{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE CPP #-}
#if __GLASGOW_HASKELL__ >= 702
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE DeriveGeneric #-}
#endif
#if __GLASGOW_HASKELL__ >= 707
{-# LANGUAGE DataKinds #-}
#endif

#if __GLASGOW_HASKELL__ >= 800
{-# LANGUAGE DeriveLift #-}
#endif

#ifndef MIN_VERSION_hashable
#define MIN_VERSION_hashable(x,y,z) 1
#endif

#ifndef MIN_VERSION_vector
#define MIN_VERSION_vector(x,y,z) 1
#endif

#ifndef MIN_VERSION_transformers
#define MIN_VERSION_transformers(x,y,z) 1
#endif
-----------------------------------------------------------------------------
-- |
-- 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

import Control.Applicative
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
#if (MIN_VERSION_hashable(1,2,5))
import Data.Hashable.Lifted
#endif
#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
#if __GLASGOW_HASKELL__ >= 707
import qualified Data.Vector as V
#endif
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(..))
#if __GLASGOW_HASKELL__ >= 702
import GHC.Generics (Generic)
#endif
#if __GLASGOW_HASKELL__ >= 706
import GHC.Generics (Generic1)
#endif
#if __GLASGOW_HASKELL__ >= 800
import Language.Haskell.TH.Syntax (Lift)
#endif
import Linear.Epsilon
import Linear.Metric
#if __GLASGOW_HASKELL__ >= 707
import Linear.V
#endif
import Linear.V2
import Linear.V3
import Linear.Vector
import System.Random

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

-- | A 4-dimensional vector.
data V4 a = V4 !a !a !a !a deriving (V4 a -> V4 a -> Bool
(V4 a -> V4 a -> Bool) -> (V4 a -> V4 a -> Bool) -> Eq (V4 a)
forall a. Eq a => V4 a -> V4 a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: V4 a -> V4 a -> Bool
$c/= :: forall a. Eq a => V4 a -> V4 a -> Bool
== :: V4 a -> V4 a -> Bool
$c== :: forall a. Eq a => V4 a -> V4 a -> Bool
Eq,Eq (V4 a)
Eq (V4 a)
-> (V4 a -> V4 a -> Ordering)
-> (V4 a -> V4 a -> Bool)
-> (V4 a -> V4 a -> Bool)
-> (V4 a -> V4 a -> Bool)
-> (V4 a -> V4 a -> Bool)
-> (V4 a -> V4 a -> V4 a)
-> (V4 a -> V4 a -> V4 a)
-> Ord (V4 a)
V4 a -> V4 a -> Bool
V4 a -> V4 a -> Ordering
V4 a -> V4 a -> V4 a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (V4 a)
forall a. Ord a => V4 a -> V4 a -> Bool
forall a. Ord a => V4 a -> V4 a -> Ordering
forall a. Ord a => V4 a -> V4 a -> V4 a
min :: V4 a -> V4 a -> V4 a
$cmin :: forall a. Ord a => V4 a -> V4 a -> V4 a
max :: V4 a -> V4 a -> V4 a
$cmax :: forall a. Ord a => V4 a -> V4 a -> V4 a
>= :: V4 a -> V4 a -> Bool
$c>= :: forall a. Ord a => V4 a -> V4 a -> Bool
> :: V4 a -> V4 a -> Bool
$c> :: forall a. Ord a => V4 a -> V4 a -> Bool
<= :: V4 a -> V4 a -> Bool
$c<= :: forall a. Ord a => V4 a -> V4 a -> Bool
< :: V4 a -> V4 a -> Bool
$c< :: forall a. Ord a => V4 a -> V4 a -> Bool
compare :: V4 a -> V4 a -> Ordering
$ccompare :: forall a. Ord a => V4 a -> V4 a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (V4 a)
Ord,Int -> V4 a -> ShowS
[V4 a] -> ShowS
V4 a -> String
(Int -> V4 a -> ShowS)
-> (V4 a -> String) -> ([V4 a] -> ShowS) -> Show (V4 a)
forall a. Show a => Int -> V4 a -> ShowS
forall a. Show a => [V4 a] -> ShowS
forall a. Show a => V4 a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [V4 a] -> ShowS
$cshowList :: forall a. Show a => [V4 a] -> ShowS
show :: V4 a -> String
$cshow :: forall a. Show a => V4 a -> String
showsPrec :: Int -> V4 a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> V4 a -> ShowS
Show,ReadPrec [V4 a]
ReadPrec (V4 a)
Int -> ReadS (V4 a)
ReadS [V4 a]
(Int -> ReadS (V4 a))
-> ReadS [V4 a]
-> ReadPrec (V4 a)
-> ReadPrec [V4 a]
-> Read (V4 a)
forall a. Read a => ReadPrec [V4 a]
forall a. Read a => ReadPrec (V4 a)
forall a. Read a => Int -> ReadS (V4 a)
forall a. Read a => ReadS [V4 a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
readListPrec :: ReadPrec [V4 a]
$creadListPrec :: forall a. Read a => ReadPrec [V4 a]
readPrec :: ReadPrec (V4 a)
$creadPrec :: forall a. Read a => ReadPrec (V4 a)
readList :: ReadS [V4 a]
$creadList :: forall a. Read a => ReadS [V4 a]
readsPrec :: Int -> ReadS (V4 a)
$creadsPrec :: forall a. Read a => Int -> ReadS (V4 a)
Read,Typeable (V4 a)
DataType
Constr
Typeable (V4 a)
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> V4 a -> c (V4 a))
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (V4 a))
-> (V4 a -> Constr)
-> (V4 a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (V4 a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a)))
-> ((forall b. Data b => b -> b) -> V4 a -> V4 a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r)
-> (forall u. (forall d. Data d => d -> u) -> V4 a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> V4 a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> V4 a -> m (V4 a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> V4 a -> m (V4 a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> V4 a -> m (V4 a))
-> Data (V4 a)
V4 a -> DataType
V4 a -> Constr
(forall d. Data d => c (t d)) -> Maybe (c (V4 a))
(forall b. Data b => b -> b) -> V4 a -> V4 a
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V4 a -> c (V4 a)
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V4 a)
forall a. Data a => Typeable (V4 a)
forall a. Data a => V4 a -> DataType
forall a. Data a => V4 a -> Constr
forall a. Data a => (forall b. Data b => b -> b) -> V4 a -> V4 a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> V4 a -> u
forall a u. Data a => (forall d. Data d => d -> u) -> V4 a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V4 a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V4 a -> c (V4 a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (V4 a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a))
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> V4 a -> u
forall u. (forall d. Data d => d -> u) -> V4 a -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V4 a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V4 a -> c (V4 a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (V4 a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a))
$cV4 :: Constr
$tV4 :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
gmapMp :: (forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
gmapM :: (forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> V4 a -> m (V4 a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> V4 a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> V4 a -> u
gmapQ :: (forall d. Data d => d -> u) -> V4 a -> [u]
$cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> V4 a -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r
gmapT :: (forall b. Data b => b -> b) -> V4 a -> V4 a
$cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> V4 a -> V4 a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (V4 a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (V4 a))
dataTypeOf :: V4 a -> DataType
$cdataTypeOf :: forall a. Data a => V4 a -> DataType
toConstr :: V4 a -> Constr
$ctoConstr :: forall a. Data a => V4 a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V4 a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V4 a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V4 a -> c (V4 a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V4 a -> c (V4 a)
$cp1Data :: forall a. Data a => Typeable (V4 a)
Data,Typeable
#if __GLASGOW_HASKELL__ >= 702
                                    ,(forall x. V4 a -> Rep (V4 a) x)
-> (forall x. Rep (V4 a) x -> V4 a) -> Generic (V4 a)
forall x. Rep (V4 a) x -> V4 a
forall x. V4 a -> Rep (V4 a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (V4 a) x -> V4 a
forall a x. V4 a -> Rep (V4 a) x
$cto :: forall a x. Rep (V4 a) x -> V4 a
$cfrom :: forall a x. V4 a -> Rep (V4 a) x
Generic
#endif
#if __GLASGOW_HASKELL__ >= 706
                                    ,(forall a. V4 a -> Rep1 V4 a)
-> (forall a. Rep1 V4 a -> V4 a) -> Generic1 V4
forall a. Rep1 V4 a -> V4 a
forall a. V4 a -> Rep1 V4 a
forall k (f :: k -> *).
(forall (a :: k). f a -> Rep1 f a)
-> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
$cto1 :: forall a. Rep1 V4 a -> V4 a
$cfrom1 :: forall a. V4 a -> Rep1 V4 a
Generic1
#endif
#if __GLASGOW_HASKELL__ >= 800
                                    ,V4 a -> Q Exp
V4 a -> Q (TExp (V4 a))
(V4 a -> Q Exp) -> (V4 a -> Q (TExp (V4 a))) -> Lift (V4 a)
forall a. Lift a => V4 a -> Q Exp
forall a. Lift a => V4 a -> Q (TExp (V4 a))
forall t. (t -> Q Exp) -> (t -> Q (TExp t)) -> Lift t
liftTyped :: V4 a -> Q (TExp (V4 a))
$cliftTyped :: forall a. Lift a => V4 a -> Q (TExp (V4 a))
lift :: V4 a -> Q Exp
$clift :: forall a. Lift a => V4 a -> Q Exp
Lift
#endif
                                    )

