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+% Copyright 2019 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 pseudorandom numbers.
+%
+% Version 1.414213 29/9/2007
+
+% Pseudo-random number generation.
+%
+% See:
+% \book@{pressetal1992,
+% author = {William H. Press and Brian P. Flannery and Saul A.
+% Teukolsky and William T. Vetterling},
+% title = {Numerical Recipies in C},
+% edition = {Second},
+% publisher = {Cambridge University Press}
+% }
+%
+% See also, the documentation for the lcg package by Erich Janka:
+% (http://www.ctan.org/tex-archive/macros/latex/contrib/lcg/lcg.pdf)
+%
+\def\pgfmath@rnd@m{2147483647}% LaTeX Maximum.
+
+\begingroup
+\c@pgfmath@counta=\time%
+\multiply\c@pgfmath@counta by\year%
+\ifnum\c@pgfmath@counta=0
+ \c@pgfmath@counta=1
+\fi
+\xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}% The seed.
+\endgroup
+
+% \pgfmathsetseed
+%
+% Explicitly set the seed for the generator
+%
+% #1 -> the new seed.
+%
+\def\pgfmathsetseed#1{%
+ % Attention pgflibraryluamath.code.tex relies on the fact that
+ % this method also modifies \pgfmathresult:
+ \pgfmathparse{#1}\expandafter\pgfmath@setseed\pgfmathresult.0\pgfmath@stop
+}%
+\def\pgfmath@setseed#1.#2\pgfmath@stop{\def\pgfmath@rnd@z{#1}}%
+
+% Alternative parameters - see Press et al (1992) p278-279,
+% for discussion.
+%
+% a=16807 q=127773 r=2836
+% a=48271 q=4488 r=3399
+%
+\def\pgfmath@rnd@a{69621}
+\def\pgfmath@rnd@r{23902}
+\def\pgfmath@rnd@q{30845}
+
+% \pgfmathgeneratepseudorandomnumber
+%
+% A linear congruency generator for generating
+% pseudo-random numbers. Generates numbers in
+% the range 1 - 2^31-1.
+%
+\def\pgfmathgeneratepseudorandomnumber{%
+ \begingroup%
+ \c@pgfmath@counta=\pgfmath@rnd@z%
+ \c@pgfmath@countb=\pgfmath@rnd@z%
+ \c@pgfmath@countc=\pgfmath@rnd@q%
+ \divide\c@pgfmath@counta by\c@pgfmath@countc%
+ \multiply\c@pgfmath@counta by-\c@pgfmath@countc%
+ \advance\c@pgfmath@counta by\c@pgfmath@countb
+ \c@pgfmath@countc=\pgfmath@rnd@a%
+ \multiply\c@pgfmath@counta by\c@pgfmath@countc%
+ \c@pgfmath@countc=\pgfmath@rnd@q%
+ \divide\c@pgfmath@countb by\c@pgfmath@countc%
+ \c@pgfmath@countc=\pgfmath@rnd@r%
+ \multiply\c@pgfmath@countb by\c@pgfmath@countc%
+ \advance\c@pgfmath@counta by-\c@pgfmath@countb%
+ \ifnum\c@pgfmath@counta<0\relax%
+ \c@pgfmath@countb=\pgfmath@rnd@m%
+ \advance\c@pgfmath@counta by\c@pgfmath@countb%
+ \fi%
+ \xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}%
+ \endgroup%
+ \edef\pgfmathresult{\pgfmath@rnd@z}%
+}
+
+% \pgfmathrnd
+%
+% Generates a pseudo-random number between 0 and 1.
+%
+\pgfmathdeclarefunction{rnd}{0}{%
+ \begingroup%
+ \pgfmathgeneratepseudorandomnumber%
+ \c@pgfmath@counta\pgfmathresult%
+ \c@pgfmath@countb\c@pgfmath@counta%
+ \divide\c@pgfmath@countb100001\relax% To get one.
+ \multiply\c@pgfmath@countb-100001\relax%
+ \advance\c@pgfmath@countb\c@pgfmath@counta%
+ \advance\c@pgfmath@countb1000000\relax%
+ \expandafter\pgfmathrnd@@\the\c@pgfmath@countb\pgfmath@%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
+}%
+
+\def\pgfmathrnd@@#1#2#3\pgfmath@{%
+ \edef\pgfmath@temp{#2.#3}%
+ \pgfmath@x=\pgfmath@temp pt\relax%
+}%
+
+% \pgfmathrand
+%
+% Generates a pseudo-random number between -1 and 1.
