Matlab class for large binary numbers

classdef bin
    % Class for binary numbers of up to 2^16 digits
    % Main property is Expo, the vector of exponents, e.g. [0 1 2] for 7.
    % bin([])      == bin(0,'dec') == bin('0')   == bin('') == bin
    % bin([0 1 2]) == bin(7,'dec') == bin('111')
    % bin([m n ...],'pre') preallocates an array of size [m n ...] (use [m 1] or [1 m] for vectors)

    properties
        Expo  % exponents where the binary number has a 1
        Weight  % length of Expo, number of binary 1s
        Maxi  % highest exponent (Maxi+1 is the length of a positive binary number)
    end

    methods

        function o = bin(x,parameter)  % constructor
            if nargin == 0
                o = bin('') ;
            elseif nargin==1
                if isnumeric(x)
                    if ~isempty(x)
                        o.Expo   = uint16(   sort(x)          ) ;
                        o.Weight = uint16(   length(o.Expo)   ) ;
                    else
                        o.Expo   = uint16(   zeros(1,0)       ) ;
                        o.Weight = uint16(   0                ) ;
                    end
                else
                    long = length(x) ;
                    o.Weight = uint16(   sum( char2mat(x) )   ) ;
                    expo     = uint16(   zeros(1,o.Weight)    ) ;
                    count = 1 ;
                    for m=0:long-1
                        if x(long-m)=='1'
                            expo(count) = m ;
                            count = count+1 ;
                        end
                    end
                    o.Expo = expo ;
                end
                o.Maxi = max(o.Expo) ;
            else
                if strcmp(parameter,'dec')  % dec for decimal, intended for integers up to 2^16
                    if x==0
                        o = bin('0') ;
                    else
                        long = floor( log2(double(x)) ) + 1 ;
                        X = double(x) ;
                        str = repmat('0',1,long) ;
                        count = long-1;
                        while count >= 0
                            rest = X - 2^count ;
                            if rest >= 0
                                X = rest ;
                                str(long-count) = '1' ;
                            end
                            count = count - 1 ;
                        end
                        o = bin(str) ;
                    end
                elseif strcmp(parameter,'pre')  % pre for pre-allocate
                    o = repmat( bin , x ) ;
                end
            end
        end

        function y = sym(o)  % to symbolic object (overload)
            s = sym(0) ;
            for m=1:o.Weight
                s = s + 2^(sym( o.Expo(m) )) ;
            end
            y = s ;
        end
        function y = uint16(o)  % to uint16 (overload)
            s = uint16(0) ;
            for m=1:o.Weight
                s = s + 2^o.Expo(m) ;
            end
            y = s ;
        end
        function y = string(o)  % to string
            if ~isequal( bin([]) , o )
                long = o.Maxi + 1 ;
                s = repmat('0',1,long) ;
                for m=1:o.Weight
                    s( long - o.Expo(m) ) = '1' ;
                end
                y = s ;
            else
                y = '0' ;
            end
        end
        function y = bitand(x1,x2)  % overload bitand
            y = bin( intersect(x1.Expo,x2.Expo) ) ;
        end
        function y = bitor(x1,x2)  % overload bitor
            y = bin( union(x1.Expo,x2.Expo) ) ;
        end
        function y = bitxor(x1,x2)  % overload bitxor
            y = bin(   setdiff( union(x1.Expo,x2.Expo) , intersect(x1.Expo,x2.Expo) )   ) ;
        end
        function y = eq(x1,x2)  % overload ==
            y = isequal(x1,x2) ;
        end
        function y = ne(x1,x2)  % overload ~=
            y = ~isequal(x1,x2) ;
        end
        function y = plus(x1,x2)  % overload +
            e1 = x1.Expo ;
            e2 = x2.Expo ;
            OR = union(e1,e2) ;
            AND = intersect(e1,e2) ;
            XOR = setdiff(OR,AND) ;
            if ~isempty(AND)  % if there is overflow
                y = bin(XOR) + bin(AND+1) ;  % recursion
            else
            y = bin(XOR) ;
            end
        end
        function y = mtimes(x1,x2)  % overload *
            if x1.Maxi > x2.Maxi
                a = x2 ;
                b = x1 ;
            else
                a = x1 ;
                b = x2 ;
            end  % if one of the binary numbers is longer, that is now b
            s = bin('0') ;  % sum
            for m = 1 : a.Weight
                s = s + bin( b.Expo + a.Expo(m) ) ;
            end
            y = s ;
        end

    end

end

%{
function [y] = char2mat(x)
% Turns a matrix of type CHAR without spaces
% into a matrix of type DOUBLE.
    high = size(x,1) ;
    wide = size(x,2) ;
    Y = zeros(high,wide) ;
    for m = 1:high
        for n = 1:wide
            Y(m,n) = str2double( x(m,n) ) ;
        end
    end
    y = Y ;
end
%}