module lab1

open System
open System.Net
open System.IO
open System.Collections.Specialized

// почтовый адрес
let email = "annafedyushkina@gmail.com"
// общий тип для возвращаемых вашими функциями значений, где первая часть кортежа это само значение функции, вторая - кол-во операций
type Result = float * int
let delta = 1e-10

// *** Первая часть

let fTailor x : float = (1 + x ** 2) / 2 * atan x - x / 2 // функция, которую раскладываем
let n, a, b = 20., 0.1, 0.6 // интервал

let tailor x : Result =
    let rec tailor_function x result i =
        let current = ((-1)**(float(n) + 1))*(x**(2*(float(n)) + 1))/(4*((float(n))**2) - 1)
        if abs (current) < delta
            then (result, i)
        else
            tailor_function x (result + current) (i + 1)
    tailor_function x 0. 1

let tailorA x : Result =
    let rec tailor_function x result prev i =
        let current = prev*(-1)*(x**2)*(4*((i-1)**2) - 1)/(4*(n**2 - 1)
        if abs (current) < delta
            then (result, i)
        else
            tailor_function x (result + current) current (i + 1)
    tailor_function x 0. x 1


let printTailor () =
    [a .. (b-a)/n .. b]
    |> List.map (fun x -> let (firstRes, firstCou), (secondRes, secondCou) = tailor x, tailorA x in (x, firstRes, firstCou, secondRes, secondCou, fTailor x))
    |> List.iter (fun (a,b,c,d,e,f) -> printf "%f\t%f\t%d\t%f\t%d\t%f\n" a b c d e f )

// *** Вторая часть

let fSolve = [ (fun x -> x + (x ** (1./2.)) + (x ** (1./3.)) - 2.5); // функции, решения которых ищем
                (fun x -> x - 1. / (3. + sin(3.6*x)));
                fun x -> 0.1*(x**2) - x*(log(x))]

let diap = [(0.4, 1.); (0., 0.85); (1., 2.)]

let iter f a b : Result = (42., 0)
    let touch = (b-a) / (f b - f a)
    let rec iterA i f x =
        let x1 = x - touch * (f x)
        if abs (x1 - x) < delta
            then (x1, i)
        else
            iterA (i + 1) f x1
    iterA 0 f ((a + b) / 2.)

let newton f a b : Result =
    let rec newtonA i f x xprev =
        if abs (x - xprev) < delta then
            (x, i)
        else
            newtonA (i + 1) f (x - (f x) * (x - xprev) / ((f x) - (f xprev))) x
    newtonA 0 f ((a + b) / 2.) a

let dichotomy =
    let rec dichotomyA i f a b : Result =
        let t = (a + b) / 2.
        if b - a < delta
            then (t, i)
        else
            if (f t) * (f a) < 0.
                then dichotomyA (i+1) f a t
            else dichotomyA (i+1) f t b
    dichotomyA 0

let printSolve () =
    [iter; newton; dichotomy]
    |> List.map (fun f -> f fSolve a b)
    |> List.iter (fun (res, cou) -> printf "%f\t%d\n" res cou)

let main () =
  let values = new NameValueCollection()
  values.Add("email", email)
  values.Add("content", File.ReadAllText(__SOURCE_DIRECTORY__ + @"/" + __SOURCE_FILE__))

  let client = new WebClient()
  let response = client.UploadValues(new Uri("http://mipt.eu01.aws.af.cm/lab1"), values)
  let responseString = Text.Encoding.Default.GetString(response)

  printf "%A\n" responseString