function demo2_1a;
% the ``IDEAL'' bisection method 
% for solving f(x)=0 on [A,B]
% 
eps=0.00001;
A=1;
B=4;
%
a=A;
b=B;
p=(a+b)/2;
%
% MAIN LOOP
while (f(p)~=0) & (abs(b-a)>eps)
if (f(a)*f(p))<0 
   a=a;  % this line is redundant --- it does nothing, it is left for better resemblance with the algorithm in the book
   b=p;
else    
   a=p;
   b=b; % this line is again, redundant
end
p=(a+b)/2;
end
%% To display all decimals, switch default print formatting to ''long''
format long 
%%%%%
p
pi
abs(pi-p)

function y=f(x);
y=sin(x);