{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DeriveLift #-}
#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
module Linear.V3
( V3(..)
, cross, triple
, R1(..)
, R2(..)
, _yx
, R3(..)
, _xz, _yz, _zx, _zy
, _xzy, _yxz, _yzx, _zxy, _zyx
, ex, ey, ez
) 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
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.Vector
import System.Random (Random(..))
data V3 a = V3 !a !a !a deriving (V3 a -> V3 a -> Bool
(V3 a -> V3 a -> Bool) -> (V3 a -> V3 a -> Bool) -> Eq (V3 a)
forall a. Eq a => V3 a -> V3 a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: V3 a -> V3 a -> Bool
$c/= :: forall a. Eq a => V3 a -> V3 a -> Bool
== :: V3 a -> V3 a -> Bool
$c== :: forall a. Eq a => V3 a -> V3 a -> Bool
Eq,Eq (V3 a)
Eq (V3 a)
-> (V3 a -> V3 a -> Ordering)
-> (V3 a -> V3 a -> Bool)
-> (V3 a -> V3 a -> Bool)
-> (V3 a -> V3 a -> Bool)
-> (V3 a -> V3 a -> Bool)
-> (V3 a -> V3 a -> V3 a)
-> (V3 a -> V3 a -> V3 a)
-> Ord (V3 a)
V3 a -> V3 a -> Bool
V3 a -> V3 a -> Ordering
V3 a -> V3 a -> V3 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 (V3 a)
forall a. Ord a => V3 a -> V3 a -> Bool
forall a. Ord a => V3 a -> V3 a -> Ordering
forall a. Ord a => V3 a -> V3 a -> V3 a
min :: V3 a -> V3 a -> V3 a
$cmin :: forall a. Ord a => V3 a -> V3 a -> V3 a
max :: V3 a -> V3 a -> V3 a
$cmax :: forall a. Ord a => V3 a -> V3 a -> V3 a
>= :: V3 a -> V3 a -> Bool
$c>= :: forall a. Ord a => V3 a -> V3 a -> Bool
> :: V3 a -> V3 a -> Bool
$c> :: forall a. Ord a => V3 a -> V3 a -> Bool
<= :: V3 a -> V3 a -> Bool
$c<= :: forall a. Ord a => V3 a -> V3 a -> Bool
< :: V3 a -> V3 a -> Bool
$c< :: forall a. Ord a => V3 a -> V3 a -> Bool
compare :: V3 a -> V3 a -> Ordering
$ccompare :: forall a. Ord a => V3 a -> V3 a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (V3 a)
Ord,Int -> V3 a -> ShowS
[V3 a] -> ShowS
V3 a -> String
(Int -> V3 a -> ShowS)
-> (V3 a -> String) -> ([V3 a] -> ShowS) -> Show (V3 a)
forall a. Show a => Int -> V3 a -> ShowS
forall a. Show a => [V3 a] -> ShowS
forall a. Show a => V3 a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [V3 a] -> ShowS
$cshowList :: forall a. Show a => [V3 a] -> ShowS
show :: V3 a -> String
$cshow :: forall a. Show a => V3 a -> String
showsPrec :: Int -> V3 a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> V3 a -> ShowS
Show,ReadPrec [V3 a]
ReadPrec (V3 a)
Int -> ReadS (V3 a)
ReadS [V3 a]
(Int -> ReadS (V3 a))
-> ReadS [V3 a]
-> ReadPrec (V3 a)
-> ReadPrec [V3 a]
-> Read (V3 a)
forall a. Read a => ReadPrec [V3 a]
forall a. Read a => ReadPrec (V3 a)
forall a. Read a => Int -> ReadS (V3 a)
forall a. Read a => ReadS [V3 a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
readListPrec :: ReadPrec [V3 a]
$creadListPrec :: forall a. Read a => ReadPrec [V3 a]
readPrec :: ReadPrec (V3 a)
$creadPrec :: forall a. Read a => ReadPrec (V3 a)
readList :: ReadS [V3 a]
$creadList :: forall a. Read a => ReadS [V3 a]
readsPrec :: Int -> ReadS (V3 a)
$creadsPrec :: forall a. Read a => Int -> ReadS (V3 a)
Read,Typeable (V3 a)
DataType
Constr
Typeable (V3 a)
-> (forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a))
-> (forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a))
-> (V3 a -> Constr)
-> (V3 a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (V3 a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)))
-> ((forall b. Data b => b -> b) -> V3 a -> V3 a)
-> (forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r)
-> (forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r)
