linear-1.23.3: src/Linear/V4.hs

{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DeriveLift #-}

-----------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2012-2015 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  experimental
-- Portability :  non-portable
--
-- 4-D Vectors
----------------------------------------------------------------------------
module Linear.V4
  ( V4(..)
  , vector, point, normalizePoint
  , R1(..)
  , R2(..)
  , _yx
  , R3(..)
  , _xz, _yz, _zx, _zy
  , _xzy, _yxz, _yzx, _zxy, _zyx
  , R4(..)
  , _xw, _yw, _zw, _wx, _wy, _wz
  , _xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy
  , _wxy, _wxz, _wyx, _wyz, _wzx, _wzy
  , _xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz
  , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz
  , _wyzx, _wzxy, _wzyx
  , ex, ey, ez, ew
  ) where

#if !MIN_VERSION_base(4,18,0)
import Control.Applicative
#endif
import Control.DeepSeq (NFData(rnf))
import Control.Monad (liftM)
import Control.Monad.Fix
import Control.Monad.Zip
import Control.Lens as Lens hiding ((<.>))
import Data.Binary as Binary
import Data.Bytes.Serial
import Data.Data
import Data.Distributive
import Data.Foldable
import qualified Data.Foldable.WithIndex as WithIndex
import Data.Functor.Bind
import Data.Functor.Classes
import Data.Functor.Rep
import qualified Data.Functor.WithIndex as WithIndex
import Data.Hashable
import Data.Hashable.Lifted
#if !(MIN_VERSION_base(4,11,0))
import Data.Semigroup
#endif
import Data.Semigroup.Foldable
import Data.Serialize as Cereal
import qualified Data.Traversable.WithIndex as WithIndex
import qualified Data.Vector as V
import qualified Data.Vector.Generic.Mutable as M
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed.Base as U
import Foreign.Ptr (castPtr)
import Foreign.Storable (Storable(..))
import GHC.Arr (Ix(..))
import GHC.Generics (Generic, Generic1)
#if defined(MIN_VERSION_template_haskell)
import Language.Haskell.TH.Syntax (Lift)
#endif
import Linear.Epsilon
import Linear.Metric
import Linear.V
import Linear.V2
import Linear.V3
import Linear.Vector
import System.Random (Random(..), Uniform)
import System.Random.Stateful (UniformRange(..))

-- $setup
-- >>> import Control.Lens hiding (index)

-- | A 4-dimensional vector.
data V4 a = V4 !a !a !a !a deriving (Eq,Ord,Show,Read,Data
                                    ,Generic,Generic1
#if defined(MIN_VERSION_template_haskell)
                                    ,Lift
#endif
                                    )

instance Finite V4 where
  type Size V4 = 4
  toV (V4 a b c d) = V (V.fromListN 4 [a,b,c,d])
  fromV (V v) = V4 (v V.! 0) (v V.! 1) (v V.! 2) (v V.! 3)

instance Functor V4 where
  fmap f (V4 a b c d) = V4 (f a) (f b) (f c) (f d)
  {-# INLINE fmap #-}
  a <$ _ = V4 a a a a
  {-# INLINE (<$) #-}

instance Foldable V4 where
  foldMap f (V4 a b c d) = f a `mappend` f b `mappend` f c `mappend` f d
  {-# INLINE foldMap #-}
#if MIN_VERSION_base(4,13,0)
  foldMap' f (V4 a b c d) = ((f a `mappend` f b) `mappend` f c) `mappend` f d
  {-# INLINE foldMap' #-}
#endif
  null _ = False
  length _ = 4

instance Random a => Random (V4 a) where
  random g = case random g of
    (a, g') -> case random g' of
      (b, g'') -> case random g'' of
        (c, g''') -> case random g''' of
          (d, g'''') -> (V4 a b c d, g'''')
  randomR (V4 a b c d, V4 a' b' c' d') g = case randomR (a,a') g of
    (a'', g') -> case randomR (b,b') g' of
      (b'', g'') -> case randomR (c,c') g'' of
        (c'', g''') -> case randomR (d,d') g''' of
          (d'', g'''') -> (V4 a'' b'' c'' d'', g'''')

