #2 #3\pgf@stop{%
\edef\pgfmathfp@marshal{%
\noexpand\pgfplotstreampoint{\noexpand\pgfpointxy{\pgfmathfpplotscalex#1}{\pgfmathfpplotscaley#2}}%
}%
\pgfmathfp@marshal%
}%
\def\pgfmathfp@parsexyzline#1 #2 #3 #4\pgf@stop{%
\edef\pgfmathfp@marshal{%
\noexpand\pgfplotstreampoint{%
\noexpand\pgfpointxyz{\pgfmathfpplotscalex#1}{\pgfmathfpplotscaley#2}{\pgfmathfpplotscalez#3}%
}%
}%
\pgfmathfp@marshal%
}%
%
\def\pgfmathfp@parser@install{%
%
\expandafter\ifx\csname FP@version\endcsname\relax%
\pgferror{You need to say `\string\usepackage{fp}' to use %
fixed point arithmetic}%
\else%
%
% Don't want messages.
%
\FPmessagesfalse%
\FPdebugfalse%
%
% Install float commands...
%
\let\pgfmathadd@=\pgfmathfpadd@%
\let\pgfmathsubtract@=\pgfmathfpsubtract@%
\let\pgfmathmultiply@=\pgfmathfpmultiply@%
\let\pgfmathdivide@=\pgfmathfpdivide@%
\let\pgfmathabs@=\pgfmathfpabs@%
\let\pgfmathneg@=\pgfmathfpneg@%
\let\pgfmathround@=\pgfmathfpround@%
\let\pgfmathfloor@=\pgfmathfpfloor@%
\let\pgfmathceil@=\pgfmathfpceil@%
\let\pgfmathmod@=\pgfmathfpmod@%
\let\pgfmathmax@=\pgfmathfpmax@%
\let\pgfmathmin@=\pgfmathfpmin@%
\let\pgfmathsin@=\pgfmathfpsin@%
\let\pgfmathcos@=\pgfmathfpcos@%
\let\pgfmathtan@=\pgfmathfptan@%
\let\pgfmathdeg@=\pgfmathfpdeg@%
\let\pgfmathrad@=\pgfmathfprad@%
\let\pgfmathatan@=\pgfmathfpatan@%
\let\pgfmathasin@=\pgfmathfpasin@%
\let\pgfmathacos@=\pgfmathfpacos@%
\let\pgfmathcot@=\pgfmathfpcot@%
\let\pgfmathsec@=\pgfmathfpsec@%
\let\pgfmathcosec@=\pgfmathfpcosec@%
\let\pgfmathpow@=\pgfmathfppow@%
\let\pgfmathexp@=\pgfmathfpexp@%
\let\pgfmathln@=\pgfmathfpln@%
\let\pgfmathsqrt@=\pgfmathfpsqrt@%
\let\pgfmath@pi=\pgfmathfppi@%
\let\pgfmathveclen@=\pgfmathfpveclen@%
\let\pgfmathe@=\pgfmathfpe@%
%
\let\pgfmathlessthan@=\pgfmathfplessthan@%
\let\pgfmathgreaterthan@=\pgfmathfpgreaterthan@%
\let\pgfmathequalto@=\pgfmathfpequalto@%
%
\let\pgfmathrnd=\pgfmathfprnd%
\let\pgfmathrand=\pgfmathfprand%
\let\pgfmathsetseed=\pgfmathfpsetseed%
%
\let\pgfmathscientific=\pgfmathfpscientific%
\fi%
}%
\def\pgfmathfpe@{let\pgfmathresult=\FPe}%
\def\pgfmathfppi@{let\pgfmathresult=\FPpi}%
% Scientific notation.
\def\pgfmathfpscientific#1#2{%
\begingroup%
\FPpow\pgfmathresult{10}{#2}\unskip% Needed.
\FPmul\pgfmathresult{#1}{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% Comparison stuff...
% lessthan
%
\def\pgfmathfplessthan#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfplessthan@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfplessthan@#1#2{%
\begingroup%
\FPiflt{#1}{#2}%
\def\pgfmathresult{1.0}%
\else%
\def\pgfmathresult{0.0}%
\fi%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% greaterthan
%
\def\pgfmathfpgreaterthan#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpgreaterthan@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpgreaterthan@#1#2{%
\begingroup%
\FPifgt{#1}{#2}%
\def\pgfmathresult{1.0}%
\else%
\def\pgfmathresult{0.0}%
\fi%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% equalto
%
\def\pgfmathfpequalto#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpequalto@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpequalto@#1#2{%
\begingroup%
\FPifeq{#1}{#2}%
\def\pgfmathresult{1.0}%
\else%
\def\pgfmathresult{0.0}%
\fi%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% Basic arithmetic stuff...
