function eps64
% MCS471f04 Bisection Approximation for 64 bit Machine Epsilon:
%   maceps = min(eps: eps > 0; 1 + eps > 1); 
%   Matlab default word size is 64 bits;
clc % clear command window
fprintf('MCS471f04 Bisection Approximation for 64 bit Machine Epsilon:');
kmax = 100; % Maximum Bisections;
eps0 = 1; % start:
epsplus1 = 1 + eps0; %  Get floating point value of sum;
for k = 1:kmax 	% Bisection counter	
    epssave = eps0; % Save old value;
	eps0 = 1/2^k;   % Bisection Update Step for trial eps = 2^(1;
	epsplus1 = 1 + eps0; % Float of Sum;   
	fprintf('\n  k = %i; eps0 = %12.7e; eps0+1 = %22.16e;',k,eps0,epsplus1);
	if epsplus1 <= 1.e0  % This eps0 failed machine epsilon test!
        ksave = k-1; % turn counter back one to last success: 1+eps0 > 1;
		break; 	
	end 
end
fprintf('\nBisection Approximation Answer for 64 Bit Precision:');	
fprintf('\n ksave = %2i; epssave = 1/2^ksave = %12.7e; epssave+1 = %22.16e;' ...
    ,ksave,epssave,epssave+1);	
pchop = 1-log(epssave)/log(2.e0); % find chopping precision if maceps = 2^(1-pchop);
pround = -log(epssave)/log(2.e0); % find rounding precision if maceps = 2^(-pchop);
fprintf('\nprecision: pchop = %10.7f or pround = %10.7f binary digits?' ...
    ,pchop,pround);
fprintf('\n1. Which is Correct, the Official Chopped (2^(1-p)) ')
fprintf('\nor Rounded Value (2^(1-p)/2) for Precision p?');
fprintf('\n   Give a Written Answer with Your Justification Here:\n\n');
% Double check for rounding through refinement: 
fprintf('\n\nRounding Double Check Data to Sneak Up on a Better Answer:');
eps0 = 0;
deleps = 2^(-1-pchop); % start with bisection maceps/4;
fprintf('\n deleps = %12.7e;',deleps); 
for kd = 1:7   
	eps0 = eps0 + deleps;   
	epsplus1 = eps0 + 1;   
	fprintf('\n kd = %i; eps0 = %12.7e; eps0+1 = %22.16e',kd,eps0,epsplus1);
end
fprintf('\n2. Is Rounding or Chopping Demonstrated?');
fprintf('\n   Give a Written Answer to Question with Your Justification Here (see kd=3):\n\n');
fprintf('\n3. Can You Find A Smaller eps0 = epsilon?');
fprintf('\n   Write and Run Your Code Fragment Justification Here If You Can:\n\n');
% end MATLAB main function