//module lab1

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

// почтовый адрес
let email = "nikitayusupov@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 = Math.Exp(Math.Cos(x)) * Math.Cos(Math.Sin(x)) // функция, которую раскладываем
let n, a, b = 20., 0.1, 0.6 // интервал

let tailor x : Result =
    let rec tailor' (n:int) acc (prevFactorial:float): Result =
        let nextCoefficient = Math.Cos((float)n * x) / ((prevFactorial * (float)n))
        if abs(nextCoefficient) < delta then ((acc + nextCoefficient), n)
        else tailor' (n + 1) (acc + nextCoefficient) ((float)n * prevFactorial)
    tailor' 1 1.0 1.0
let tailorA x : Result =
    let factorial n =
        let rec factorial' (n:int) (acc:float) =
            if n = 0 then acc
            else factorial' (n - 1) (acc * (float)n)
        factorial' n 1.0
    let coefficient n = Math.Cos((float)n * x) / (float)(factorial n)
    let rec tailorA' (n:int) acc : Result =
        let nextCoefficient = coefficient n
        if abs(nextCoefficient) < delta then ((acc + nextCoefficient), n)
        else tailorA' (n + 1) (acc + nextCoefficient)
    tailorA' 0 0.0

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 a' = 1.
let b' = 3.
let fSolve = fun x -> Math.Sin(Math.Log(x))-Math.Cos(Math.Log(x)) + 2. * Math.Log(x) // функция, решение которой ищем

let fDerivative f x = (f (x + delta) - f(x)) / delta

let iter f a b : Result =
    let lambda_0 = 1. / (fDerivative f ((a+b) / 2.))
    let rec iter' cnt prevX : Result =
        let nextX = prevX - lambda_0 * (f prevX)
        if abs(nextX - prevX) < delta then (nextX, cnt)
        else iter' (cnt + 1) nextX
    iter' 0 ((a + b) / 2.)
let newton f a b : Result =
    let rec newton' cnt prevX : Result =
        let nextX = prevX - (f prevX) / (fDerivative f prevX)
        if abs(nextX - prevX) < delta then (nextX, cnt)
        else newton' (cnt + 1) nextX
    newton' 0 ((a + b) / 2.)
let dichotomy =
    let rec dichotomyA i (f:float->float) (a:float) (b:float) : Result =
        let mid = (a + b) / 2.
        if b - a < delta then (mid, i)
        else if f(a) * f(mid) < 0. then dichotomyA (i + 1) f a mid
        else dichotomyA (i + 1) f mid b
    dichotomyA 0

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://91.239.142.110:13666/lab1"), values)
  let responseString = Text.Encoding.Default.GetString(response)

  printf "%A\n" responseString