Write a matlab routine in double precision to implement the following algorithm for computing

integer k; real a,b,c,d,e,f,g;

for k=1 to 5 do

output k, f, |f-pi|, g, |g-pi|

end for

which converges faster, f or g?

How accurate are the final values?

Also compare with the double precision computation or 4arctan(1).

(note that the value of pi correct to 36 digits is 3.141592653589793236846264338327950288)