%This script simulates the Linear congruential random number generator developed by Knuth.
%This random number generator generates random number uniformly distributed between 0 and 1.
%The random number generator implments a recursive algorithm of the form:
%
%    x(n) = (a*x(n-1)+c) mod (m) 
%    x(n) = ((a+c)*x(n-1)) mod m -> our implementation
%
%  where:     a - mulitplier from 0 <= a < m
%             c - increment 0 <= c < m
%             m - modulus 0 < m
%             x(-1) - iniital condition - seed
%
%To make the random number generator uniformly distributed between -1 and +1 we take each 
%sample from the random number generator; scale it; subtract by the mean of the 0 to 1 random
%number generator which is .5; and multiply by 2. Please note that that x(n-1) is the value 
%BEFORE any shifting is done or the recursive algorithm will not work.
%
%This simulation compares Matlabs random number generator and our developed random number 
%generator by displaying adjacent histograms.

clear
NUM_OF_POINTS = 10000;%000;
NUM_OF_BITS = 15;
Xn = zeros(NUM_OF_POINTS,1);
Yn = zeros(NUM_OF_POINTS,1);
seed = 5141; % $1415 The starting value 0 < seed < m
a = 3; %The Multiplier 0 <= a < m
c = 2^8; %The increment 0 <= c < m
m = 2^NUM_OF_BITS; %The modulus 0 < m

Xn(1) = seed;

for i = 2:NUM_OF_POINTS
   x = (a+c)*Xn(i-1);                       
   Xn(i) = x - m*(floor(x/m));  %calculate mod(x,m)
   Yn(i) = 2*((Xn(i)/m) - .5);  %Adjust the RNG to be distributed between -1 and +1
                                            %Notice we place the output in Yn instead of Xn so
                                            %Knuth's algorithm can operate properly.
end
matlab_RNG = rand(NUM_OF_POINTS,1);
subplot(2,1,1), hist(Yn),title('Histogram of my random number generator with distribution from -1 to 1');
matlab_RNG = (2*(matlab_RNG - .5));      %shift matlab's uniform RNG between -1 and +1
subplot(2,1,2), hist(matlab_RNG),title('Histogram of Matlab random number generator with distribution from -1 to 1');

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