#if __GLASGOW_HASKELL__ >= 707
instance Finite V4 where
  type Size V4 = 4
  toV :: V4 a -> V (Size V4) a
toV (V4 a
a a
b a
c a
d) = Vector a -> V 4 a
forall k (n :: k) a. Vector a -> V n a
V (Int -> [a] -> Vector a
forall a. Int -> [a] -> Vector a
V.fromListN Int
4 [a
a,a
b,a
c,a
d])
  fromV :: V (Size V4) a -> V4 a
fromV (V Vector a
v) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
0) (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
1) (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
2) (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
3)
#endif

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

instance Foldable V4 where
  foldMap :: (a -> m) -> V4 a -> m
foldMap a -> m
f (V4 a
a a
b a
c a
d) = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
d
  {-# INLINE foldMap #-}
#if __GLASGOW_HASKELL__ >= 710
  null :: V4 a -> Bool
null V4 a
_ = Bool
False
  length :: V4 a -> Int
length V4 a
_ = Int
4
#endif

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

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

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

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

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

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

instance Additive V4 where
  zero :: V4 a
zero = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
0
  {-# INLINE zero #-}
  liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a
liftU2 = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
  {-# INLINE liftU2 #-}
  liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c
liftI2 = (a -> b -> c) -> V4 a -> V4 b -> V4 c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
  {-# INLINE liftI2 #-}

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

instance Monad V4 where
  return :: a -> V4 a
return a
a = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
a a
a a
a
  {-# INLINE return #-}
  V4 a
a a
b a
c a
d >>= :: V4 a -> (a -> V4 b) -> V4 b
>>= a -> V4 b
f = b -> b -> b -> b -> V4 b
forall a. a -> a -> a -> a -> V4 a
V4 b
a' b
b' b
c' b
d' where
    V4 b
a' b
_ b
_ b
_ = a -> V4 b
f a
a
    V4 b
_ b
b' b
_ b
_ = a -> V4 b
f a
b
    V4 b
_ b
_ b
c' b
_ = a -> V4 b
f a
c
    V4 b
_ b
_ b
_ b
d' = a -> V4 b
f a
d
  {-# INLINE (>>=) #-}

