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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 provides basic macros for converting between bases.
%
% Version 1.4142135 8/11/2008
% Base conversion operations for the parser.
%
\pgfmathdeclarefunction{bin}{1}{%
\begingroup%
\afterassignment\pgfmath@gobbletilpgfmath@%
\c@pgfmath@counta=#1\relax\pgfmath@%
\expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{2}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
\pgfmathdeclarefunction{hex}{1}{%
\begingroup%
\afterassignment\pgfmath@gobbletilpgfmath@%
\c@pgfmath@counta=#1\relax\pgfmath@%
\expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{16}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
\pgfmathdeclarefunction{Hex}{1}{%
\begingroup%
\afterassignment\pgfmath@gobbletilpgfmath@%
\c@pgfmath@counta=#1\relax\pgfmath@%
\expandafter\pgfmathbasetoBase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{16}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
\pgfmathdeclarefunction{oct}{1}{%
\begingroup%
\afterassignment\pgfmath@gobbletilpgfmath@%
\c@pgfmath@counta=#1\relax\pgfmath@%
\expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{8}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
% Additional macros:
% \pgfmathbasetodec
%
% Convert a representation of an integer from
% the specified base to base 10.
%
% #1 - a macro to store the result.
% #2 - the representation of a number (i.e. not a register)
% #3 - the current base.
%
% e.g.
%
% \pgfmathbasetodec\mynumber{10111}{2}
%
% \mynumber <- 23
%
\def\pgfmathbasetodec#1#2#3{%
\pgfmath@checknumber{#2}%
\pgfmath@checkbase{#3}%
\def\pgfmath@base{#3}%
\def\pgfmath@base@macro{#1}%
\c@pgfmath@counta=1\relax%
\let\pgfmath@reversed=\pgfmath@empty%
\expandafter\pgfmathbasetodec@#2\pgfmath@base@stop}
\def\pgfmathbasetodec@#1{%
\ifx#1\pgfmath@base@stop%
\c@pgfmath@countb=0%
\divide\c@pgfmath@counta by\pgfmath@base\relax%
\expandafter\pgfmathbasetodec@@%
\else%
\edef\pgfmath@reversed{\pgfmath@reversed#1}%
\expandafter\multiply\expandafter\c@pgfmath@counta\pgfmath@base\relax%
\expandafter\pgfmathbasetodec@%
\fi}
\def\pgfmathbasetodec@@{\expandafter\pgfmathbasetodec@@@\pgfmath@reversed\pgfmathbasetodec}
\def\pgfmathbasetodec@@@#1{%
\ifx\pgfmathbasetodec#1\relax%
\expandafter\edef\pgfmath@base@macro{\the\c@pgfmath@countb}%
\let\pgfmath@next=\pgfmathbasetodec@@@@%
\else%
\chardef\pgfmath@charnum`#1\relax%
\c@pgfmath@countc=\pgfmath@charnum\relax%
\ifnum\c@pgfmath@countc>96\relax%
\advance\c@pgfmath@countc by-87\relax%
\else
\ifnum\c@pgfmath@countc>64\relax%
\advance\c@pgfmath@countc by-55\relax%
\else
\advance\c@pgfmath@countc by-48\relax%
\fi%
\fi%
\ifnum\c@pgfmath@countc<\pgfmath@base\relax%
\multiply\c@pgfmath@countc by\c@pgfmath@counta%
\advance\c@pgfmath@countb by\c@pgfmath@countc%
\divide\c@pgfmath@counta by\pgfmath@base\relax%
\let\pgfmath@next\pgfmathbasetodec@@@%
\else
\pgfmath@error{Digit `#1' invalid for base \pgfmath@base}{}%
\let\pgfmath@next=\relax%
\fi%
\fi%
\pgfmath@next}
\def\pgfmathbasetodec@@@@{%
\expandafter\pgfmath@ensurenumberlength\expandafter{\pgfmath@base@macro}%
}
% \pgfmathdectobase
%
% Convert a representation of an integer from
% base 10 to the specified base. Letters for bases
% greater than 10 are in lowercase.
%
% #1 - a macro to store the result.
% #2 - a number in base 10 (in a macro, not a register)
% #3 - the required base.
%
% e.g.
%
% \pgfmathdectobase\mynumber{127}{16}
%
% \mynumber <- 7f
%
\def\pgfmathdectobase#1#2#3{%
\pgfmath@checknumber{#2}%
\pgfmath@checkbase{#3}%
\c@pgfmath@counta=#2\relax%
\let#1=\pgfmath@empty%
\pgfmathloop
\ifnum\c@pgfmath@counta>0\relax%
\c@pgfmath@countb=\c@pgfmath@counta%
\divide\c@pgfmath@countb by#3\relax%
\multiply\c@pgfmath@countb by-#3\relax%
\advance\c@pgfmath@countb by\c@pgfmath@counta%
\edef#1{\csname pgfmath@lowercase digit@\the\c@pgfmath@countb\endcsname#1}%
\divide\c@pgfmath@counta by#3\relax%
\repeatpgfmathloop%
\pgfmath@ensurenumberlength{#1}}
% \pgfmathdectoBase
%
% Convert a representation of an integer from
% base 10 to the specified base. Letters for bases
% greater than 10 are in uppercase.
%
% #1 - a macro to store the result.
% #2 - a number in base 10 (in a macro, not a register)
% #3 - the required base.