instance Uniform a => Uniform (V4 a) where

instance UniformRange a => UniformRange (V4 a) where
  uniformRM (V4 a b c d, V4 a' b' c' d') g = V4
    <$> uniformRM (a, a') g
    <*> uniformRM (b, b') g
    <*> uniformRM (c, c') g
    <*> uniformRM (d, d') g

instance Traversable V4 where
  traverse f (V4 a b c d) = V4 <$> f a <*> f b <*> f c <*> f d
  {-# INLINE traverse #-}

instance Foldable1 V4 where
  foldMap1 f (V4 a b c d) = f a <> f b <> f c <> f d
  {-# INLINE foldMap1 #-}

instance Traversable1 V4 where
  traverse1 f (V4 a b c d) = V4 <$> f a <.> f b <.> f c <.> f d
  {-# INLINE traverse1 #-}

instance Applicative V4 where
  pure a = V4 a a a a
  {-# INLINE pure #-}
  V4 a b c d <*> V4 e f g h = V4 (a e) (b f) (c g) (d h)
  {-# INLINE (<*>) #-}

instance Apply V4 where
  V4 a b c d <.> V4 e f g h = V4 (a e) (b f) (c g) (d h)
  {-# INLINE (<.>) #-}

instance Additive V4 where
  zero = pure 0
  {-# INLINE zero #-}
  liftU2 = liftA2
  {-# INLINE liftU2 #-}
  liftI2 = liftA2
  {-# INLINE liftI2 #-}

instance Bind V4 where
  V4 a b c d >>- f = V4 a' b' c' d' where
    V4 a' _ _ _ = f a
    V4 _ b' _ _ = f b
    V4 _ _ c' _ = f c
    V4 _ _ _ d' = f d
  {-# INLINE (>>-) #-}

instance Monad V4 where
#if !(MIN_VERSION_base(4,11,0))
  return a = V4 a a a a
  {-# INLINE return #-}
#endif
  V4 a b c d >>= f = V4 a' b' c' d' where
    V4 a' _ _ _ = f a
    V4 _ b' _ _ = f b
    V4 _ _ c' _ = f c
    V4 _ _ _ d' = f d
  {-# INLINE (>>=) #-}

instance Num a => Num (V4 a) where
  (+) = liftA2 (+)
  {-# INLINE (+) #-}
  (*) = liftA2 (*)
  {-# INLINE (-) #-}
  (-) = liftA2 (-)
  {-# INLINE (*) #-}
  negate = fmap negate
  {-# INLINE negate #-}
  abs = fmap abs
  {-# INLINE abs #-}
  signum = fmap signum
  {-# INLINE signum #-}
  fromInteger = pure . fromInteger
  {-# INLINE fromInteger #-}

instance Fractional a => Fractional (V4 a) where
  recip = fmap recip
  {-# INLINE recip #-}
  (/) = liftA2 (/)
  {-# INLINE (/) #-}
  fromRational = pure . fromRational
  {-# INLINE fromRational #-}

instance Floating a => Floating (V4 a) where
    pi = pure pi
    {-# INLINE pi #-}
    exp = fmap exp
    {-# INLINE exp #-}
    sqrt = fmap sqrt
    {-# INLINE sqrt #-}
    log = fmap log
    {-# INLINE log #-}
    (**) = liftA2 (**)
    {-# INLINE (**) #-}
    logBase = liftA2 logBase
    {-# INLINE logBase #-}
    sin = fmap sin
    {-# INLINE sin #-}
    tan = fmap tan
    {-# INLINE tan #-}
    cos = fmap cos
    {-# INLINE cos #-}
    asin = fmap asin
    {-# INLINE asin #-}
    atan = fmap atan
    {-# INLINE atan #-}
    acos = fmap acos
    {-# INLINE acos #-}
    sinh = fmap sinh
    {-# INLINE sinh #-}
    tanh = fmap tanh
    {-# INLINE tanh #-}
    cosh = fmap cosh
    {-# INLINE cosh #-}
    asinh = fmap asinh
    {-# INLINE asinh #-}
    atanh = fmap atanh
    {-# INLINE atanh #-}
    acosh = fmap acosh
    {-# INLINE acosh #-}

instance Metric V4 where
  dot (V4 a b c d) (V4 e f g h) = a * e + b * f + c * g + d * h
  {-# INLINE dot #-}

