```{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Linear.V3
-- Copyright   :  (C) 2012-2013 Edward Kmett,
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  experimental
-- Portability :  non-portable
--
-- 3-D Vectors
----------------------------------------------------------------------------
module Linear.V3
( V3(..)
, cross, triple
, R2(..)
, R3(..)
) where

import Control.Applicative
import Data.Data
import Data.Distributive
import Data.Foldable
import Data.Functor.Bind
import Data.Traversable
import Data.Semigroup
import Data.Semigroup.Foldable
import Data.Semigroup.Traversable
import Foreign.Ptr (castPtr)
import Foreign.Storable (Storable(..))
import GHC.Arr (Ix(..))
import Linear.Core
import Linear.Epsilon
import Linear.Metric
import Linear.V2
import Linear.Vector

{-# ANN module "HLint: ignore Reduce duplication" #-}

-- | A 3-dimensional vector
data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Functor V3 where
fmap f (V3 a b c) = V3 (f a) (f b) (f c)
{-# INLINE fmap #-}
a <\$ _ = V3 a a a
{-# INLINE (<\$) #-}

instance Foldable V3 where
foldMap f (V3 a b c) = f a `mappend` f b `mappend` f c
{-# INLINE foldMap #-}

instance Traversable V3 where
traverse f (V3 a b c) = V3 <\$> f a <*> f b <*> f c
{-# INLINE traverse #-}

instance Foldable1 V3 where
foldMap1 f (V3 a b c) = f a <> f b <> f c
{-# INLINE foldMap1 #-}

instance Traversable1 V3 where
traverse1 f (V3 a b c) = V3 <\$> f a <.> f b <.> f c
{-# INLINE traverse1 #-}

instance Apply V3 where
V3 a b c <.> V3 d e f = V3 (a d) (b e) (c f)
{-# INLINE (<.>) #-}

instance Applicative V3 where
pure a = V3 a a a
{-# INLINE pure #-}
V3 a b c <*> V3 d e f = V3 (a d) (b e) (c f)
{-# INLINE (<*>) #-}

zero = pure 0
{-# INLINE zero #-}
liftU2 = liftA2
{-# INLINE liftU2 #-}
liftI2 = liftA2
{-# INLINE liftI2 #-}

instance Bind V3 where
V3 a b c >>- f = V3 a' b' c' where
V3 a' _ _ = f a
V3 _ b' _ = f b
V3 _ _ c' = f c
{-# INLINE (>>-) #-}

return a = V3 a a a
{-# INLINE return #-}
V3 a b c >>= f = V3 a' b' c' where
V3 a' _ _ = f a
V3 _ b' _ = f b
V3 _ _ c' = f c
{-# INLINE (>>=) #-}

instance Num a => Num (V3 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 (V3 a) where
recip = fmap recip
{-# INLINE recip #-}
(/) = liftA2 (/)
{-# INLINE (/) #-}
fromRational = pure . fromRational
{-# INLINE fromRational #-}

instance Metric V3 where
dot (V3 a b c) (V3 d e f) = a * d + b * e + c * f
{-# INLINABLE dot #-}

instance Distributive V3 where
distribute f = V3 (fmap (\(V3 x _ _) -> x) f) (fmap (\(V3 _ y _) -> y) f) (fmap (\(V3 _ _ z) -> z) f)
{-# INLINE distribute #-}

-- | A space that distinguishes 3 orthogonal basis vectors: '_x', '_y', and '_z'. (It may have more)
class R2 t => R3 t where
-- |
-- @
-- '_z' :: Lens' (t a) a
-- @
_z :: Functor f => (a -> f a) -> t a -> f (t a)
-- |
-- @
-- '_xyz' :: Lens' (t a) ('V3' a)
-- @
_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)

instance R2 V3 where
_x f (V3 a b c) = (\a' -> V3 a' b c) <\$> f a
{-# INLINE _x #-}
_y f (V3 a b c) = (\b' -> V3 a b' c) <\$> f b
{-# INLINE _y #-}
_xy f (V3 a b c) = (\(V2 a' b') -> V3 a' b' c) <\$> f (V2 a b)
{-# INLINE _xy #-}

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

instance Core V3 where
core f = V3 (f _x) (f _y) (f _z)
{-# INLINE core #-}

instance Storable a => Storable (V3 a) where
sizeOf _ = 3 * sizeOf (undefined::a)
{-# INLINE sizeOf #-}
alignment _ = alignment (undefined::a)
{-# INLINE alignment #-}
poke ptr (V3 x y z) = do poke ptr' x
pokeElemOff ptr' 1 y
pokeElemOff ptr' 2 z
where ptr' = castPtr ptr
{-# INLINE poke #-}
peek ptr = V3 <\$> peek ptr' <*> peekElemOff ptr' 1 <*> peekElemOff ptr' 2
where ptr' = castPtr ptr
{-# INLINE peek #-}

-- | cross product
cross :: Num a => V3 a -> V3 a -> V3 a
cross (V3 a b c) (V3 d e f) = V3 (b*f-c*e) (c*d-a*f) (a*e-b*d)
{-# INLINABLE cross #-}

-- | scalar triple product
triple :: Num a => V3 a -> V3 a -> V3 a -> a
triple a b c = dot a (cross b c)
{-# INLINE triple #-}

instance Epsilon a => Epsilon (V3 a) where
{-# INLINE nearZero #-}

instance Ix a => Ix (V3 a) where
{-# SPECIALISE instance Ix (V3 Int) #-}

range (V3 l1 l2 l3,V3 u1 u2 u3) =
[V3 i1 i2 i3 | i1 <- range (l1,u1)
, i2 <- range (l2,u2)
, i3 <- range (l3,u3)
]
{-# INLINE range #-}

unsafeIndex (V3 l1 l2 l3,V3 u1 u2 u3) (V3 i1 i2 i3) =
unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) *
unsafeIndex (l1,u1) i1)
{-# INLINE unsafeIndex #-}

inRange (V3 l1 l2 l3,V3 u1 u2 u3) (V3 i1 i2 i3) =
inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
inRange (l3,u3) i3
{-# INLINE inRange #-}
```