instance Num a => Num (V4 a) where
  + :: V4 a -> V4 a -> V4 a
(+) = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Num a => a -> a -> a
(+)
  {-# INLINE (+) #-}
  * :: V4 a -> V4 a -> V4 a
(*) = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Num a => a -> a -> a
(*)
  {-# INLINE (-) #-}
  (-) = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (-)
  {-# INLINE (*) #-}
  negate :: V4 a -> V4 a
negate = (a -> a) -> V4 a -> V4 a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
forall a. Num a => a -> a
negate
  {-# INLINE negate #-}
  abs :: V4 a -> V4 a
abs = (a -> a) -> V4 a -> V4 a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
forall a. Num a => a -> a
abs
  {-# INLINE abs #-}
  signum :: V4 a -> V4 a
signum = (a -> a) -> V4 a -> V4 a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
forall a. Num a => a -> a
signum
  {-# INLINE signum #-}
  fromInteger :: Integer -> V4 a
fromInteger = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V4 a) -> (Integer -> a) -> Integer -> V4 a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> a
forall a. Num a => Integer -> a
fromInteger
  {-# INLINE fromInteger #-}

instance Fractional a => Fractional (V4 a) where
  recip :: V4 a -> V4 a
recip = (a -> a) -> V4 a -> V4 a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
forall a. Fractional a => a -> a
recip
  {-# INLINE recip #-}
  / :: V4 a -> V4 a -> V4 a
(/) = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Fractional a => a -> a -> a
(/)
  {-# INLINE (/) #-}
  fromRational :: Rational -> V4 a
fromRational = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V4 a) -> (Rational -> a) -> Rational -> V4 a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> a
forall a. Fractional a => Rational -> a
fromRational
  {-# INLINE fromRational #-}

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

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

instance Distributive V4 where
  distribute :: f (V4 a) -> V4 (f a)
distribute f (V4 a)
f = f a -> f a -> f a -> f a -> V4 (f a)
forall a. a -> a -> a -> a -> V4 a
V4 ((V4 a -> a) -> f (V4 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V4 a
x a
_ a
_ a
_) -> a
x) f (V4 a)
f)
                    ((V4 a -> a) -> f (V4 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V4 a
_ a
y a
_ a
_) -> a
y) f (V4 a)
f)
                    ((V4 a -> a) -> f (V4 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V4 a
_ a
_ a
z a
_) -> a
z) f (V4 a)
f)
                    ((V4 a -> a) -> f (V4 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V4 a
_ a
_ a
_ a
w) -> a
w) f (V4 a)
f)
  {-# INLINE distribute #-}

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

#if (MIN_VERSION_hashable(1,2,5))
instance Hashable1 V4 where
  liftHashWithSalt :: (Int -> a -> Int) -> Int -> V4 a -> Int
liftHashWithSalt Int -> a -> Int
h Int
s (V4 a
a a
b a
c a
d) = Int
s Int -> a -> Int
`h` a
a Int -> a -> Int
`h` a
b Int -> a -> Int
`h` a
c Int -> a -> Int
`h` a
d
  {-# INLINE liftHashWithSalt #-}
#endif

-- | 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 :: Lens' (t a) (V2 a)
_xw V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a a
d) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
a' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c a
d'
{-# INLINE _xw #-}

_yw :: Lens' (t a) (V2 a)
_yw V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
b a
d) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
b' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c a
d'
{-# INLINE _yw #-}

_zw :: Lens' (t a) (V2 a)
_zw V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
c a
d) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
c' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c' a
d'
{-# INLINE _zw #-}

_wx :: Lens' (t a) (V2 a)
_wx V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
d a
a) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
d' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c a
d'
{-# INLINE _wx #-}

_wy :: Lens' (t a) (V2 a)
_wy V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
d a
b) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
d' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c a
d'
{-# INLINE _wy #-}

_wz :: Lens' (t a) (V2 a)
_wz V2 a -> f (V2 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
d a
c) f (V2 a) -> (V2 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
d' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c' a
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 :: Lens' (t a) (V3 a)
_xyw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
a' a
b' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _xyw #-}

_xzw :: Lens' (t a) (V3 a)
_xzw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
c a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
a' a
c' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _xzw #-}

_xwy :: Lens' (t a) (V3 a)
_xwy V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
d a
b) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
a' a
d' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _xwy #-}

_xwz :: Lens' (t a) (V3 a)
_xwz V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
d a
c) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
a' a
d' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _xwz #-}

_yxw :: Lens' (t a) (V3 a)
_yxw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
a a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
a' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _yxw #-}

_yzw :: Lens' (t a) (V3 a)
_yzw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
c a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
c' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
d'
{-# INLINE _yzw #-}

_ywx :: Lens' (t a) (V3 a)
_ywx V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
d a
a) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
d' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _ywx #-}

_ywz :: Lens' (t a) (V3 a)
_ywz V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
d a
c) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
d' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
d'
{-# INLINE _ywz #-}

_zxw :: Lens' (t a) (V3 a)
_zxw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
a a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
a' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _zxw #-}

_zyw :: Lens' (t a) (V3 a)
_zyw V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
b a
d) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
b' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
d'
{-# INLINE _zyw #-}

_zwx :: Lens' (t a) (V3 a)
_zwx V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
d a
a) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
d' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _zwx #-}

_zwy :: Lens' (t a) (V3 a)
_zwy V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
d a
b) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
d' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
d'
{-# INLINE _zwy #-}

_wxy :: Lens' (t a) (V3 a)
_wxy V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
a a
b) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
a' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _wxy #-}

_wxz :: Lens' (t a) (V3 a)
_wxz V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
a a
c) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
a' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _wxz #-}

_wyx :: Lens' (t a) (V3 a)
_wyx V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
b a
a) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
b' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c a
d'
{-# INLINE _wyx #-}

_wyz :: Lens' (t a) (V3 a)
_wyz V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
b a
c) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
b' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
d'
{-# INLINE _wyz #-}