instance Distributive V4 where
  distribute f = V4 (fmap (\(V4 x _ _ _) -> x) f)
                    (fmap (\(V4 _ y _ _) -> y) f)
                    (fmap (\(V4 _ _ z _) -> z) f)
                    (fmap (\(V4 _ _ _ w) -> w) f)
  {-# INLINE distribute #-}

instance Hashable a => Hashable (V4 a) where
  hashWithSalt s (V4 a b c d) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c `hashWithSalt` d
  {-# INLINE hashWithSalt #-}

instance Hashable1 V4 where
  liftHashWithSalt h s (V4 a b c d) = s `h` a `h` b `h` c `h` d
  {-# INLINE liftHashWithSalt #-}

-- | A space that distinguishes orthogonal basis vectors '_x', '_y', '_z', '_w'. (It may have more.)
class R3 t => R4 t where
  -- |
  -- >>> V4 1 2 3 4 ^._w
  -- 4
  _w :: Lens' (t a) a
  _xyzw :: Lens' (t a) (V4 a)

_xw, _yw, _zw, _wx, _wy, _wz :: R4 t => Lens' (t a) (V2 a)
_xw f = _xyzw $ \(V4 a b c d) -> f (V2 a d) <&> \(V2 a' d') -> V4 a' b c d'
{-# INLINE _xw #-}

_yw f = _xyzw $ \(V4 a b c d) -> f (V2 b d) <&> \(V2 b' d') -> V4 a b' c d'
{-# INLINE _yw #-}

_zw f = _xyzw $ \(V4 a b c d) -> f (V2 c d) <&> \(V2 c' d') -> V4 a b c' d'
{-# INLINE _zw #-}

_wx f = _xyzw $ \(V4 a b c d) -> f (V2 d a) <&> \(V2 d' a') -> V4 a' b c d'
{-# INLINE _wx #-}

_wy f = _xyzw $ \(V4 a b c d) -> f (V2 d b) <&> \(V2 d' b') -> V4 a b' c d'
{-# INLINE _wy #-}

_wz f = _xyzw $ \(V4 a b c d) -> f (V2 d c) <&> \(V2 d' c') -> V4 a b c' d'
{-# INLINE _wz #-}

_xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy, _wxy, _wxz, _wyx, _wyz, _wzx, _wzy :: R4 t => Lens' (t a) (V3 a)
_xyw f = _xyzw $ \(V4 a b c d) -> f (V3 a b d) <&> \(V3 a' b' d') -> V4 a' b' c d'
{-# INLINE _xyw #-}

_xzw f = _xyzw $ \(V4 a b c d) -> f (V3 a c d) <&> \(V3 a' c' d') -> V4 a' b c' d'
{-# INLINE _xzw #-}

_xwy f = _xyzw $ \(V4 a b c d) -> f (V3 a d b) <&> \(V3 a' d' b') -> V4 a' b' c d'
{-# INLINE _xwy #-}

_xwz f = _xyzw $ \(V4 a b c d) -> f (V3 a d c) <&> \(V3 a' d' c') -> V4 a' b c' d'
{-# INLINE _xwz #-}

_yxw f = _xyzw $ \(V4 a b c d) -> f (V3 b a d) <&> \(V3 b' a' d') -> V4 a' b' c d'
{-# INLINE _yxw #-}

_yzw f = _xyzw $ \(V4 a b c d) -> f (V3 b c d) <&> \(V3 b' c' d') -> V4 a b' c' d'
{-# INLINE _yzw #-}

_ywx f = _xyzw $ \(V4 a b c d) -> f (V3 b d a) <&> \(V3 b' d' a') -> V4 a' b' c d'
{-# INLINE _ywx #-}

_ywz f = _xyzw $ \(V4 a b c d) -> f (V3 b d c) <&> \(V3 b' d' c') -> V4 a b' c' d'
{-# INLINE _ywz #-}

_zxw f = _xyzw $ \(V4 a b c d) -> f (V3 c a d) <&> \(V3 c' a' d') -> V4 a' b c' d'
{-# INLINE _zxw #-}

_zyw f = _xyzw $ \(V4 a b c d) -> f (V3 c b d) <&> \(V3 c' b' d') -> V4 a b' c' d'
{-# INLINE _zyw #-}

