{-# LANGUAGE MultiParamTypeClasses #-}
module Basement.Alg.Mutable
    ( inplaceSortBy
    ) where

import           GHC.Types
import           GHC.Prim
import           Basement.Compat.Base
import           Basement.Numerical.Additive
import           Basement.Numerical.Multiplicative
import           Basement.Types.OffsetSize
import           Basement.PrimType
import           Basement.Monad
import           Basement.Alg.Class

inplaceSortBy :: (PrimMonad prim, RandomAccess container prim ty) 
              => (ty -> ty -> Ordering)
              -- ^ Function defining the ordering relationship
              -> (Offset ty) -- ^ Offset to first element to sort
              -> (CountOf ty) -- ^ Number of elements to sort
              -> container -- ^ Data to be sorted
              -> prim ()
inplaceSortBy :: forall (prim :: * -> *) container ty.
(PrimMonad prim, RandomAccess container prim ty) =>
(ty -> ty -> Ordering)
-> Offset ty -> CountOf ty -> container -> prim ()
inplaceSortBy ty -> ty -> Ordering
ford Offset ty
start CountOf ty
len container
mvec
    = Offset ty -> Offset ty -> prim ()
qsort Offset ty
start (Offset ty
start Offset ty -> CountOf ty -> Offset ty
forall ty. Offset ty -> CountOf ty -> Offset ty
`offsetPlusE` CountOf ty
len Offset ty -> Offset ty -> Offset ty
forall a. Offset a -> Offset a -> Offset a
`offsetSub` Offset ty
1)
    where
        qsort :: Offset ty -> Offset ty -> prim ()
qsort Offset ty
lo Offset ty
hi
            | Offset ty
lo Offset ty -> Offset ty -> Bool
forall a. Ord a => a -> a -> Bool
>= Offset ty
hi  = () -> prim ()
forall a. a -> prim a
forall (f :: * -> *) a. Applicative f => a -> f a
pure ()
            | Bool
otherwise = do
                p <- Offset ty -> Offset ty -> prim (Offset ty)
partition Offset ty
lo Offset ty
hi
                qsort lo (pred p)
                qsort (p+1) hi
        pivotStrategy :: Offset ty -> Offset ty -> prim ty
pivotStrategy (Offset Int
low) hi :: Offset ty
hi@(Offset Int
high) = do
            let mid :: Offset ty
mid = Int -> Offset ty
forall ty. Int -> Offset ty
Offset (Int -> Offset ty) -> Int -> Offset ty
forall a b. (a -> b) -> a -> b
$ (Int
low Int -> Int -> Int
forall a. Additive a => a -> a -> a
+ Int
high) Int -> Int -> Int
forall a. IDivisible a => a -> a -> a
`div` Int
2
            pivot <- container -> Offset ty -> prim ty
forall container (prim :: * -> *) ty.
RandomAccess container prim ty =>
container -> Offset ty -> prim ty
read container
mvec Offset ty
mid
            read mvec hi >>= write mvec mid
            write mvec hi pivot -- move pivot @ pivotpos := hi
            pure pivot
        partition :: Offset ty -> Offset ty -> prim (Offset ty)
partition Offset ty
lo Offset ty
hi = do
            pivot <- Offset ty -> Offset ty -> prim ty
pivotStrategy Offset ty
lo Offset ty
hi
            -- RETURN: index of pivot with [<pivot | pivot | >=pivot]
            -- INVARIANT: i & j are valid array indices; pivotpos==hi
            let go Offset ty
i Offset ty
j = do
                    -- INVARIANT: k <= pivotpos
                    let fw :: Offset ty -> prim (Offset ty, ty)
fw Offset ty
k = do ak <- container -> Offset ty -> prim ty
forall container (prim :: * -> *) ty.
RandomAccess container prim ty =>
container -> Offset ty -> prim ty
read container
mvec Offset ty
k
                                  if ford ak pivot == LT 
                                    then fw (k+1)
                                    else pure (k, ak)
                    (i, ai) <- Offset ty -> prim (Offset ty, ty)
fw Offset ty
i -- POST: ai >= pivot
                    -- INVARIANT: k >= i
                    let bw Offset ty
k | Offset ty
kOffset ty -> Offset ty -> Bool
forall a. Eq a => a -> a -> Bool
==Offset ty
i = (Offset ty, ty) -> prim (Offset ty, ty)
forall a. a -> prim a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Offset ty
i, ty
ai)
                             | Bool
otherwise = do ak <- container -> Offset ty -> prim ty
forall container (prim :: * -> *) ty.
RandomAccess container prim ty =>
container -> Offset ty -> prim ty
read container
mvec Offset ty
k
                                              if ford ak pivot /= LT
                                                then bw (pred k)
                                                else pure (k, ak)
                    (j, aj) <- bw j -- POST: i==j OR (aj<pivot AND j<pivotpos)
                    -- POST: ai>=pivot AND (i==j OR aj<pivot AND (j<pivotpos))
                    if i < j
                        then do -- (ai>=p AND aj<p) AND (i<j<pivotpos)
                            -- swap two non-pivot elements and proceed
                            write mvec i aj
                            write mvec j ai
                            -- POST: (ai < pivot <= aj)
                            go (i+1) (pred j)
                        else do -- ai >= pivot 
                            -- complete partitioning by swapping pivot to the center
                            write mvec hi ai 
                            write mvec i pivot
                            pure i
            go lo hi
{-# INLINE inplaceSortBy #-}