%
% e.g.
%
% \pgfmathdectoBase\mynumber{127}{16}
%
% \mynumber <- 7F
%
\def\pgfmathdectoBase#1#2#3{%
\pgfmath@checkbase{#3}%
\pgfmath@checknumber{#2}%
\c@pgfmath@counta=#2\relax%
\let#1=\pgfmath@empty%
\pgfmathloop
\ifnum\c@pgfmath@counta>0\relax%
\c@pgfmath@countb=\c@pgfmath@counta%
\divide\c@pgfmath@countb by#3\relax%
\multiply\c@pgfmath@countb by-#3\relax%
\advance\c@pgfmath@countb by\c@pgfmath@counta%
\edef#1{\csname pgfmath@uppercase digit@\the\c@pgfmath@countb\endcsname#1}%
\divide\c@pgfmath@counta by#3\relax%
\repeatpgfmathloop%
\pgfmath@ensurenumberlength{#1}}
\def\pgfmath@base@digits@create{%
\def\pgfmath@base@digit@style{lowercase digit}%
\c@pgfmath@counta=0\relax%
\pgfmath@base@digits@create@0123456789abcdefghijklmnopqrstuvwxyz\pgfmath@base@digits@create%
\def\pgfmath@base@digit@style{uppercase digit}%
\c@pgfmath@counta=0\relax%
\pgfmath@base@digits@create@0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\pgfmath@base@digits@create}
\def\pgfmath@base@digits@create@#1{%
\ifx\pgfmath@base@digits@create#1\relax%
\else%
\expandafter\pgfmath@def\expandafter{\pgfmath@base@digit@style}{\the\c@pgfmath@counta}{#1}%
\advance\c@pgfmath@counta by1\relax%
\expandafter\pgfmath@base@digits@create@%
\fi}
\pgfmath@base@digits@create
% \pgfmathbasetobase
%
% Convert a representation of an integer from
% between the specified bases. Letters for target
% bases greater than 10 are in uppercase.
%
% #1 - a macro to store the result.
% #2 - a number (in a macro, not a register)
% #3 - the source base.
% #4 - the target base.
%
% e.g.
%
% \pgfmathbasetobase\mynumber{4321}{5}{9}
%
% \mynumber <- 721
%
\def\pgfmathbasetobase#1#2#3#4{%
\pgfmathbasetodec{\pgfmath@base@temp}{#2}{#3}%
\pgfmathdectobase{#1}{\pgfmath@base@temp}{#4}%
}
% \pgfmathbasetobase
%
% Convert a representation of an integer from
% between the specified bases. Letters for target
% bases greater than 10 are in uppercase.
%
% #1 - a macro to store the result.
% #2 - a number (in a macro, not a register)
% #3 - the source base.
% #4 - the target base.
%
% e.g.
%
% \pgfmathbasetobase\mynumber{1234}{5}{12}
%
% \mynumber <- 142
%
\def\pgfmathbasetoBase#1#2#3#4{%
\pgfmathbasetodec{\pgfmath@base@temp}{#2}{#3}%
\pgfmathdectoBase{#1}{\pgfmath@base@temp}{#4}%
}
\def\pgfmath@checkbase#1{%
\ifnum#1<2\relax%
\pgfmath@error{Cannot process numbers in base `#1'.}{}%
\else%
\ifnum#1>36\relax%
\pgfmath@error{Cannot process numbers in base `#1'.}{}%
\fi%
\fi}
\def\pgfmath@checknumber#1{%
\expandafter\pgfmath@checknumber@#1\pgfmath@}
\def\pgfmath@checknumber@#1#2\pgfmath@{%
\ifx#1-%
\pgfmath@error{Cannot process negative numbers.}{}%
\fi}
% \pgfmath@ensurenumberlength
%
% Internal macro for making a representation of a number have
% a specific length, byte prefixing zeros to the number.
%
% #1 - a macro containing a representation of an integer.
% #2 - the number of digits to ensure.
%
% e.g.
%
% \foo <- 7FF
%
% \pgfmathsetnumberlength{8}%
% \pgfmath@ensurenumberlength\foo
%
% \foo <- 000007FF
%
\def\pgfmath@ensurenumberlength#1{%
\def\pgfmath@base@tempa{#1}%
\expandafter\c@pgfmath@counta\pgfmath@basenumberlength\relax%
\expandafter\pgfmath@ensurenumberlength@#1\pgfmath@ensurenumberlength}
\def\pgfmath@ensurenumberlength@#1{%
\ifx\pgfmath@ensurenumberlength#1\relax%
\expandafter\pgfmath@ensurenumberlength@@%
\else%
\advance\c@pgfmath@counta by-1\relax%
\expandafter\pgfmath@ensurenumberlength@
\fi}
\def\pgfmath@ensurenumberlength@@{%
\edef\pgfmath@base@tempb{\pgfmath@base@tempa}%
\pgfmath@ensurenumberlength@@@}
\def\pgfmath@ensurenumberlength@@@{%
\ifnum\c@pgfmath@counta>0\relax%
\advance\c@pgfmath@counta by-1\relax%
\edef\pgfmath@base@tempb{0\pgfmath@base@tempb}%
\expandafter\pgfmath@ensurenumberlength@@@%
\fi%
\expandafter\edef\pgfmath@base@tempa{\pgfmath@base@tempb}}
\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%
}