_zwx f = _xyzw $ \(V4 a b c d) -> f (V3 c d a) <&> \(V3 c' d' a') -> V4 a' b c' d'
{-# INLINE _zwx #-}

_zwy f = _xyzw $ \(V4 a b c d) -> f (V3 c d b) <&> \(V3 c' d' b') -> V4 a b' c' d'
{-# INLINE _zwy #-}

_wxy f = _xyzw $ \(V4 a b c d) -> f (V3 d a b) <&> \(V3 d' a' b') -> V4 a' b' c d'
{-# INLINE _wxy #-}

_wxz f = _xyzw $ \(V4 a b c d) -> f (V3 d a c) <&> \(V3 d' a' c') -> V4 a' b c' d'
{-# INLINE _wxz #-}

_wyx f = _xyzw $ \(V4 a b c d) -> f (V3 d b a) <&> \(V3 d' b' a') -> V4 a' b' c d'
{-# INLINE _wyx #-}

_wyz f = _xyzw $ \(V4 a b c d) -> f (V3 d b c) <&> \(V3 d' b' c') -> V4 a b' c' d'
{-# INLINE _wyz #-}

_wzx f = _xyzw $ \(V4 a b c d) -> f (V3 d c a) <&> \(V3 d' c' a') -> V4 a' b c' d'
{-# INLINE _wzx #-}

_wzy f = _xyzw $ \(V4 a b c d) -> f (V3 d c b) <&> \(V3 d' c' b') -> V4 a b' c' d'
{-# INLINE _wzy #-}

_xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz
  , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz
  , _wyzx, _wzxy, _wzyx :: R4 t => Lens' (t a) (V4 a)
_xywz f = _xyzw $ \(V4 a b c d) -> f (V4 a b d c) <&> \(V4 a' b' d' c') -> V4 a' b' c' d'
{-# INLINE _xywz #-}

_xzyw f = _xyzw $ \(V4 a b c d) -> f (V4 a c b d) <&> \(V4 a' c' b' d') -> V4 a' b' c' d'
{-# INLINE _xzyw #-}

_xzwy f = _xyzw $ \(V4 a b c d) -> f (V4 a c d b) <&> \(V4 a' c' d' b') -> V4 a' b' c' d'
{-# INLINE _xzwy #-}

_xwyz f = _xyzw $ \(V4 a b c d) -> f (V4 a d b c) <&> \(V4 a' d' b' c') -> V4 a' b' c' d'
{-# INLINE _xwyz #-}

_xwzy f = _xyzw $ \(V4 a b c d) -> f (V4 a d c b) <&> \(V4 a' d' c' b') -> V4 a' b' c' d'
{-# INLINE _xwzy #-}

_yxzw f = _xyzw $ \(V4 a b c d) -> f (V4 b a c d) <&> \(V4 b' a' c' d') -> V4 a' b' c' d'
{-# INLINE _yxzw #-}

_yxwz f = _xyzw $ \(V4 a b c d) -> f (V4 b a d c) <&> \(V4 b' a' d' c') -> V4 a' b' c' d'
{-# INLINE _yxwz #-}

_yzxw f = _xyzw $ \(V4 a b c d) -> f (V4 b c a d) <&> \(V4 b' c' a' d') -> V4 a' b' c' d'
{-# INLINE _yzxw #-}

_yzwx f = _xyzw $ \(V4 a b c d) -> f (V4 b c d a) <&> \(V4 b' c' d' a') -> V4 a' b' c' d'
{-# INLINE _yzwx #-}

_ywxz f = _xyzw $ \(V4 a b c d) -> f (V4 b d a c) <&> \(V4 b' d' a' c') -> V4 a' b' c' d'
{-# INLINE _ywxz #-}

_ywzx f = _xyzw $ \(V4 a b c d) -> f (V4 b d c a) <&> \(V4 b' d' c' a') -> V4 a' b' c' d'
{-# INLINE _ywzx #-}

_zxyw f = _xyzw $ \(V4 a b c d) -> f (V4 c a b d) <&> \(V4 c' a' b' d') -> V4 a' b' c' d'
{-# INLINE _zxyw #-}