% add
%
\def\pgfmathfpadd#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpadd@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpadd@#1#2{%
\begingroup%
\FPadd\pgfmathresult{#1}{#2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% subtract
%
\def\pgfmathfpsubtract#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpsubtract@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpsubtract@#1#2{%
\begingroup%
\FPsub\pgfmathresult{#1}{#2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% multiply
%
\def\pgfmathfpmultiply#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpmultiply@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpmultiply@#1#2{%
\begingroup%
\FPmul\pgfmathresult{#1}{#2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% divide
%
\def\pgfmathfpdivide#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpdivide@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpdivide@#1#2{%
\begingroup%
\FPdiv\pgfmathresult{#1}{#2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% abs
%
\def\pgfmathfpabs#1{%
\pgfmathfpparse{#1}%
\pgfmathfpabs@{\pgfmathresult}%
}%
\def\pgfmathfpabs@#1{%
\begingroup%
\FPabs\pgfmathresult{#1}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% neg
%
\def\pgfmathfpneg#1{%
\pgfmathfpparse{#1}%
\pgfmathfpneg@{\pgfmathresult}%
}%
\def\pgfmathfpneg@#1{%
\begingroup%
\FPneg\pgfmathresult{#1}%
\pgfmath@smuggleone\pgfmathresult
\endgroup%
}%
% round
%
\def\pgfmathfpround#1{%
\pgfmathfpparse{#1}%
\pgfmathfpround@{\pgfmathresult}%
}%
\def\pgfmathfpround@#1{%
\begingroup%
\FPround\pgfmathresult{#1}{0}%
\edef\pgfmathresult{\pgfmathresult.0}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% floor
%
\def\pgfmathfpfloor#1{%
\pgfmathfpparse{#1}%
\pgfmathfpfloor@{\pgfmathresult}%
}%
\def\pgfmathfpfloor@#1{%
\begingroup%
\FPtrunc\pgfmathresult{#1}{0}%
\FPifneg{#1}%
\FPsub\pgfmathresult{\pgfmathresult}{1}%
\fi%
\edef\pgfmathresult{\pgfmathresult.0}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% ceil
%
\def\pgfmathfpceil#1{%
\pgfmathfpparse{#1}%
\pgfmathfpceil@{\pgfmathresult}%
}%
\def\pgfmathfpceil@#1{%
\begingroup%
\FPtrunc\pgfmathresult{#1}{0}%
\FPifpos{#1}%
\FPadd\pgfmathresult{\pgfmathresult}{1}%
\fi%
\edef\pgfmathresult{\pgfmathresult.0}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% mod
%
\def\pgfmathfpmod#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpmod@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpmod@#1#2{%
\begingroup%
\FPdiv\pgfmathresult{#1}{#2}%
\FPtrunc\pgfmathresult{\pgfmathresult}{0}%
\FPmul\pgfmathresult{\pgfmathresult}{#2}%
\FPsub\pgfmathresult{#1}{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% max
%
\def\pgfmathfpmax#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpmax@@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpmax@#1{%
\pgfmathfpmax@@#1%
}%
\def\pgfmathfpmax@@#1#2{%
\begingroup%
\FPifgt{#1}{#2}%
\def\pgfmathresult{#1}%
\else%
\def\pgfmathresult{#2}%
\fi%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% min
%
\def\pgfmathfpmin#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpmin@@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpmin@#1{%
\pgfmathfpmin@@#1%
}%
\def\pgfmathfpmin@@#1#2{%
\begingroup%
\FPiflt{#1}{#2}%
\def\pgfmathresult{#1}%
\else%
\def\pgfmathresult{#2}%
\fi%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% Functions...