_wzx :: Lens' (t a) (V3 a)
_wzx V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
c a
a) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
c' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b a
c' a
d'
{-# INLINE _wzx #-}

_wzy :: Lens' (t a) (V3 a)
_wzy V3 a -> f (V3 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d a
c a
b) f (V3 a) -> (V3 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
d' a
c' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b' a
c' a
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 :: Lens' (t a) (V4 a)
_xywz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
d a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
a' a
b' a
d' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _xywz #-}

_xzyw :: Lens' (t a) (V4 a)
_xzyw V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
c a
b a
d) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
a' a
c' a
b' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _xzyw #-}

_xzwy :: Lens' (t a) (V4 a)
_xzwy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
c a
d a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
a' a
c' a
d' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _xzwy #-}

_xwyz :: Lens' (t a) (V4 a)
_xwyz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
d a
b a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
a' a
d' a
b' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _xwyz #-}

_xwzy :: Lens' (t a) (V4 a)
_xwzy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
d a
c a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
a' a
d' a
c' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _xwzy #-}

_yxzw :: Lens' (t a) (V4 a)
_yxzw V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
a a
c a
d) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
a' a
c' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _yxzw #-}

_yxwz :: Lens' (t a) (V4 a)
_yxwz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
a a
d a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
a' a
d' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _yxwz #-}

_yzxw :: Lens' (t a) (V4 a)
_yzxw V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
c a
a a
d) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
c' a
a' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _yzxw #-}

_yzwx :: Lens' (t a) (V4 a)
_yzwx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
c a
d a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
c' a
d' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _yzwx #-}

_ywxz :: Lens' (t a) (V4 a)
_ywxz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
d a
a a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
d' a
a' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _ywxz #-}

_ywzx :: Lens' (t a) (V4 a)
_ywzx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
b a
d a
c a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
b' a
d' a
c' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _ywzx #-}

_zxyw :: Lens' (t a) (V4 a)
_zxyw V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
a a
b a
d) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
a' a
b' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zxyw #-}

_zxwy :: Lens' (t a) (V4 a)
_zxwy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
a a
d a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
a' a
d' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zxwy #-}

_zyxw :: Lens' (t a) (V4 a)
_zyxw V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
b a
a a
d) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
b' a
a' a
d') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zyxw #-}

_zywx :: Lens' (t a) (V4 a)
_zywx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
b a
d a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
b' a
d' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zywx #-}

_zwxy :: Lens' (t a) (V4 a)
_zwxy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
d a
a a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
d' a
a' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zwxy #-}

_zwyx :: Lens' (t a) (V4 a)
_zwyx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
c a
d a
b a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
c' a
d' a
b' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _zwyx #-}

_wxyz :: Lens' (t a) (V4 a)
_wxyz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
a a
b a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
a' a
b' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wxyz #-}

_wxzy :: Lens' (t a) (V4 a)
_wxzy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
a a
c a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
a' a
c' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wxzy #-}

_wyxz :: Lens' (t a) (V4 a)
_wyxz V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
b a
a a
c) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
b' a
a' a
c') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wyxz #-}

_wyzx :: Lens' (t a) (V4 a)
_wyzx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
b a
c a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
b' a
c' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wyzx #-}

_wzxy :: Lens' (t a) (V4 a)
_wzxy V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
c a
a a
b) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
c' a
a' a
b') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wzxy #-}

_wzyx :: Lens' (t a) (V4 a)
_wzyx V4 a -> f (V4 a)
f = (V4 a -> f (V4 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((V4 a -> f (V4 a)) -> t a -> f (t a))
-> (V4 a -> f (V4 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V4 a
a a
b a
c a
d) -> V4 a -> f (V4 a)
f (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
c a
b a
a) f (V4 a) -> (V4 a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V4 a
d' a
c' a
b' a
a') -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a' a
b' a
c' a
d'
{-# INLINE _wzyx #-}

ew :: R4 t => E t
ew :: E t
ew = (forall x. Lens' (t x) x) -> E t
forall (t :: * -> *). (forall x. Lens' (t x) x) -> E t
E forall x. Lens' (t x) x
forall (t :: * -> *) a. R4 t => Lens' (t a) a
_w

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

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

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

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

instance Storable a => Storable (V4 a) where
  sizeOf :: V4 a -> Int
sizeOf V4 a
_ = Int
4 Int -> Int -> Int
forall a. Num a => a -> a -> a
* a -> Int
forall a. Storable a => a -> Int
sizeOf (a
forall a. HasCallStack => a
undefined::a)
  {-# INLINE sizeOf #-}
  alignment :: V4 a -> Int
alignment V4 a
_ = a -> Int
forall a. Storable a => a -> Int
alignment (a
forall a. HasCallStack => a
undefined::a)
  {-# INLINE alignment #-}
  poke :: Ptr (V4 a) -> V4 a -> IO ()
poke Ptr (V4 a)
ptr (V4 a
x a
y a
z a
w) = do Ptr a -> a -> IO ()
forall a. Storable a => Ptr a -> a -> IO ()
poke Ptr a
ptr' a
x
                             Ptr a -> Int -> a -> IO ()
forall a. Storable a => Ptr a -> Int -> a -> IO ()
pokeElemOff Ptr a
ptr' Int
1 a
y
                             Ptr a -> Int -> a -> IO ()
forall a. Storable a => Ptr a -> Int -> a -> IO ()
pokeElemOff Ptr a
ptr' Int
2 a
z
                             Ptr a -> Int -> a -> IO ()
forall a. Storable a => Ptr a -> Int -> a -> IO ()
pokeElemOff Ptr a
ptr' Int
3 a
w
    where ptr' :: Ptr a
ptr' = Ptr (V4 a) -> Ptr a
forall a b. Ptr a -> Ptr b
castPtr Ptr (V4 a)
ptr
  {-# INLINE poke #-}
  peek :: Ptr (V4 a) -> IO (V4 a)
peek Ptr (V4 a)
ptr = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (a -> a -> a -> a -> V4 a) -> IO a -> IO (a -> a -> a -> V4 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Ptr a -> IO a
forall a. Storable a => Ptr a -> IO a
peek Ptr a
ptr' IO (a -> a -> a -> V4 a) -> IO a -> IO (a -> a -> V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Ptr a -> Int -> IO a
forall a. Storable a => Ptr a -> Int -> IO a
peekElemOff Ptr a
ptr' Int
1
                IO (a -> a -> V4 a) -> IO a -> IO (a -> V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Ptr a -> Int -> IO a
forall a. Storable a => Ptr a -> Int -> IO a
peekElemOff Ptr a
ptr' Int
2 IO (a -> V4 a) -> IO a -> IO (V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Ptr a -> Int -> IO a
forall a. Storable a => Ptr a -> Int -> IO a
peekElemOff Ptr a
ptr' Int
3
    where ptr' :: Ptr a
ptr' = Ptr (V4 a) -> Ptr a
forall a b. Ptr a -> Ptr b
castPtr Ptr (V4 a)
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 -> V4 a
vector (V3 a
a a
b a
c) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
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 -> V4 a
point (V3 a
a a
b a
c) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
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 -> V3 a
normalizePoint (V4 a
a a
b a
c a
w) = (a
1a -> a -> a
forall a. Fractional a => a -> a -> a
/a
w) a -> V3 a -> V3 a
forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^ a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b a
c
{-# INLINE normalizePoint #-}