_zxwy f = _xyzw $ \(V4 a b c d) -> f (V4 c a d b) <&> \(V4 c' a' d' b') -> V4 a' b' c' d'
{-# INLINE _zxwy #-}

_zyxw f = _xyzw $ \(V4 a b c d) -> f (V4 c b a d) <&> \(V4 c' b' a' d') -> V4 a' b' c' d'
{-# INLINE _zyxw #-}

_zywx f = _xyzw $ \(V4 a b c d) -> f (V4 c b d a) <&> \(V4 c' b' d' a') -> V4 a' b' c' d'
{-# INLINE _zywx #-}

_zwxy f = _xyzw $ \(V4 a b c d) -> f (V4 c d a b) <&> \(V4 c' d' a' b') -> V4 a' b' c' d'
{-# INLINE _zwxy #-}

_zwyx f = _xyzw $ \(V4 a b c d) -> f (V4 c d b a) <&> \(V4 c' d' b' a') -> V4 a' b' c' d'
{-# INLINE _zwyx #-}

_wxyz f = _xyzw $ \(V4 a b c d) -> f (V4 d a b c) <&> \(V4 d' a' b' c') -> V4 a' b' c' d'
{-# INLINE _wxyz #-}

_wxzy f = _xyzw $ \(V4 a b c d) -> f (V4 d a c b) <&> \(V4 d' a' c' b') -> V4 a' b' c' d'
{-# INLINE _wxzy #-}

_wyxz f = _xyzw $ \(V4 a b c d) -> f (V4 d b a c) <&> \(V4 d' b' a' c') -> V4 a' b' c' d'
{-# INLINE _wyxz #-}

_wyzx f = _xyzw $ \(V4 a b c d) -> f (V4 d b c a) <&> \(V4 d' b' c' a') -> V4 a' b' c' d'
{-# INLINE _wyzx #-}

_wzxy f = _xyzw $ \(V4 a b c d) -> f (V4 d c a b) <&> \(V4 d' c' a' b') -> V4 a' b' c' d'
{-# INLINE _wzxy #-}

_wzyx f = _xyzw $ \(V4 a b c d) -> f (V4 d c b a) <&> \(V4 d' c' b' a') -> V4 a' b' c' d'
{-# INLINE _wzyx #-}

ew :: R4 t => E t
ew = E _w

instance R1 V4 where
  _x f (V4 a b c d) = (\a' -> V4 a' b c d) <$> f a
  {-# INLINE _x #-}

instance R2 V4 where
  _y f (V4 a b c d) = (\b' -> V4 a b' c d) <$> f b
  {-# INLINE _y #-}
  _xy f (V4 a b c d) = (\(V2 a' b') -> V4 a' b' c d) <$> f (V2 a b)
  {-# INLINE _xy #-}

instance R3 V4 where
  _z f (V4 a b c d) = (\c' -> V4 a b c' d) <$> f c
  {-# INLINE _z #-}
  _xyz f (V4 a b c d) = (\(V3 a' b' c') -> V4 a' b' c' d) <$> f (V3 a b c)
  {-# INLINE _xyz #-}

instance R4 V4 where
  _w f (V4 a b c d) = V4 a b c <$> f d
  {-# INLINE _w #-}
  _xyzw = id
  {-# INLINE _xyzw #-}

instance Storable a => Storable (V4 a) where
  sizeOf _ = 4 * sizeOf (undefined::a)
  {-# INLINE sizeOf #-}
  alignment _ = alignment (undefined::a)
  {-# INLINE alignment #-}
  poke ptr (V4 x y z w) = do poke ptr' x
                             pokeElemOff ptr' 1 y
                             pokeElemOff ptr' 2 z
                             pokeElemOff ptr' 3 w
    where ptr' = castPtr ptr
  {-# INLINE poke #-}
  peek ptr = V4 <$> peek ptr' <*> peekElemOff ptr' 1
                <*> peekElemOff ptr' 2 <*> peekElemOff ptr' 3
    where ptr' = castPtr ptr
  {-# INLINE peek #-}

-- | Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector,
-- i.e. sets the @w@ coordinate to 0.
vector :: Num a => V3 a -> V4 a
vector (V3 a b c) = V4 a b c 0
{-# INLINE vector #-}

-- | Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector,
-- i.e. sets the @w@ coordinate to 1.
point :: Num a => V3 a -> V4 a
point (V3 a b c) = V4 a b c 1
{-# INLINE point #-}

-- | Convert 4-dimensional projective coordinates to a 3-dimensional
-- point. This operation may be denoted, @euclidean [x:y:z:w] = (x\/w,
-- y\/w, z\/w)@ where the projective, homogenous, coordinate
-- @[x:y:z:w]@ is one of many associated with a single point @(x\/w,
-- y\/w, z\/w)@.
normalizePoint :: Fractional a => V4 a -> V3 a
normalizePoint (V4 a b c w) = (1/w) *^ V3 a b c
{-# INLINE normalizePoint #-}

instance Epsilon a => Epsilon (V4 a) where
  nearZero = nearZero . quadrance
  {-# INLINE nearZero #-}

instance Ix a => Ix (V4 a) where
  {-# SPECIALISE instance Ix (V4 Int) #-}

  range (V4 l1 l2 l3 l4,V4 u1 u2 u3 u4) =
    [V4 i1 i2 i3 i4 | i1 <- range (l1,u1)
                    , i2 <- range (l2,u2)
                    , i3 <- range (l3,u3)
                    , i4 <- range (l4,u4)
                    ]
  {-# INLINE range #-}

  unsafeIndex (V4 l1 l2 l3 l4,V4 u1 u2 u3 u4) (V4 i1 i2 i3 i4) =
    unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
    unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
    unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) *
    unsafeIndex (l1,u1) i1))
  {-# INLINE unsafeIndex #-}

  inRange (V4 l1 l2 l3 l4,V4 u1 u2 u3 u4) (V4 i1 i2 i3 i4) =
    inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
    inRange (l3,u3) i3 && inRange (l4,u4) i4
  {-# INLINE inRange #-}

instance Representable V4 where
  type Rep V4 = E V4
  tabulate f = V4 (f ex) (f ey) (f ez) (f ew)
  {-# INLINE tabulate #-}
  index xs (E l) = view l xs
  {-# INLINE index #-}

instance WithIndex.FunctorWithIndex (E V4) V4 where
  imap f (V4 a b c d) = V4 (f ex a) (f ey b) (f ez c) (f ew d)
  {-# INLINE imap #-}

instance WithIndex.FoldableWithIndex (E V4) V4 where
  ifoldMap f (V4 a b c d) = f ex a `mappend` f ey b `mappend` f ez c `mappend` f ew d
  {-# INLINE ifoldMap #-}

instance WithIndex.TraversableWithIndex (E V4) V4 where
  itraverse f (V4 a b c d) = V4 <$> f ex a <*> f ey b <*> f ez c <*> f ew d
  {-# INLINE itraverse #-}

#if !MIN_VERSION_lens(5,0,0)
instance Lens.FunctorWithIndex     (E V4) V4 where imap      = WithIndex.imap
instance Lens.FoldableWithIndex    (E V4) V4 where ifoldMap  = WithIndex.ifoldMap
instance Lens.TraversableWithIndex (E V4) V4 where itraverse = WithIndex.itraverse
#endif

type instance Index (V4 a) = E V4
type instance IxValue (V4 a) = a

instance Ixed (V4 a) where
  ix i = el i

instance Each (V4 a) (V4 b) a b where
  each = traverse

data instance U.Vector    (V4 a) =  V_V4 {-# UNPACK #-} !Int !(U.Vector    a)
data instance U.MVector s (V4 a) = MV_V4 {-# UNPACK #-} !Int !(U.MVector s a)
instance U.Unbox a => U.Unbox (V4 a)

instance U.Unbox a => M.MVector U.MVector (V4 a) where
  basicLength (MV_V4 n _) = n
  basicUnsafeSlice m n (MV_V4 _ v) = MV_V4 n (M.basicUnsafeSlice (4*m) (4*n) v)
  basicOverlaps (MV_V4 _ v) (MV_V4 _ u) = M.basicOverlaps v u
  basicUnsafeNew n = liftM (MV_V4 n) (M.basicUnsafeNew (4*n))
  basicUnsafeRead (MV_V4 _ v) i =
    do let o = 4*i
       x <- M.basicUnsafeRead v o
       y <- M.basicUnsafeRead v (o+1)
       z <- M.basicUnsafeRead v (o+2)
       w <- M.basicUnsafeRead v (o+3)
       return (V4 x y z w)
  basicUnsafeWrite (MV_V4 _ v) i (V4 x y z w) =
    do let o = 4*i
       M.basicUnsafeWrite v o     x
       M.basicUnsafeWrite v (o+1) y
       M.basicUnsafeWrite v (o+2) z
       M.basicUnsafeWrite v (o+3) w
  basicInitialize (MV_V4 _ v) = M.basicInitialize v

