gameServer/OfficialServer/Glicko2.hs
author sheepluva
Mon, 05 Aug 2019 00:20:45 +0200
changeset 15295 f382ec6dba11
parent 11390 36e1bbb6ecea
permissions -rw-r--r--
In hindsight my emscripten-ifdef (70d416a8f63f) is nonsense. As fpcrtl_glShaderSource() would not be defined and lead to compiling issues. So either it's 3 ifdefs (in pas2cRedo, pas2cSystem and misc.c), in order to toggle between fpcrtl_ and the native function, or alternatively have no ifdef for it at all. I'm going with none at all, which means emscripten will compile with the original (const) function prototype, being wrapped by the fpcrtl_ function, same as non-emscripten builds.

{-
    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