//Zagitov Asgar
//17 in list

// Print a table of a given function f, computed by taylor series

// function to compute
let f(x) = 0.5 * log(x)

let a = 0.2
let b = 0.7
let n = 10

// Define a function to compute f using naive taylor series method

let taylor_nf x n = (1. / (2. * float(n) + 1.)) * ((x - 1.)/(x + 1.) ** (2. * float(n) + 1.))

let rec taylor_naive_loop f x n iter =
    if (abs(f x n) < 0.00000001) then (f x n, 1);
    else (+) fst((f x n)) fst((taylor_naive_loop f x (n + 1)))

let taylor_naive x = taylor_naive_loop taylor_nf x 0

// Define a function to do the same in a more efficient way
let rec taylor_loop prev x n =
    let current = (2.*float(n) - 1.)/(2.*float(n) + 1.) * (((x - 1.)/(x + 1.)) ** 2.) * prev
    if (abs(current) < 0.00000001) then current;
    else (+) prev (taylor_loop current x (n + 1))

let taylor x =
    let current = (float(x) - 1.)/(float(x) + 1.)
    taylor_loop current x 1

let main =
   for i = 0 to n do
     let x = a+(float i)/(float n)*(b-a)
     printfn "%5.2f  %10.6f  %10.6f   %10.6f" x (f x) (taylor_naive x) (taylor x)

main