instance U.Unbox a => G.Vector U.Vector (V4 a) where
  basicUnsafeFreeze (MV_V4 n v) = liftM ( V_V4 n) (G.basicUnsafeFreeze v)
  basicUnsafeThaw   ( V_V4 n v) = liftM (MV_V4 n) (G.basicUnsafeThaw   v)
  basicLength       ( V_V4 n _) = n
  basicUnsafeSlice m n (V_V4 _ v) = V_V4 n (G.basicUnsafeSlice (4*m) (4*n) v)
  basicUnsafeIndexM (V_V4 _ v) i =
    do let o = 4*i
       x <- G.basicUnsafeIndexM v o
       y <- G.basicUnsafeIndexM v (o+1)
       z <- G.basicUnsafeIndexM v (o+2)
       w <- G.basicUnsafeIndexM v (o+3)
       return (V4 x y z w)

instance MonadZip V4 where
  mzipWith = liftA2

instance MonadFix V4 where
  mfix f = V4 (let V4 a _ _ _ = f a in a)
              (let V4 _ a _ _ = f a in a)
              (let V4 _ _ a _ = f a in a)
              (let V4 _ _ _ a = f a in a)

instance Bounded a => Bounded (V4 a) where
  minBound = pure minBound
  {-# INLINE minBound #-}
  maxBound = pure maxBound
  {-# INLINE maxBound #-}

instance NFData a => NFData (V4 a) where
  rnf (V4 a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d

instance Serial1 V4 where
  serializeWith = traverse_
  deserializeWith k = V4 <$> k <*> k <*> k <*> k

instance Serial a => Serial (V4 a) where
  serialize = serializeWith serialize
  deserialize = deserializeWith deserialize

instance Binary a => Binary (V4 a) where
  put = serializeWith Binary.put
  get = deserializeWith Binary.get

instance Serialize a => Serialize (V4 a) where
  put = serializeWith Cereal.put
  get = deserializeWith Cereal.get

instance Eq1 V4 where
  liftEq k (V4 a b c d) (V4 e f g h) = k a e && k b f && k c g && k d h
instance Ord1 V4 where
  liftCompare k (V4 a b c d) (V4 e f g h) = k a e `mappend` k b f `mappend` k c g `mappend` k d h
instance Read1 V4 where
  liftReadsPrec k _ z = readParen (z > 10) $ \r ->
     [ (V4 a b c d, r5)
     | ("V4",r1) <- lex r
     , (a,r2) <- k 11 r1
     , (b,r3) <- k 11 r2
     , (c,r4) <- k 11 r3
     , (d,r5) <- k 11 r4
     ]
instance Show1 V4 where
  liftShowsPrec f _ z (V4 a b c d) = showParen (z > 10) $
     showString "V4 " . f 11 a . showChar ' ' . f 11 b . showChar ' ' . f 11 c . showChar ' ' . f 11 d

instance Field1 (V4 a) (V4 a) a a where
  _1 f (V4 x y z w) = f x <&> \x' -> V4 x' y z w

instance Field2 (V4 a) (V4 a) a a where
  _2 f (V4 x y z w) = f y <&> \y' -> V4 x y' z w

instance Field3 (V4 a) (V4 a) a a where
  _3 f (V4 x y z w) = f z <&> \z' -> V4 x y z' w

instance Field4 (V4 a) (V4 a) a a where
  _4 f (V4 x y z w) = f w <&> \w' -> V4 x y z w'

instance Semigroup a => Semigroup (V4 a) where
 (<>) = liftA2 (<>)

instance Monoid a => Monoid (V4 a) where
  mempty = pure mempty
#if !(MIN_VERSION_base(4,11,0))
  mappend = liftA2 mappend
#endif