instance Epsilon a => Epsilon (V4 a) where
  nearZero :: V4 a -> Bool
nearZero = a -> Bool
forall a. Epsilon a => a -> Bool
nearZero (a -> Bool) -> (V4 a -> a) -> V4 a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. V4 a -> a
forall (f :: * -> *) a. (Metric f, Num a) => f a -> a
quadrance
  {-# INLINE nearZero #-}

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

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

  unsafeIndex :: (V4 a, V4 a) -> V4 a -> Int
unsafeIndex (V4 a
l1 a
l2 a
l3 a
l4,V4 a
u1 a
u2 a
u3 a
u4) (V4 a
i1 a
i2 a
i3 a
i4) =
    (a, a) -> a -> Int
forall a. Ix a => (a, a) -> a -> Int
unsafeIndex (a
l4,a
u4) a
i4 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ (a, a) -> Int
forall a. Ix a => (a, a) -> Int
unsafeRangeSize (a
l4,a
u4) Int -> Int -> Int
forall a. Num a => a -> a -> a
* (
    (a, a) -> a -> Int
forall a. Ix a => (a, a) -> a -> Int
unsafeIndex (a
l3,a
u3) a
i3 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ (a, a) -> Int
forall a. Ix a => (a, a) -> Int
unsafeRangeSize (a
l3,a
u3) Int -> Int -> Int
forall a. Num a => a -> a -> a
* (
    (a, a) -> a -> Int
forall a. Ix a => (a, a) -> a -> Int
unsafeIndex (a
l2,a
u2) a
i2 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ (a, a) -> Int
forall a. Ix a => (a, a) -> Int
unsafeRangeSize (a
l2,a
u2) Int -> Int -> Int
forall a. Num a => a -> a -> a
*
    (a, a) -> a -> Int
forall a. Ix a => (a, a) -> a -> Int
unsafeIndex (a
l1,a
u1) a
i1))
  {-# INLINE unsafeIndex #-}

  inRange :: (V4 a, V4 a) -> V4 a -> Bool
inRange (V4 a
l1 a
l2 a
l3 a
l4,V4 a
u1 a
u2 a
u3 a
u4) (V4 a
i1 a
i2 a
i3 a
i4) =
    (a, a) -> a -> Bool
forall a. Ix a => (a, a) -> a -> Bool
inRange (a
l1,a
u1) a
i1 Bool -> Bool -> Bool
&& (a, a) -> a -> Bool
forall a. Ix a => (a, a) -> a -> Bool
inRange (a
l2,a
u2) a
i2 Bool -> Bool -> Bool
&&
    (a, a) -> a -> Bool
forall a. Ix a => (a, a) -> a -> Bool
inRange (a
l3,a
u3) a
i3 Bool -> Bool -> Bool
&& (a, a) -> a -> Bool
forall a. Ix a => (a, a) -> a -> Bool
inRange (a
l4,a
u4) a
i4
  {-# INLINE inRange #-}

instance Representable V4 where
  type Rep V4 = E V4
  tabulate :: (Rep V4 -> a) -> V4 a
tabulate Rep V4 -> a
f = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (Rep V4 -> a
f Rep V4
forall (t :: * -> *). R1 t => E t
ex) (Rep V4 -> a
f Rep V4
forall (t :: * -> *). R2 t => E t
ey) (Rep V4 -> a
f Rep V4
forall (t :: * -> *). R3 t => E t
ez) (Rep V4 -> a
f Rep V4
forall (t :: * -> *). R4 t => E t
ew)
  {-# INLINE tabulate #-}
  index :: V4 a -> Rep V4 -> a
index V4 a
xs (E l) = Getting a (V4 a) a -> V4 a -> a
forall s (m :: * -> *) a. MonadReader s m => Getting a s a -> m a
view Getting a (V4 a) a
forall a. Lens' (V4 a) a
l V4 a
xs
  {-# INLINE index #-}

instance WithIndex.FunctorWithIndex (E V4) V4 where
  imap :: (E V4 -> a -> b) -> V4 a -> V4 b
imap E V4 -> a -> b
f (V4 a
a a
b a
c a
d) = b -> b -> b -> b -> V4 b
forall a. a -> a -> a -> a -> V4 a
V4 (E V4 -> a -> b
f E V4
forall (t :: * -> *). R1 t => E t
ex a
a) (E V4 -> a -> b
f E V4
forall (t :: * -> *). R2 t => E t
ey a
b) (E V4 -> a -> b
f E V4
forall (t :: * -> *). R3 t => E t
ez a
c) (E V4 -> a -> b
f E V4
forall (t :: * -> *). R4 t => E t
ew a
d)
  {-# INLINE imap #-}

