{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE ScopedTypeVariables #-}

module PPL.Internal
  ( uniform,
    Prob (..),
    Meas,
    score,
    scoreLog,
    sample,
    samples,
    newTree,
    HashMap,
    Tree(..),
  )
where

import Control.Monad
import Control.Monad.IO.Class
import Control.Monad.Trans.Class
import Control.Monad.Trans.Writer
import Data.Bifunctor
import Data.Monoid
import qualified Language.Haskell.TH.Syntax as TH
import Numeric.Log
import System.Random hiding (split, uniform)
import qualified System.Random as R
import Data.IORef
import System.IO.Unsafe
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.Vector.Hashtables as H
import Data.Word
import Data.Bits

type HashMap k v = H.Dictionary (H.PrimState IO) UM.MVector k UM.MVector v

-- Simple hashing scheme into 64-bit space based on mzHash64
data Hash = Hash Int Word64 deriving (Eq, Ord, Show)

unhash :: Hash -> Word64
unhash (Hash _ state) = state

pushbit :: Bool -> Hash -> Hash
pushbit b (Hash i state) = Hash (i+1) $ (0xB2DEEF07CB4ACD43 * (fromIntegral i + fromBool b)) `xor` (state `shiftL` 2) `xor` (state `shiftR` 2)
  where
    fromBool True = 1
    fromBool False = 0

initHash = Hash 0 0xE297DA430DB2DF1A

-- Reimplementation of the LazyPPL monads to avoid some dependencies

data Tree = Tree
  { draw :: !Double,
    split :: (Tree, Tree)
  }

{-# INLINE newTree #-}
newTree :: IORef (HashMap Word64 Double, StdGen) -> Tree
newTree s = go initHash
  where
    go :: Hash -> Tree
    go id = Tree (unsafePerformIO $ do
      (m, g) <- readIORef s
      H.lookup m (unhash id) >>= \case
        Nothing -> do
          let (x, g') = R.random g
          H.insert m (unhash id) x
          writeIORef s (m, g')
          pure x
        Just x -> pure x) (go (pushbit False id), go (pushbit True id))

newtype Prob a = Prob {runProb :: Tree -> a}

instance Monad Prob where
  Prob f >>= g = Prob $ \t ->
    let (t1, t2) = split t
        (Prob g') = g (f t1)
     in g' t2

instance Functor Prob where fmap = liftM

instance Applicative Prob where pure = Prob . const; (<*>) = ap

uniform = Prob $ \(Tree r _) -> r

newtype Meas a = Meas (WriterT (Product (Log Double)) Prob a)
  deriving (Functor, Applicative, Monad)

{-# INLINE score #-}
score :: Double -> Meas ()
score = scoreLog . Exp . log . max eps
  where
    eps = $(TH.lift (2 * until ((== 1) . (1 +)) (/ 2) (1 :: Double))) -- machine epsilon, force compile time eval

{-# INLINE scoreLog #-}
scoreLog :: Log Double -> Meas ()
scoreLog = Meas . tell . Product

{-# INLINE sample #-}
sample :: Prob a -> Meas a
sample = Meas . lift

{-# INLINE samples #-}
samples :: forall a. Meas a -> Tree -> [(a, Log Double)]
samples (Meas m) = map (second getProduct) . runProb f
  where
    f = runWriterT m >>= \x -> (x :) <$> f