{-

    Glicko2, as described in http://www.glicko.net/glicko/glicko2.pdf

-}

module OfficialServer.Glicko2 where

data RatingData = RatingData {

        ratingValue

        , rD

        , volatility :: Double

    }

data GameData = GameData {

        opponentRating :: RatingData,

        gameScore :: Double

    }

τ, ε :: Double

τ = 0.2

ε = 0.000001

g_φ :: Double -> Double

g_φ φ = 1 / sqrt (1 + 3 * φ^2 / pi^2)

calcE :: RatingData -> GameData -> (Double, Double, Double)

calcE oldRating (GameData oppRating s) = (

    1 / (1 + exp (g_φᵢ * (μᵢ - μ)))

    , g_φᵢ

    , s

    )

    where

        μ = (ratingValue oldRating - 1500) / 173.7178

        φ = rD oldRating / 173.7178

        μᵢ = (ratingValue oppRating - 1500) / 173.7178

        φᵢ = rD oppRating / 173.7178

        g_φᵢ = g_φ φᵢ

calcNewRating :: RatingData -> [GameData] -> (Int, RatingData)

calcNewRating oldRating [] = (0, RatingData (ratingValue oldRating) (173.7178 * sqrt (φ ^ 2 + σ ^ 2)) σ)

    where

        φ = rD oldRating / 173.7178

        σ = volatility oldRating

calcNewRating oldRating games = (length games, RatingData (173.7178 * μ' + 1500) (173.7178 * sqrt φ'sqr) σ')

    where

        _Es = map (calcE oldRating) games

        υ = 1 / sum (map υ_p _Es)

        υ_p (_Eᵢ, g_φᵢ, _) = g_φᵢ ^ 2 * _Eᵢ * (1 - _Eᵢ)

        _Δ = υ * part1

        part1 = sum (map _Δ_p _Es)

        _Δ_p (_Eᵢ, g_φᵢ, sᵢ) = g_φᵢ * (sᵢ - _Eᵢ)

        μ = (ratingValue oldRating - 1500) / 173.7178

        φ = rD oldRating / 173.7178

        σ = volatility oldRating

        a = log (σ ^ 2)

        f :: Double -> Double

        f x = exp x * (_Δ ^ 2 - φ ^ 2 - υ - exp x) / 2 / (φ ^ 2 + υ + exp x) ^ 2 - (x - a) / τ ^ 2

        _A = a

        _B = if _Δ ^ 2 > φ ^ 2 + υ then log (_Δ ^ 2 - φ ^ 2 - υ) else head . dropWhile ((>) 0 . f) . map (\k -> a - k * τ) $ [1 ..]

        fA = f _A

        fB = f _B

        σ' = (\(_A, _, _, _) -> exp (_A / 2)) . head . dropWhile (\(_A, _, _B, _) -> abs (_B - _A) > ε) $ iterate step5 (_A, fA, _B, fB)

        step5 (_A, fA, _B, fB) = let _C = _A + (_A - _B) * fA / (fB - fA); fC = f _C in

                                     if fC * fB < 0 then (_B, fB, _C, fC) else (_A, fA / 2, _C, fC)

        φ'sqr = 1 / (1 / (φ ^ 2 + σ' ^ 2) + 1 / υ)

        μ' = μ + φ'sqr * part1