{-# LANGUAGE FlexibleInstances          #-}

module HaskellWorks.Data.Excess.MinMaxExcess0
  ( MinMaxExcess0(..)
  , MaxExcess
  , MinExcess
  ) where

import qualified Data.Vector.Storable                 as DVS
import           Data.Word
import           HaskellWorks.Data.Bits.BitWise
import           HaskellWorks.Data.Bits.FixedBitSize
import           HaskellWorks.Data.Naive

type MinExcess = Int
type MaxExcess = Int
type Excess    = Int

class MinMaxExcess0 a where
  minMaxExcess0 :: a -> (MinExcess, Excess, MaxExcess)

instance MinMaxExcess0 [Bool] where
  minMaxExcess0 = go 0 0 0
    where go minE maxE e (x:xs)                   = let ne = if x then e - 1 else e + 1 in
                                                        go (minE `min` ne) (maxE `max` ne) ne xs
          go minE maxE e _                        = (minE, e, maxE)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (Naive Word8) where
  minMaxExcess0 = go 0 0 0 0 . naive
    where go minE maxE e n w | n < fixedBitSize w = let ne = if w .?. fromIntegral n then e - 1 else e + 1 in
                                                        go (minE `min` ne) (maxE `max` ne) ne (n + 1) w
          go minE maxE e _ _                       = (minE, e, maxE)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (Naive Word16) where
  minMaxExcess0 = go 0 0 0 0 . naive
    where go minE maxE e n w | n < fixedBitSize w = let ne = if w .?. fromIntegral n then e - 1 else e + 1 in
                                                        go (minE `min` ne) (maxE `max` ne) ne (n + 1) w
          go minE maxE e _ _                      = (minE, e, maxE)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (Naive Word32) where
  minMaxExcess0 = go 0 0 0 0 . naive
    where go minE maxE e n w | n < fixedBitSize w = let ne = if w .?. fromIntegral n then e - 1 else e + 1 in
                                                        go (minE `min` ne) (maxE `max` ne) ne (n + 1) w
          go minE maxE e _ _                      = (minE, e, maxE)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (Naive Word64) where
  minMaxExcess0 = go 0 0 0 0 . naive
    where go minE maxE e n w | n < fixedBitSize w = let ne = if w .?. fromIntegral n then e - 1 else e + 1 in
                                                        go (minE `min` ne) (maxE `max` ne) ne (n + 1) w
          go minE maxE e _ _                      = (minE, e, maxE)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 Word8 where
  minMaxExcess0 w = ( word8Excess0Min DVS.! fromIntegral w
                    , word8Excess0    DVS.! fromIntegral w
                    , word8Excess0Max DVS.! fromIntegral w
                    )
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 Word16 where
  minMaxExcess0 w = ( minExcessA `min` (minExcessB + allExcessA)
                    , allExcessA + allExcessB
                    , maxExcessA `max` (maxExcessB + allExcessA))
    where (minExcessA, allExcessA, maxExcessA) = minMaxExcess0 (fromIntegral  w        :: Word8)
          (minExcessB, allExcessB, maxExcessB) = minMaxExcess0 (fromIntegral (w .>. 8) :: Word8)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 Word32 where
  minMaxExcess0 w = ( minExcessA `min` (minExcessB + allExcessA)
                    , allExcessA + allExcessB
                    , maxExcessA `max` (maxExcessB + allExcessA))
    where (minExcessA, allExcessA, maxExcessA) = minMaxExcess0 (fromIntegral  w         :: Word16)
          (minExcessB, allExcessB, maxExcessB) = minMaxExcess0 (fromIntegral (w .>. 16) :: Word16)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 Word64 where
  minMaxExcess0 w = ( minExcessA `min` (minExcessB + allExcessA)
                    , allExcessA + allExcessB
                    , maxExcessA `max` (maxExcessB + allExcessA))
    where (minExcessA, allExcessA, maxExcessA) = minMaxExcess0 (fromIntegral  w         :: Word32)
          (minExcessB, allExcessB, maxExcessB) = minMaxExcess0 (fromIntegral (w .>. 32) :: Word32)
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (DVS.Vector Word8) where
  minMaxExcess0 = DVS.foldl gen (0, 0, 0)
    where gen :: (MinExcess, Excess, MaxExcess) -> Word8 -> (MinExcess, Excess, MaxExcess)
          gen (minE, e, maxE) w = let (wMinE, wE, wMaxE) = minMaxExcess0 w  in
                                  (minE `min` (wMinE + e), e + wE, maxE `max` (wMaxE + e))
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (DVS.Vector Word16) where
  minMaxExcess0 = DVS.foldl gen (0, 0, 0)
    where gen :: (MinExcess, Excess, MaxExcess) -> Word16 -> (MinExcess, Excess, MaxExcess)
          gen (minE, e, maxE) w = let (wMinE, wE, wMaxE) = minMaxExcess0 w  in
                                  (minE `min` (wMinE + e), e + wE, maxE `max` (wMaxE + e))
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (DVS.Vector Word32) where
  minMaxExcess0 = DVS.foldl gen (0, 0, 0)
    where gen :: (MinExcess, Excess, MaxExcess) -> Word32 -> (MinExcess, Excess, MaxExcess)
          gen (minE, e, maxE) w = let (wMinE, wE, wMaxE) = minMaxExcess0 w  in
                                  (minE `min` (wMinE + e), e + wE, maxE `max` (wMaxE + e))
  {-# INLINE minMaxExcess0 #-}

