%% CS3220 -- Jan 27 2010
% Save this in a file with extension ".m"
% Then you can open it in Matlab and execute the "cells" one by one
% using "Evaluate Current Cell."
%
% First: a simple rounding error.
a = 1
a + 10^-6
a + 1e-8
a + 1e-14
a + 1e-16
%% Now try that with single precision
a = single(1)
a + 1e-6
a + 1e-8
a + 1e-14
a + 1e-16

%% Overflow.
a = single(1e38)
b = a + a + a
b - a - a
b = a + a + a + a
b - a - a - a

%% Discretization, graphically
% Generate a lot of points in the square [-0.5,0.5]^2
y = single(rand(100000,1)) - 0.5;
x = single(rand(100000,1)) - 0.5;
% plot them.  Use the zoom tool to zoom in.  Any structure visible?
plot(x,y, '.')
%%
% Shift them far from the origin (not even that far...)
plot(x + 1e4, y + 1e4, '.')
% Now zoom in; is there structure?
%%
% Shift them farther...
plot(x + 1e6, y + 1e6, '.')
%%
% ...and farther
plot(x + 2e6, y + 2e6, '.')
%%
% Now shift them to a boundary between exponent values
plot(x + 32768, y + 32768, '.')
% Zoom in.  What is going on here?

%% Rounding in the homework example
% show results in raw bits
format hex
single(4/3)
ans - 1
3 * ans
ans - 1
format
%%
% Now look at them in normal decimal output
format long
single(4/3)
ans - 1
3 * ans
ans - 1
format
% Try this in double precision -- why is the result different?