instance WithIndex.FoldableWithIndex (E V4) V4 where
  ifoldMap :: (E V4 -> a -> m) -> V4 a -> m
ifoldMap E V4 -> a -> m
f (V4 a
a a
b a
c a
d) = E V4 -> a -> m
f E V4
forall (t :: * -> *). R1 t => E t
ex a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` E V4 -> a -> m
f E V4
forall (t :: * -> *). R2 t => E t
ey a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` E V4 -> a -> m
f E V4
forall (t :: * -> *). R3 t => E t
ez a
c m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` E V4 -> a -> m
f E V4
forall (t :: * -> *). R4 t => E t
ew a
d
  {-# INLINE ifoldMap #-}

instance WithIndex.TraversableWithIndex (E V4) V4 where
  itraverse :: (E V4 -> a -> f b) -> V4 a -> f (V4 b)
itraverse E V4 -> a -> f b
f (V4 a
a a
b a
c a
d) = b -> b -> b -> b -> V4 b
forall a. a -> a -> a -> a -> V4 a
V4 (b -> b -> b -> b -> V4 b) -> f b -> f (b -> b -> b -> V4 b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> E V4 -> a -> f b
f E V4
forall (t :: * -> *). R1 t => E t
ex a
a f (b -> b -> b -> V4 b) -> f b -> f (b -> b -> V4 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> E V4 -> a -> f b
f E V4
forall (t :: * -> *). R2 t => E t
ey a
b f (b -> b -> V4 b) -> f b -> f (b -> V4 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> E V4 -> a -> f b
f E V4
forall (t :: * -> *). R3 t => E t
ez a
c f (b -> V4 b) -> f b -> f (V4 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> E V4 -> a -> f b
f E V4
forall (t :: * -> *). R4 t => E t
ew a
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 :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a))
ix Index (V4 a)
i = E V4 -> forall a. Lens' (V4 a) a
forall (t :: * -> *). E t -> forall x. Lens' (t x) x
el Index (V4 a)
E V4
i

instance Each (V4 a) (V4 b) a b where
  each :: (a -> f b) -> V4 a -> f (V4 b)
each = (a -> f b) -> V4 a -> f (V4 b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
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 :: MVector s (V4 a) -> Int
basicLength (MV_V4 n _) = Int
n
  basicUnsafeSlice :: Int -> Int -> MVector s (V4 a) -> MVector s (V4 a)
basicUnsafeSlice Int
m Int
n (MV_V4 _ v) = Int -> MVector s a -> MVector s (V4 a)
forall s a. Int -> MVector s a -> MVector s (V4 a)
MV_V4 Int
n (Int -> Int -> MVector s a -> MVector s a
forall (v :: * -> * -> *) a s.
MVector v a =>
Int -> Int -> v s a -> v s a
M.basicUnsafeSlice (Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
m) (Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n) MVector s a
v)
  basicOverlaps :: MVector s (V4 a) -> MVector s (V4 a) -> Bool
basicOverlaps (MV_V4 _ v) (MV_V4 _ u) = MVector s a -> MVector s a -> Bool
forall (v :: * -> * -> *) a s.
MVector v a =>
v s a -> v s a -> Bool
M.basicOverlaps MVector s a
v MVector s a
u
  basicUnsafeNew :: Int -> m (MVector (PrimState m) (V4 a))
basicUnsafeNew Int
n = (MVector (PrimState m) a -> MVector (PrimState m) (V4 a))
-> m (MVector (PrimState m) a) -> m (MVector (PrimState m) (V4 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (Int -> MVector (PrimState m) a -> MVector (PrimState m) (V4 a)
forall s a. Int -> MVector s a -> MVector s (V4 a)
MV_V4 Int
n) (Int -> m (MVector (PrimState m) a)
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
Int -> m (v (PrimState m) a)
M.basicUnsafeNew (Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n))
  basicUnsafeRead :: MVector (PrimState m) (V4 a) -> Int -> m (V4 a)
basicUnsafeRead (MV_V4 _ v) Int
i =
    do let o :: Int
o = Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
i
       a
x <- MVector (PrimState m) a -> Int -> m a
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> m a
M.basicUnsafeRead MVector (PrimState m) a
v Int
o
       a
y <- MVector (PrimState m) a -> Int -> m a
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> m a
M.basicUnsafeRead MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)
       a
z <- MVector (PrimState m) a -> Int -> m a
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> m a
M.basicUnsafeRead MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
2)
       a
w <- MVector (PrimState m) a -> Int -> m a
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> m a
M.basicUnsafeRead MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
3)
       V4 a -> m (V4 a)
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y a
z a
w)
  basicUnsafeWrite :: MVector (PrimState m) (V4 a) -> Int -> V4 a -> m ()
basicUnsafeWrite (MV_V4 _ v) Int
i (V4 a
x a
y a
z a
w) =
    do let o :: Int
o = Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
i
       MVector (PrimState m) a -> Int -> a -> m ()
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> a -> m ()
M.basicUnsafeWrite MVector (PrimState m) a
v Int
o     a
x
       MVector (PrimState m) a -> Int -> a -> m ()
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> a -> m ()
M.basicUnsafeWrite MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1) a
y
       MVector (PrimState m) a -> Int -> a -> m ()
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> a -> m ()
M.basicUnsafeWrite MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
2) a
z
       MVector (PrimState m) a -> Int -> a -> m ()
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> Int -> a -> m ()
M.basicUnsafeWrite MVector (PrimState m) a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
3) a
w
#if MIN_VERSION_vector(0,11,0)
  basicInitialize :: MVector (PrimState m) (V4 a) -> m ()
basicInitialize (MV_V4 _ v) = MVector (PrimState m) a -> m ()
forall (v :: * -> * -> *) a (m :: * -> *).
(MVector v a, PrimMonad m) =>
v (PrimState m) a -> m ()
M.basicInitialize MVector (PrimState m) a
v
#endif

