confusion regarding code of FFT decimation in time?

Below is the code , i got it from MATLAB FEX.

Although i am getting valid answers using this function but I am confused regarding value/variable "Half" and its justification in context/view of decimation in time

function [ y ] = FFT_DIT_R2(x)            

p= nextpow2(length(x))                          % checking the size of the input array
x= [x zeros(1,(2^p)-length(x))]                 % complementing an array of zeros if necessary
N= length(x)                                    % computing the array size
S= log2(N)                                      % computing the number of conversion stages
Half= 1                                         % Seting the initial "Half" value
x= bitrevorder(x)                               

for stage= 1:S                                  % stages of transformation
           stage
    for index= 0:(2^stage):(N-1)                % series of "butterflies" for each stage
               index
        for n= 0:(Half-1)                       % creating "butterfly" and saving the results
               n
               pos= n+index+1                   % index of the data sample
               pow= (2^(S-stage))*n             % part of power of the complex multiplier
               w= exp((-1i)*(2*pi)*pow/N)       % complex multiplier
               a= x(pos)+x(pos+Half).*w         % 1-st part of the "butterfly" creating operation
               b= x(pos)-x(pos+Half).*w         % 2-nd part of the "butterfly" creating operation
               x(pos)= a                        % saving computation of the 1-st part
               x(pos+Half)= b                   % saving computation of the 2-nd part
        end;
    end;
Half= 2*Half                                    % computing the next "Half" value
end;

y= x;                                           % returning the result from function
end