%--------------------------------------------------------------------------
% modulo_rng.m                                      (P335: 3/05)
%
% Modulo random number generator
% Creates a squence of psuedo-random numbers in range [0,1) using the algorithm:
%    x(i) = a*x(i-1) + c (mod(m))
% The maxiumum "cycle time" of this type of generator is m however a poor
% choice of a, c, and m can result in a MUCH shorter cycle time as was
% the case with the disaterous IBM (a=65539, c=0, m=2^31) generator.
%
% Here are some "good" generators (although they have relatively small m vales):
%   (a,c,m) = (17221,107839,510300), (4096,150889,714025), (2416,374441,1771875)
% Here's an obviously "bad" generator:
%   (a,c,m) = (1277,0,2^15)
%
% This program generates a sequnce of NUM psuedo-random numbers in the array
% x(i) and plots x(i) versus i.
%
% PRESS F5 KEY TO RUN
% 
clear all;  %Clears all variables

%------------------------------------------------------------------------
%USER SET PARAMETERS (all integers):
NUM=1000;  %Total number of numbers generated
a=29;      % Define the (a,m,c)-generator:
c=7;
m=2^20;

seed=1071;  % Seed value to start generator
%-------------------------------------------------------------------------

% start with 1-dim array of zeros
x=zeros(1,NUM);

% use for loop to fill x(i) array with sequence of random numbers
nold=seed;
for i=1:NUM
	nnew=mod((a*nold+c),m);
	x(i)=nnew/m;
	nold=nnew;
end

figure(1);    %create figure window
plot(x,'.');  %plot x(i) values as points
axis([0 NUM -0.5 1.5]); %sets x and y range for plot
title(['a=',num2str(a),' m=',num2str(m), ' c=',num2str(c),':  ',num2str(NUM), ' random numbers'])