\pgfmathdectobase macro \pgfmathresult digit index or bitwise operators

Question

Is there a way to access each digit of a macro returned by \pgfmathdectobase (or \pgfmathresult) which is a binary number ? This would be useful for a function which prints the power set of a given set (according to binary representations of numbers between 0 and 2^|given set|).

I can think of two versions 1) convert macro to an array and loop or 2) calculate size of macro and loop with \foreach if there is way to access the digits. Unfortunately I was not able to find anything near in the pgfmanual.

Also another possible solution would be with bit-masks. Does tikz support anything like that? Or any idea on a package that does?

I would be happy with any other package that can use the results from \pgfmathdectobase, too, if there is way to use it outside of tikz. Thanks!

Answer 1

In order to examine bit by bit the number, the scheme might be like this

\def\temp{10111}
\newcount\bitnumber
\def\slowbinary#1{%
  \ifx\relax#1% end
  \else
    \advance\bitnumber by 1
    \ifcase#1\relax\docasezero\or\docaseone\fi
  \expandafter\slowbinary
  \fi}
\def\processbinary#1{\bitnumber=-1 % reset the counter (we will start at 0)
  \expandafter\slowbinary#1\relax}

\def\docasezero{\message{^^JZero seen}}
\def\docaseone{\message{^^JOne seen}}

\processbinary\temp
\processbinary{1010}

In case you need to start from the less significant bit, you have to reverse the number first.

\makeatletter
\def\processbinaryrev#1{%
  \bitnumber=-1 % reset the counter (we will start at 0)
  \@reverse{#1}%
  \expandafter\slowbinary\@esrever \relax}

\def\@reverse#1{%
  \edef\@temp{#1}%
  \def\@esrever{}%
  \loop\unless\ifx\@temp\@empty
    \edef\@esrever{\expandafter\@car\@temp\@nil\@esrever}%
    \edef\@temp{\expandafter\@cdr\@temp\@nil}%
  \repeat}
\makeatother

\processbinaryrev\temp

There are many loops around for reversing strings. Maybe also PGF has some.

Instead of \temp you can use \pgfmathresult or the first argument to \pgfmathdectobase.

Of course you'll give more meaningful actions to \docasezero and \docaseone; these actions can use the value of \bitnumber. You can define a set of macros as

\def\docasezero{\csname casezero\romannumeral\bitnumber\endcsname}
\def\docaseone{\csname caseone\romannumeral\bitnumber\endcsname}

\def\casezero{What to do when bit 0 is 0}
\def\caseone{What to do when bit 0 is 1}
\def\casezeroi{What to do when bit 1 is 0}
\def\caseonei{What to do when bit 1 is 1}
\def\casezeroii{What to do when bit 2 is 0}
\def\caseoneii{What to do when bit 2 is 1}
...

Here is a complete example (where I've changed a bit the programming style, using @ and constants provided by the LaTeX kernel):

\documentclass[a4paper]{article}

\makeatletter
\newcount\@bitnumber

\def\@slowbinary#1{%
  \ifx\relax#1% end
  \else
    \advance\@bitnumber\@ne
    \ifcase#1\relax\do@casezero\or\do@caseone\fi
  \expandafter\@slowbinary
  \fi}

\def\@reverse#1{%
  \edef\@temp{#1}%
  \def\@esrever{}%
  \loop\unless\ifx\@temp\@empty
    \edef\@esrever{\expandafter\@car\@temp\@nil\@esrever}%
    \edef\@temp{\expandafter\@cdr\@temp\@nil}%
  \repeat}

% \def\processbinary#1{\@bitnumber\m@ne
%   \expandafter\@slowbinary#1\relax}

\def\processbinaryrev#1{\@reverse{#1}\@bitnumber=-1
  \expandafter\@slowbinary\@esrever \relax}

\def\do@casezero{\csname casezero\romannumeral\@bitnumber\endcsname\relax}
\def\do@caseone{\csname caseone\romannumeral\@bitnumber\endcsname\relax}

\makeatother

\def\casezero{What to do when bit 0 is 0\par}
\def\caseone{What to do when bit 0 is 1\par}
\def\casezeroi{What to do when bit 1 is 0\par}
\def\caseonei{What to do when bit 1 is 1\par}
\def\casezeroii{What to do when bit 2 is 0\par}
\def\caseoneii{What to do when bit 2 is 1\par}
\def\casezeroiii{What to do when bit 3 is 0\par}
\def\caseoneiii{What to do when bit 3 is 1\par}
\def\casezeroiv{What to do when bit 4 is 0\par}
\def\caseoneiv{What to do when bit 4 is 1\par}
\def\casezerov{What to do when bit 5 is 0\par}
\def\caseonev{What to do when bit 5 is 1\par}

\def\temp{10111}

\begin{document}

\temp

\processbinaryrev\temp

\bigskip

101110

\processbinaryrev{101110}

\end{document}

Answer 2

From your sub-question about bit masks I assume that you are dealing with bin/oct/dec/hex bases only? If that is the case, I strongly recommend using the bitset package by Heiko Oberdiek, which provides all common operators for bit-wise manipulation of data.