instance MinMaxExcess0 (DVS.Vector Word64) where
  minMaxExcess0 = DVS.foldl gen (0, 0, 0)
    where gen :: (MinExcess, Excess, MaxExcess) -> Word64 -> (MinExcess, Excess, MaxExcess)
          gen (minE, e, maxE) w = let (wMinE, wE, wMaxE) = minMaxExcess0 w  in
                                  (minE `min` (wMinE + e), e + wE, maxE `max` (wMaxE + e))
  {-# INLINE minMaxExcess0 #-}

word8Excess0Min :: DVS.Vector Int
word8Excess0Min =  DVS.fromList
  [  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1, -1, -3, -1, -3, -3, -5
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1, -1, -3, -1, -3, -3, -5
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1, -1, -3, -1, -3, -3, -5
  ,  0, -1, -1, -3, -1, -3, -3, -5, -1, -3, -3, -5, -3, -5, -5, -7
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1, -1, -3, -1, -3, -3, -5
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  0, -1,  0, -2,  0, -1, -1, -3,  0, -1,  0, -2,  0, -2, -2, -4
  ,  0, -1,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  0, -1,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  0, -2, -2, -4, -2, -4, -4, -6, -2, -4, -4, -6, -4, -6, -6, -8
  ]

word8Excess0 :: DVS.Vector Int
word8Excess0 =  DVS.fromList
  [  8,  6,  6,  4,  6,  4,  4,  2,  6,  4,  4,  2,  4,  2,  2,  0
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  0, -2
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  0, -2
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  0, -2
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  2,  0,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  0, -2
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  2,  0,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  4,  2,  2,  0,  2,  0,  0, -2,  2,  0,  0, -2,  0, -2, -2, -4
  ,  2,  0,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  2,  0,  0, -2,  0, -2, -2, -4,  0, -2, -2, -4, -2, -4, -4, -6
  ,  0, -2, -2, -4, -2, -4, -4, -6, -2, -4, -4, -6, -4, -6, -6, -8
  ]

word8Excess0Max :: DVS.Vector Int
word8Excess0Max =  DVS.fromList
  [  8,  6,  6,  4,  6,  4,  4,  2,  6,  4,  4,  2,  4,  2,  2,  0
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  1,  0
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  5,  3,  3,  1,  3,  1,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  7,  5,  5,  3,  5,  3,  3,  1,  5,  3,  3,  1,  3,  1,  1,  0
  ,  5,  3,  3,  1,  3,  1,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  5,  3,  3,  1,  3,  1,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  6,  4,  4,  2,  4,  2,  2,  0,  4,  2,  2,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  5,  3,  3,  1,  3,  1,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ,  4,  2,  2,  0,  2,  0,  1,  0,  3,  1,  1,  0,  2,  0,  1,  0
  ]