+%
+\pgfmathdeclarefunction{rand}{0}{%
+ \begingroup%
+ \pgfmathgeneratepseudorandomnumber%
+ \c@pgfmath@counta\pgfmathresult%
+ \c@pgfmath@countb\c@pgfmath@counta%
+ \divide\c@pgfmath@countb200001\relax%
+ \multiply\c@pgfmath@countb-200001\relax%
+ \advance\c@pgfmath@countb\c@pgfmath@counta%
+ \advance\c@pgfmath@countb-100000\relax%
+ \ifnum\c@pgfmath@countb<0\relax%
+ \advance\c@pgfmath@countb-1000000\relax%
+ \else%
+ \advance\c@pgfmath@countb1000000\relax%
+ \fi%
+ \expandafter\pgfmathrand@@\the\c@pgfmath@countb\pgfmath@%
+ \pgfmath@returnone\pgfmath@x%
+ \endgroup%
+}%
+
+\def\pgfmathrand@@#1#2#3#4\pgfmath@{%
+ \ifx#1-%
+ \edef\pgfmath@temp{-#3.#4}%
+ \else%
+ \edef\pgfmath@temp{#2.#3#4}%
+ \fi%
+ \pgfmath@x=\pgfmath@temp pt\relax%
+}%
+
+\pgfmathdeclarefunction{random}{...}{%
+ \begingroup%
+ \def\pgfmath@temp{#1}%
+ \ifx\pgfmath@temp\pgfmath@empty%
+ \pgfmathrnd@%
+ \else%
+ \expandafter\pgfmathrandom@@#1\pgfmath@stop%
+ \fi%
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup}
+
+\def\pgfmathrandom@@{\futurelet\pgfmath@token\pgfmathrandom@@@}
+\def\pgfmathrandom@@@{%
+ \ifx\pgfmath@token\bgroup%
+ \expandafter\pgfmath@random@@@@%
+ \else%
+ \expandafter\pgfmath@random@@@@@%
+ \fi%
+}
+\def\pgfmath@random@@@@@#1\pgfmath@stop{%
+ \pgfmathrandominteger\pgfmathresult{1}{#1}%
+}
+\def\pgfmath@random@@@@#1#2\pgfmath@stop{%
+ \pgfmathrandominteger\pgfmathresult{#1}{#2}%
+}
+
+% \pgfmathrandominteger
+%
+% Return a 'randomly' selected integer in the range #2 - #3 (inclusive).
+%
+% #1 - a macro to store the integer (not a count register).
+% #2 - the lower limit of the range.
+% #3 - the upper limit of the range.
+%
+\def\pgfmathrandominteger#1#2#3{%
+ \begingroup%
+ \pgfmathsetcount\c@pgfmath@counta{#2}%
+ \pgfmathsetcount\c@pgfmath@countb{#3}%
+ \c@pgfmath@countc\c@pgfmath@countb%
+ % OK. Maybe #2 > #3.
+ \ifnum\c@pgfmath@counta>\c@pgfmath@countb\relax%
+ \c@pgfmath@countc\c@pgfmath@counta%
+ \c@pgfmath@counta\c@pgfmath@countb%
+ \c@pgfmath@countb\c@pgfmath@countc%
+ \fi%
+ \c@pgfmath@countd\c@pgfmath@counta
+ \advance\c@pgfmath@countc1\relax%
+ \advance\c@pgfmath@countc-\c@pgfmath@counta%
+ \pgfmathgeneratepseudorandomnumber%
+ \c@pgfmath@counta\pgfmathresult\relax%
+ \c@pgfmath@countb\c@pgfmath@counta%
+ \divide\c@pgfmath@countb\c@pgfmath@countc%
+ \multiply\c@pgfmath@countb-\c@pgfmath@countc%
+ \advance\c@pgfmath@counta\c@pgfmath@countb%
+ \advance\c@pgfmath@counta\c@pgfmath@countd
+ \edef\pgfmathresult{\the\c@pgfmath@counta}%
+ \pgfmath@smuggleone{\pgfmathresult}%
+ \endgroup%
+ \edef#1{\pgfmathresult}%
+}
+
+% \pgfmathdeclarerandomlist
+%
+% Create a list to be used with \pgfmathrandomelement.
+%
+% #1 - the name of the list
+% #2 - a list of elements (e.g., {item-1}{item-2}...{item-n}).
+%
+\def\pgfmathdeclarerandomlist#1#2{%
+ \def\pgfmath@randomlistname{#1}%
+ \begingroup%
+ \c@pgfmath@counta=1\relax%
+ % {} is a possible random element so (locally)
+ % redefine \pgfmath@empty.
+ \def\pgfmath@empty{pgfmath@empty}%
+ \expandafter\pgfmath@scanrandomlist#2{pgfmath@empty}}
+\def\pgfmath@scanrandomlist#1{%
+ \def\pgfmath@scanneditem{#1}%
+ \ifx\pgfmath@scanneditem\pgfmath@empty%
+ \advance\c@pgfmath@counta-1\relax%
+ \expandafter\xdef\csname pgfmath@randomlist@\pgfmath@randomlistname\endcsname{\the\c@pgfmath@counta}%
+ \endgroup%
+ \else%
+ \expandafter\gdef\csname pgfmath@randomlist@\pgfmath@randomlistname @\the\c@pgfmath@counta\endcsname{#1}%
+ \advance\c@pgfmath@counta1\relax%
+ \expandafter\pgfmath@scanrandomlist%
+ \fi}
+
+% \pgfmathrandomitem
+%
+% Return a 'randomly' selected element from a list.
+%
+% #1 - a macro to store the item.
+% #2 - the name of the list.
+%
+\def\pgfmathrandomitem#1#2{%
+ \pgfmath@ifundefined{pgfmath@randomlist@#2}{\pgfmath@error{Unknown random list `#2'}{}}{%
+ \edef\pgfmath@randomlistlength{\csname pgfmath@randomlist@#2\endcsname}%
+ \pgfmathrandominteger{\pgfmath@randomtemp}{1}{\pgfmath@randomlistlength}%
+ \expandafter\def\expandafter#1\expandafter{\csname pgfmath@randomlist@#2@\pgfmath@randomtemp\endcsname}}}