-> (forall u. (forall d. Data d => d -> u) -> V3 a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> V3 a -> u)
-> (forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a))
-> (forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a))
-> (forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a))
-> Data (V3 a)
V3 a -> DataType
V3 a -> Constr
(forall d. Data d => c (t d)) -> Maybe (c (V3 a))
(forall b. Data b => b -> b) -> V3 a -> V3 a
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a)
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a)
forall a. Data a => Typeable (V3 a)
forall a. Data a => V3 a -> DataType
forall a. Data a => V3 a -> Constr
forall a. Data a => (forall b. Data b => b -> b) -> V3 a -> V3 a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> V3 a -> u
forall a u. Data a => (forall d. Data d => d -> u) -> V3 a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (V3 a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 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) -> V3 a -> u
forall u. (forall d. Data d => d -> u) -> V3 a -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (V3 a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a))
$cV3 :: Constr
$tV3 :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
gmapMp :: (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
gmapM :: (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> V3 a -> u
gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u]
$cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> V3 a -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r
gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a
$cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> V3 a -> V3 a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (V3 a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (V3 a))
dataTypeOf :: V3 a -> DataType
$cdataTypeOf :: forall a. Data a => V3 a -> DataType
toConstr :: V3 a -> Constr
$ctoConstr :: forall a. Data a => V3 a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V3 a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V3 a -> c (V3 a)
$cp1Data :: forall a. Data a => Typeable (V3 a)
Data
,(forall x. V3 a -> Rep (V3 a) x)
-> (forall x. Rep (V3 a) x -> V3 a) -> Generic (V3 a)
forall x. Rep (V3 a) x -> V3 a
forall x. V3 a -> Rep (V3 a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (V3 a) x -> V3 a
forall a x. V3 a -> Rep (V3 a) x
$cto :: forall a x. Rep (V3 a) x -> V3 a
$cfrom :: forall a x. V3 a -> Rep (V3 a) x
Generic,(forall a. V3 a -> Rep1 V3 a)
-> (forall a. Rep1 V3 a -> V3 a) -> Generic1 V3
forall a. Rep1 V3 a -> V3 a
forall a. V3 a -> Rep1 V3 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 V3 a -> V3 a
$cfrom1 :: forall a. V3 a -> Rep1 V3 a
Generic1
#if defined(MIN_VERSION_template_haskell)
,V3 a -> Q Exp
V3 a -> Q (TExp (V3 a))
(V3 a -> Q Exp) -> (V3 a -> Q (TExp (V3 a))) -> Lift (V3 a)
forall a. Lift a => V3 a -> Q Exp
forall a. Lift a => V3 a -> Q (TExp (V3 a))
forall t. (t -> Q Exp) -> (t -> Q (TExp t)) -> Lift t
liftTyped :: V3 a -> Q (TExp (V3 a))
$cliftTyped :: forall a. Lift a => V3 a -> Q (TExp (V3 a))
lift :: V3 a -> Q Exp
$clift :: forall a. Lift a => V3 a -> Q Exp
Lift
#endif
)
instance Finite V3 where
type Size V3 = 3
toV :: V3 a -> V (Size V3) a
toV (V3 a
a a
b a
c) = Vector a -> V 3 a
forall k (n :: k) a. Vector a -> V n a
V (Int -> [a] -> Vector a
forall a. Int -> [a] -> Vector a
V.fromListN Int
3 [a
a,a
b,a
c])
fromV :: V (Size V3) a -> V3 a