instance U.Unbox a => G.Vector U.Vector (V4 a) where
  basicUnsafeFreeze :: Mutable Vector (PrimState m) (V4 a) -> m (Vector (V4 a))
basicUnsafeFreeze (MV_V4 n v) = (Vector a -> Vector (V4 a)) -> m (Vector a) -> m (Vector (V4 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM ( Int -> Vector a -> Vector (V4 a)
forall a. Int -> Vector a -> Vector (V4 a)
V_V4 Int
n) (Mutable Vector (PrimState m) a -> m (Vector a)
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, PrimMonad m) =>
Mutable v (PrimState m) a -> m (v a)
G.basicUnsafeFreeze MVector (PrimState m) a
Mutable Vector (PrimState m) a
v)
  basicUnsafeThaw :: Vector (V4 a) -> m (Mutable Vector (PrimState m) (V4 a))
basicUnsafeThaw   ( V_V4 n v) = (MVector (PrimState m) a -> MVector (PrimState m) (V4 a))
-> m (MVector (PrimState m) a) -> m (MVector (PrimState m) (V4 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (Int -> MVector (PrimState m) a -> MVector (PrimState m) (V4 a)
forall s a. Int -> MVector s a -> MVector s (V4 a)
MV_V4 Int
n) (Vector a -> m (Mutable Vector (PrimState m) a)
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, PrimMonad m) =>
v a -> m (Mutable v (PrimState m) a)
G.basicUnsafeThaw   Vector a
v)
  basicLength :: Vector (V4 a) -> Int
basicLength       ( V_V4 n _) = Int
n
  basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a)
basicUnsafeSlice Int
m Int
n (V_V4 _ v) = Int -> Vector a -> Vector (V4 a)
forall a. Int -> Vector a -> Vector (V4 a)
V_V4 Int
n (Int -> Int -> Vector a -> Vector a
forall (v :: * -> *) a. Vector v a => Int -> Int -> v a -> v a
G.basicUnsafeSlice (Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
m) (Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n) Vector a
v)
  basicUnsafeIndexM :: Vector (V4 a) -> Int -> m (V4 a)
basicUnsafeIndexM (V_V4 _ v) Int
i =
    do let o :: Int
o = Int
4Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
i
       a
x <- Vector a -> Int -> m a
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, Monad m) =>
v a -> Int -> m a
G.basicUnsafeIndexM Vector a
v Int
o
       a
y <- Vector a -> Int -> m a
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, Monad m) =>
v a -> Int -> m a
G.basicUnsafeIndexM Vector a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)
       a
z <- Vector a -> Int -> m a
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, Monad m) =>
v a -> Int -> m a
G.basicUnsafeIndexM Vector a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
2)
       a
w <- Vector a -> Int -> m a
forall (v :: * -> *) a (m :: * -> *).
(Vector v a, Monad m) =>
v a -> Int -> m a
G.basicUnsafeIndexM Vector a
v (Int
oInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
3)
       V4 a -> m (V4 a)
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y a
z a
w)

instance MonadZip V4 where
  mzipWith :: (a -> b -> c) -> V4 a -> V4 b -> V4 c
mzipWith = (a -> b -> c) -> V4 a -> V4 b -> V4 c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2

instance MonadFix V4 where
  mfix :: (a -> V4 a) -> V4 a
mfix a -> V4 a
f = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (let V4 a
a a
_ a
_ a
_ = a -> V4 a
f a
a in a
a)
              (let V4 a
_ a
a a
_ a
_ = a -> V4 a
f a
a in a
a)
              (let V4 a
_ a
_ a
a a
_ = a -> V4 a
f a
a in a
a)
              (let V4 a
_ a
_ a
_ a
a = a -> V4 a
f a
a in a
a)

instance Bounded a => Bounded (V4 a) where
  minBound :: V4 a
minBound = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Bounded a => a
minBound
  {-# INLINE minBound #-}
  maxBound :: V4 a
maxBound = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Bounded a => a
maxBound
  {-# INLINE maxBound #-}

instance NFData a => NFData (V4 a) where
  rnf :: V4 a -> ()
rnf (V4 a
a a
b a
c a
d) = a -> ()
forall a. NFData a => a -> ()
rnf a
a () -> () -> ()
`seq` a -> ()
forall a. NFData a => a -> ()
rnf a
b () -> () -> ()
`seq` a -> ()
forall a. NFData a => a -> ()
rnf a
c () -> () -> ()
`seq` a -> ()
forall a. NFData a => a -> ()
rnf a
d

instance Serial1 V4 where
  serializeWith :: (a -> m ()) -> V4 a -> m ()
serializeWith = (a -> m ()) -> V4 a -> m ()
forall (t :: * -> *) (f :: * -> *) a b.
(Foldable t, Applicative f) =>
(a -> f b) -> t a -> f ()
traverse_
  deserializeWith :: m a -> m (V4 a)
deserializeWith m a
k = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (a -> a -> a -> a -> V4 a) -> m a -> m (a -> a -> a -> V4 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m a
k m (a -> a -> a -> V4 a) -> m a -> m (a -> a -> V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> m a
k m (a -> a -> V4 a) -> m a -> m (a -> V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> m a
k m (a -> V4 a) -> m a -> m (V4 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> m a
k