% pow
%
\def\pgfmathfppow#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfppow@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfppow@#1#2{%
\begingroup%
\FPpow\pgfmathresult{#1}{#2}\unskip%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% exp
%
\def\pgfmathfpexp#1{%
\pgfmathfpparse{#1}%
\pgfmathfpexp@{\pgfmathresult}%
}%
\def\pgfmathfpexp@#1{%
\begingroup%
\FPexp\pgfmathresult{#1}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% ln
%
\def\pgfmathfpln#1{%
\pgfmathfpparse{#1}%
\pgfmathfpln@{\pgfmathresult}%
}%
\def\pgfmathfpln@#1{%
\begingroup%
\FPln\pgfmathresult{#1}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% sqrt
%
\def\pgfmathfpsqrt#1{%
\pgfmathfpparse{#1}%
\pgfmathfpsqrt@{\pgfmathresult}%
}%
\def\pgfmathfpsqrt@#1{%
\begingroup%
\FProot\pgfmathresult{#1}{2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% veclen
%
\def\pgfmathfpveclen#1#2{%
\pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult%
\pgfmathfpparse{#1}%
\pgfmathfpveclen@{\pgfmathresult}{\pgfmath@result}%
}%
\def\pgfmathfpveclen@#1#2{%
\begingroup%
\FPmul\pgfmath@result{#1}{#1}%
\FPmul\pgfmath@@result{#2}{#2}%
\FPadd\pgfmathresult{\pgfmath@result}{\pgfmath@@result}%
\FProot\pgfmathresult{\pgfmathresult}{2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% Trigonometric stuff...
% sin
%
\def\pgfmathfpsin#1{%
\pgfmathfpparse{#1}%
\pgfmathfpsin@{\pgfmathresult}%
}%
\def\pgfmathfpsin@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPsin\pgfmathresult{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% cos
%
\def\pgfmathfpcos#1{%
\pgfmathfpparse{#1}%
\pgfmathfpcos@{\pgfmathresult}%
}%
\def\pgfmathfpcos@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPcos\pgfmathresult{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% tan
%
\def\pgfmathfptan#1{%
\pgfmathfpparse{#1}%
\pgfmathfptan@{\pgfmathresult}%
}%
\def\pgfmathfptan@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPtan\pgfmathresult{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% acos
%
\def\pgfmathfpacos#1{%
\pgfmathfpparse{#1}%
\pgfmathfpacos@{\pgfmathresult}%
}%
\def\pgfmathfpacos@#1{%
\begingroup%
\FParccos\pgfmathresult{#1}%
\FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% asin
%
\def\pgfmathfpasin#1{%
\pgfmathfpparse{#1}%
\pgfmathfpasin@{\pgfmathresult}%
}%
\def\pgfmathfpasin@#1{%
\begingroup%
\FParcsin\pgfmathresult{#1}%
\FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% atan
%
\def\pgfmathfpatan#1{%
\pgfmathfpparse{#1}%
\pgfmathfpatan@{\pgfmathresult}%
}%
\def\pgfmathfpatan@#1{%
\begingroup%
\FParctan\pgfmathresult{#1}%
\FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% cot
%
\def\pgfmathfpcot#1{%
\pgfmathfpparse{#1}%
\pgfmathfpcot@{\pgfmathresult}%
}%
\def\pgfmathfpcot@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPcot\pgfmathresult{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% sec
%
\def\pgfmathfpsec#1{%
\pgfmathfpparse{#1}%
\pgfmathfpsec@{\pgfmathresult}%
}%
\def\pgfmathfpsec@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPcos\pgfmathresult{\pgfmathresult}%
\FPdiv\pgfmathresult{1}{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% cosec
%
\def\pgfmathfpcosec#1{%
\pgfmathfpparse{#1}%
\pgfmathfpcosec@{\pgfmathresult}%
}%
\def\pgfmathfpcosec@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.017453292519943295}%
\FPsin\pgfmathresult{\pgfmathresult}%
\FPdiv\pgfmathresult{1}{\pgfmathresult}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% deg
%
\def\pgfmathfpdeg#1{%
\pgfmathfpparse{#1}%
\pgfmathfpdeg@{\pgfmathresult}%
}%
\def\pgfmathfpdeg@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{57.295779513082320885}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% rad
%
\def\pgfmathfprad#1{%
\pgfmathfpparse{#1}%
\pgfmathfprad@{\pgfmathresult}%
}%
\def\pgfmathfprad@#1{%
\begingroup%
\FPmul\pgfmathresult{#1}{0.01745329251994325}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% Random stuff...
\def\pgfmathfpsetseed#1{%
\pgfmathfpparse{#1}%
\afterassignment\pgfmath@gobbletilpgfmath@%
\FPseed\pgfmathresult\relax\pgfmath@%
}%
% rnd
%
\def\pgfmathfprnd{%
\begingroup%
\FPrandom\pgfmathresult%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%
% rand
%
\def\pgfmathfprand{%
\begingroup%
\FPrandom\pgfmathresult%
\FPmul\pgfmathresult{2}{\pgfmathresult}%
\FPsub\pgfmathresult{\pgfmathresult}{1}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}%