fromV (V Vector a
v) = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
0) (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
1) (Vector a
v Vector a -> Int -> a
forall a. Vector a -> Int -> a
V.! Int
2)
instance Functor V3 where
fmap :: (a -> b) -> V3 a -> V3 b
fmap a -> b
f (V3 a
a a
b a
c) = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (a -> b
f a
a) (a -> b
f a
b) (a -> b
f a
c)
{-# INLINE fmap #-}
a
a <$ :: a -> V3 b -> V3 a
<$ V3 b
_ = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
a a
a
{-# INLINE (<$) #-}
instance Foldable V3 where
foldMap :: (a -> m) -> V3 a -> m
foldMap a -> m
f (V3 a
a a
b a
c) = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c
{-# INLINE foldMap #-}
#if MIN_VERSION_base(4,13,0)
foldMap' :: (a -> m) -> V3 a -> m
foldMap' a -> m
f (V3 a
a a
b a
c) = (a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b) m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c
{-# INLINE foldMap' #-}
#endif
null :: V3 a -> Bool
null V3 a
_ = Bool
False
length :: V3 a -> Int
length V3 a
_ = Int
3
instance Random a => Random (V3 a) where
random :: g -> (V3 a, g)
random g
g = case g -> (a, g)
forall a g. (Random a, RandomGen g) => g -> (a, g)
random g
g of
(a
a, g
g') -> case g -> (a, g)
forall a g. (Random a, RandomGen g) => g -> (a, g)
random g
g' of
(a
b, g
g'') -> case g -> (a, g)
forall a g. (Random a, RandomGen g) => g -> (a, g)
random g
g'' of
(a
c, g
g''') -> (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b a
c, g
g''')
randomR :: (V3 a, V3 a) -> g -> (V3 a, g)
randomR (V3 a
a a
b a
c, V3 a
a' a
b' a
c') g
g = case (a, a) -> g -> (a, g)
forall a g. (Random a, RandomGen g) => (a, a) -> g -> (a, g)
randomR (a
a,a
a') g
g of
(a
a'', g
g') -> case (a, a) -> g -> (a, g)
forall a g. (Random a, RandomGen g) => (a, a) -> g -> (a, g)
randomR (a
b,a
b') g
g' of
(a
b'', g
g'') -> case (a, a) -> g -> (a, g)
forall a g. (Random a, RandomGen g) => (a, a) -> g -> (a, g)
randomR (a
c,a
c') g
g'' of
(a
c'', g
g''') -> (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a'' a
b'' a
c'', g
g''')
instance Traversable V3 where
traverse :: (a -> f b) -> V3 a -> f (V3 b)
traverse a -> f b
f (V3 a
a a
b a
c) = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (b -> b -> b -> V3 b) -> f b -> f (b -> b -> V3 b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> b -> V3 b) -> f b -> f (b -> V3 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b f (b -> V3 b) -> f b -> f (V3 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
c
{-# INLINE traverse #-}
instance Foldable1 V3 where
foldMap1 :: (a -> m) -> V3 a -> m
foldMap1 a -> m
f (V3 a
a a
b a
c) = 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
{-# INLINE foldMap1 #-}
instance Traversable1 V3 where
traverse1 :: (a -> f b) -> V3 a -> f (V3 b)
traverse1 a -> f b
f (V3 a
a a
b a
c) = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (b -> b -> b -> V3 b) -> f b -> f (b -> b -> V3 b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> b -> V3 b) -> f b -> f (b -> V3 b)
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> a -> f b
f a
b f (b -> V3 b) -> f b -> f (V3 b)
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> a -> f b
f a
c
{-# INLINE traverse1 #-}
instance Apply V3 where
V3 a -> b
a a -> b
b a -> b
c <.> :: V3 (a -> b) -> V3 a -> V3 b
<.> V3 a
d a
e a
f = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (a -> b
a a
d) (a -> b
b a
e) (a -> b
c a
f)
{-# INLINE (<.>) #-}
instance Applicative V3 where
pure :: a -> V3 a
pure a
a = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
a a
a
{-# INLINE pure #-}
V3 a -> b
a a -> b
b a -> b
c <*> :: V3 (a -> b) -> V3 a -> V3 b
<*> V3 a
d a
e a
f = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (a -> b
a a
d) (a -> b
b a
e) (a -> b
c a
f)
{-# INLINE (<*>) #-}
instance Additive V3 where
zero :: V3 a
zero = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
0
{-# INLINE zero #-}
liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a
liftU2 = (a -> a -> a) -> V3 a -> V3 a -> V3 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
{-# INLINE liftU2 #-}
liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c
liftI2 = (a -> b -> c) -> V3 a -> V3 b -> V3 c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
{-# INLINE liftI2 #-}
instance Bind V3 where
V3 a
a a
b a
c >>- :: V3 a -> (a -> V3 b) -> V3 b
>>- a -> V3 b
f = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 b
a' b
b' b
c' where
V3 b
a' b
_ b
_ = a -> V3 b
f a
a
V3 b
_ b
b' b
_ = a -> V3 b
f a
b
V3 b
_ b
_ b
c' = a -> V3 b
f a
c
{-# INLINE (>>-) #-}
instance Monad V3 where
#if !(MIN_VERSION_base(4,11,0))
return a = V3 a a a
{-# INLINE return #-}
#endif
V3 a
a a
b a
c >>= :: V3 a -> (a -> V3 b) -> V3 b
>>= a -> V3 b
f = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 b
a' b
b' b
c' where
V3 b
a' b
_ b
_ = a -> V3 b
f a
a
V3 b
_ b
b' b
_ = a -> V3 b
f a
b
V3 b
_ b
_ b
c' = a -> V3 b
f a
c
{-# INLINE (>>=) #-}
instance Num a => Num (V3 a) where
+ :: V3 a -> V3 a -> V3 a
(+) = (a -> a -> a) -> V3 a -> V3 a -> V3 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) -> V3 a -> V3 a -> V3 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (-)
{-# INLINE (-) #-}
* :: V3 a -> V3 a -> V3 a
(*) = (a -> a -> a) -> V3 a -> V3 a -> V3 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 (*) #-}
negate :: V3 a -> V3 a
negate = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
abs = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
signum = (a -> a) -> V3 a -> V3 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 -> V3 a
fromInteger = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V3 a) -> (Integer -> a) -> Integer -> V3 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 (V3 a) where
recip :: V3 a -> V3 a
recip = (a -> a) -> V3 a -> V3 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 #-}
/ :: V3 a -> V3 a -> V3 a
(/) = (a -> a -> a) -> V3 a -> V3 a -> V3 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 -> V3 a
fromRational = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V3 a) -> (Rational -> a) -> Rational -> V3 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 (V3 a) where
pi :: V3 a
pi = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Floating a => a
pi
{-# INLINE pi #-}
exp :: V3 a -> V3 a
exp = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
sqrt = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
log = (a -> a) -> V3 a -> V3 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 #-}
** :: V3 a -> V3 a -> V3 a
(**) = (a -> a -> a) -> V3 a -> V3 a -> V3 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 :: V3 a -> V3 a -> V3 a
logBase = (a -> a -> a) -> V3 a -> V3 a -> V3 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 :: V3 a -> V3 a
sin = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
tan = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
cos = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
asin = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
atan = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