instance Serial a => Serial (V4 a) where
  serialize :: V4 a -> m ()
serialize = (a -> m ()) -> V4 a -> m ()
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadPut m) =>
(a -> m ()) -> f a -> m ()
serializeWith a -> m ()
forall a (m :: * -> *). (Serial a, MonadPut m) => a -> m ()
serialize
  deserialize :: m (V4 a)
deserialize = m a -> m (V4 a)
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadGet m) =>
m a -> m (f a)
deserializeWith m a
forall a (m :: * -> *). (Serial a, MonadGet m) => m a
deserialize

instance Binary a => Binary (V4 a) where
  put :: V4 a -> Put
put = (a -> Put) -> V4 a -> Put
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadPut m) =>
(a -> m ()) -> f a -> m ()
serializeWith a -> Put
forall t. Binary t => t -> Put
Binary.put
  get :: Get (V4 a)
get = Get a -> Get (V4 a)
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadGet m) =>
m a -> m (f a)
deserializeWith Get a
forall t. Binary t => Get t
Binary.get

instance Serialize a => Serialize (V4 a) where
  put :: Putter (V4 a)
put = (a -> PutM ()) -> Putter (V4 a)
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadPut m) =>
(a -> m ()) -> f a -> m ()
serializeWith a -> PutM ()
forall t. Serialize t => Putter t
Cereal.put
  get :: Get (V4 a)
get = Get a -> Get (V4 a)
forall (f :: * -> *) (m :: * -> *) a.
(Serial1 f, MonadGet m) =>
m a -> m (f a)
deserializeWith Get a
forall t. Serialize t => Get t
Cereal.get

#if (MIN_VERSION_transformers(0,5,0)) || !(MIN_VERSION_transformers(0,4,0))
instance Eq1 V4 where
  liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool
liftEq a -> b -> Bool
k (V4 a
a a
b a
c a
d) (V4 b
e b
f b
g b
h) = a -> b -> Bool
k a
a b
e Bool -> Bool -> Bool
&& a -> b -> Bool
k a
b b
f Bool -> Bool -> Bool
&& a -> b -> Bool
k a
c b
g Bool -> Bool -> Bool
&& a -> b -> Bool
k a
d b
h
instance Ord1 V4 where
  liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering
liftCompare a -> b -> Ordering
k (V4 a
a a
b a
c a
d) (V4 b
e b
f b
g b
h) = a -> b -> Ordering
k a
a b
e Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
k a
b b
f Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
k a
c b
g Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
k a
d b
h
instance Read1 V4 where
  liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V4 a)
liftReadsPrec Int -> ReadS a
k ReadS [a]
_ Int
z = Bool -> ReadS (V4 a) -> ReadS (V4 a)
forall a. Bool -> ReadS a -> ReadS a
readParen (Int
z Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (ReadS (V4 a) -> ReadS (V4 a)) -> ReadS (V4 a) -> ReadS (V4 a)
forall a b. (a -> b) -> a -> b
$ \String
r ->
     [ (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
d, String
r5)
     | (String
"V4",String
r1) <- ReadS String
lex String
r
     , (a
a,String
r2) <- Int -> ReadS a
k Int
11 String
r1
     , (a
b,String
r3) <- Int -> ReadS a
k Int
11 String
r2
     , (a
c,String
r4) <- Int -> ReadS a
k Int
11 String
r3
     , (a
d,String
r5) <- Int -> ReadS a
k Int
11 String
r4
     ]
instance Show1 V4 where
  liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS
liftShowsPrec Int -> a -> ShowS
f [a] -> ShowS
_ Int
z (V4 a
a a
b a
c a
d) = Bool -> ShowS -> ShowS
showParen (Int
z Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (ShowS -> ShowS) -> ShowS -> ShowS
forall a b. (a -> b) -> a -> b
$
     String -> ShowS
showString String
"V4 " ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> a -> ShowS
f Int
11 a
a ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Char -> ShowS
showChar Char
' ' ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> a -> ShowS
f Int
11 a
b ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Char -> ShowS
showChar Char
' ' ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> a -> ShowS
f Int
11 a
c ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Char -> ShowS
showChar Char
' ' ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> a -> ShowS
f Int
11 a
d
#else
instance Eq1 V4 where eq1 = (==)
instance Ord1 V4 where compare1 = compare
instance Show1 V4 where showsPrec1 = showsPrec
instance Read1 V4 where readsPrec1 = readsPrec
#endif

instance Field1 (V4 a) (V4 a) a a where
  _1 :: (a -> f a) -> V4 a -> f (V4 a)
_1 a -> f a
f (V4 a
x a
y a
z a
w) = a -> f a
f a
x f a -> (a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
x' -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x' a
y a
z a
w

instance Field2 (V4 a) (V4 a) a a where
  _2 :: (a -> f a) -> V4 a -> f (V4 a)
_2 a -> f a
f (V4 a
x a
y a
z a
w) = a -> f a
f a
y f a -> (a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
y' -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y' a
z a
w

instance Field3 (V4 a) (V4 a) a a where
  _3 :: (a -> f a) -> V4 a -> f (V4 a)
_3 a -> f a
f (V4 a
x a
y a
z a
w) = a -> f a
f a
z f a -> (a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
z' -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y a
z' a
w

instance Field4 (V4 a) (V4 a) a a where
  _4 :: (a -> f a) -> V4 a -> f (V4 a)
_4 a -> f a
f (V4 a
x a
y a
z a
w) = a -> f a
f a
w f a -> (a -> V4 a) -> f (V4 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
w' -> a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y a
z a
w'

instance Semigroup a => Semigroup (V4 a) where
 <> :: V4 a -> V4 a -> V4 a
(<>) = (a -> a -> a) -> V4 a -> V4 a -> V4 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Semigroup a => a -> a -> a
(<>)

instance Monoid a => Monoid (V4 a) where
  mempty :: V4 a
mempty = a -> V4 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Monoid a => a
mempty
#if !(MIN_VERSION_base(4,11,0))
  mappend = liftA2 mappend
#endif