acos = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
sinh = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
tanh = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
cosh = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
asinh = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
atanh = (a -> a) -> V3 a -> V3 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 :: V3 a -> V3 a
acosh = (a -> a) -> V3 a -> V3 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 Hashable a => Hashable (V3 a) where
hashWithSalt :: Int -> V3 a -> Int
hashWithSalt Int
s (V3 a
a a
b a
c) = 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
{-# INLINE hashWithSalt #-}
instance Hashable1 V3 where
liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int
liftHashWithSalt Int -> a -> Int
h Int
s (V3 a
a a
b a
c) = Int
s Int -> a -> Int
`h` a
a Int -> a -> Int
`h` a
b Int -> a -> Int
`h` a
c
{-# INLINE liftHashWithSalt #-}
instance Metric V3 where
dot :: V3 a -> V3 a -> a
dot (V3 a
a a
b a
c) (V3 a
d a
e a
f) = a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
d a -> a -> a
forall a. Num a => a -> a -> a
+ a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
e a -> a -> a
forall a. Num a => a -> a -> a
+ a
c a -> a -> a
forall a. Num a => a -> a -> a
* a
f
{-# INLINABLE dot #-}
instance Distributive V3 where
distribute :: f (V3 a) -> V3 (f a)
distribute f (V3 a)
f = f a -> f a -> f a -> V3 (f a)
forall a. a -> a -> a -> V3 a
V3 ((V3 a -> a) -> f (V3 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V3 a
x a
_ a
_) -> a
x) f (V3 a)
f) ((V3 a -> a) -> f (V3 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V3 a
_ a
y a
_) -> a
y) f (V3 a)
f) ((V3 a -> a) -> f (V3 a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\(V3 a
_ a
_ a
z) -> a
z) f (V3 a)
f)
{-# INLINE distribute #-}
class R2 t => R3 t where
_z :: Lens' (t a) a
_xyz :: Lens' (t a) (V3 a)
_xz, _yz, _zx, _zy :: R3 t => Lens' (t a) (V2 a)
_xz :: Lens' (t a) (V2 a)
_xz V2 a -> f (V2 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a a
c) f (V2 a) -> (V2 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
a' a
c') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b a
c'
{-# INLINE _xz #-}
_yz :: Lens' (t a) (V2 a)
_yz V2 a -> f (V2 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
b a
c) f (V2 a) -> (V2 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
b' a
c') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b' a
c'
{-# INLINE _yz #-}
_zx :: Lens' (t a) (V2 a)
_zx V2 a -> f (V2 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
c a
a) f (V2 a) -> (V2 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
c' a
a') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b a
c'
{-# INLINE _zx #-}
_zy :: Lens' (t a) (V2 a)
_zy V2 a -> f (V2 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
c a
b) f (V2 a) -> (V2 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
c' a
b') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b' a
c'
{-# INLINE _zy #-}
_xzy, _yxz, _yzx, _zxy, _zyx :: R3 t => Lens' (t a) (V3 a)
_xzy :: Lens' (t a) (V3 a)
_xzy V3 a -> f (V3 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
c a
b) f (V3 a) -> (V3 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
a' a
c' a
b') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c'
{-# INLINE _xzy #-}
_yxz :: Lens' (t a) (V3 a)
_yxz V3 a -> f (V3 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
a a
c) f (V3 a) -> (V3 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
a' a
c') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c'
{-# INLINE _yxz #-}
_yzx :: Lens' (t a) (V3 a)
_yzx V3 a -> f (V3 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
c a
a) f (V3 a) -> (V3 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
b' a
c' a
a') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c'
{-# INLINE _yzx #-}
_zxy :: Lens' (t a) (V3 a)
_zxy V3 a -> f (V3 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
a a
b) f (V3 a) -> (V3 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
a' a
b') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c'
{-# INLINE _zxy #-}
_zyx :: Lens' (t a) (V3 a)
_zyx V3 a -> f (V3 a)
f = (V3 a -> f (V3 a)) -> t a -> f (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> f (V3 a)) -> t a -> f (t a))
-> (V3 a -> f (V3 a)) -> t a -> f (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> f (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
b a
a) f (V3 a) -> (V3 a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V3 a
c' a
b' a
a') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c'
{-# INLINE _zyx #-}
ez :: R3 t => E t
ez :: E t
ez = (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. R3 t => Lens' (t a) a
_z
instance R1 V3 where
_x :: (a -> f a) -> V3 a -> f (V3 a)
_x a -> f a
f (V3 a
a a
b a
c) = (\a
a' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b a
c) (a -> V3 a) -> f a -> f (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f a
f a
a
{-# INLINE _x #-}
instance R2 V3 where
_y :: (a -> f a) -> V3 a -> f (V3 a)
_y a -> f a
f (V3 a
a a
b a
c) = (\a
b' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b' a
c) (a -> V3 a) -> f a -> f (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f a
f a
b
{-# INLINE _y #-}
_xy :: (V2 a -> f (V2 a)) -> V3 a -> f (V3 a)
_xy V2 a -> f (V2 a)
f (V3 a
a a
b a
c) = (\(V2 a
a' a
b') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c) (V2 a -> V3 a) -> f (V2 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> V2 a -> f (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a a
b)
{-# INLINE _xy #-}
instance R3 V3 where
_z :: (a -> f a) -> V3 a -> f (V3 a)
_z a -> f a
f (V3 a
a a
b a
c) = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b (a -> V3 a) -> f a -> f (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f a
f a
c
{-# INLINE _z #-}
_xyz :: (V3 a -> f (V3 a)) -> V3 a -> f (V3 a)
_xyz = (V3 a -> f (V3 a)) -> V3 a -> f (V3 a)
forall a. a -> a
id
{-# INLINE _xyz #-}
instance Storable a => Storable (V3 a) where
sizeOf :: V3 a -> Int
sizeOf V3 a
_ = Int
3 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 :: V3 a -> Int
alignment V3 a
_ = a -> Int
forall a. Storable a => a -> Int
alignment (a
forall a. HasCallStack => a
undefined::a)
{-# INLINE alignment #-}
poke :: Ptr (V3 a) -> V3 a -> IO ()
poke Ptr (V3 a)
ptr (V3 a
x a
y a
z) = 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
where ptr' :: Ptr a
ptr' = Ptr (V3 a) -> Ptr a
forall a b. Ptr a -> Ptr b
castPtr Ptr (V3 a)
ptr
{-# INLINE poke #-}
peek :: Ptr (V3 a) -> IO (V3 a)
peek Ptr (V3 a)
ptr = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a -> a -> a -> V3 a) -> IO a -> IO (a -> a -> V3 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 -> V3 a) -> IO a -> IO (a -> V3 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 -> V3 a) -> IO a -> IO (V3 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
where ptr' :: Ptr a
ptr' = Ptr (V3 a) -> Ptr a
forall a b. Ptr a -> Ptr b
castPtr Ptr (V3 a)
ptr
{-# INLINE peek #-}
cross :: Num a => V3 a -> V3 a -> V3 a
cross :: V3 a -> V3 a -> V3 a
cross (V3 a
a a
b a
c) (V3 a
d a
e a
f) = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a
ba -> a -> a
forall a. Num a => a -> a -> a
*a
fa -> a -> a
forall a. Num a => a -> a -> a
-a
ca -> a -> a
forall a. Num a => a -> a -> a
*a
e) (a
ca -> a -> a
forall a. Num a => a -> a -> a
*a
da -> a -> a
forall a. Num a => a -> a -> a
-a
aa -> a -> a
forall a. Num a => a -> a -> a
*a
f) (a
aa -> a -> a
forall a. Num a => a -> a -> a
*a
ea -> a -> a
forall a. Num a => a -> a -> a
-a
ba -> a -> a
forall a. Num a => a -> a -> a
*a
d)
{-# INLINABLE cross #-}
triple :: Num a => V3 a -> V3 a -> V3 a -> a
triple :: V3 a -> V3 a -> V3 a -> a
triple V3 a
a V3 a
b V3 a
c = V3 a -> V3 a -> a
forall (f :: * -> *) a. (Metric f, Num a) => f a -> f a -> a
dot V3 a
a (V3 a -> V3 a -> V3 a
forall a. Num a => V3 a -> V3 a -> V3 a
cross V3 a
b V3 a
c)
{-# INLINE triple #-}
instance Epsilon a => Epsilon (V3 a) where
nearZero :: V3 a -> Bool
nearZero = a -> Bool
forall a. Epsilon a => a -> Bool
nearZero (a -> Bool) -> (V3 a -> a) -> V3 a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. V3 a -> a
forall (f :: * -> *) a. (Metric f, Num a) => f a -> a
quadrance
{-# INLINE nearZero #-}
instance Ix a => Ix (V3 a) where
{-# SPECIALISE instance Ix (V3 Int) #-}
range :: (V3 a, V3 a) -> [V3 a]
range (V3 a
l1 a
l2 a
l3,V3 a
u1 a
u2 a
u3) =
[a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
i1 a
i2 a
i3 | 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)
]
{-# INLINE range #-}
unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int
unsafeIndex (V3 a
l1 a
l2 a
l3,V3 a
u1 a
u2 a
u3) (V3 a
i1 a
i2 a
i3) =
(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 :: (V3 a, V3 a) -> V3 a -> Bool
inRange (V3 a
l1 a
l2 a
l3,V3 a
u1 a
u2 a
u3) (V3 a
i1 a
i2 a
i3) =
(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
{-# INLINE inRange #-}
instance Representable V3 where
type Rep V3 = E V3
tabulate :: (Rep V3 -> a) -> V3 a
tabulate Rep V3 -> a
f = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (Rep V3 -> a
f Rep V3
forall (t :: * -> *). R1 t => E t
ex) (Rep V3 -> a
f Rep V3
forall (t :: * -> *). R2 t => E t
ey) (Rep V3 -> a
f Rep V3
forall (t :: * -> *). R3 t => E t
ez)
{-# INLINE tabulate #-}
index :: V3 a -> Rep V3 -> a
index V3 a
xs (E l) = Getting a (V3 a) a -> V3 a -> a
forall s (m :: * -> *) a. MonadReader s m => Getting a s a -> m a
view Getting a (V3 a) a
forall a. Lens' (V3 a) a
l V3 a
xs
{-# INLINE index #-}
instance WithIndex.FunctorWithIndex (E V3) V3 where
imap :: (E V3 -> a -> b) -> V3 a -> V3 b
imap E V3 -> a -> b
f (V3 a
a a
b a
c) = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (E V3 -> a -> b
f E V3
forall (t :: * -> *). R1 t => E t
ex a
a) (E V3 -> a -> b
f E V3
forall (t :: * -> *). R2 t => E t
ey a
b) (E V3 -> a -> b
f E V3
forall (t :: * -> *). R3 t => E t
ez a
c)
{-# INLINE imap #-}
instance WithIndex.FoldableWithIndex (E V3) V3 where
ifoldMap :: (E V3 -> a -> m) -> V3 a -> m
ifoldMap E V3 -> a -> m
f (V3 a
a a
b a
c) = E V3 -> a -> m
f E V3
forall (t :: * -> *). R1 t => E t
ex a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` E V3 -> a -> m
f E V3
forall (t :: * -> *). R2 t => E t
ey a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` E V3 -> a -> m
f E V3
forall (t :: * -> *). R3 t => E t
ez a
c
{-# INLINE ifoldMap #-}
instance WithIndex.TraversableWithIndex (E V3) V3 where
itraverse :: (E V3 -> a -> f b) -> V3 a -> f (V3 b)
itraverse E V3 -> a -> f b
f (V3 a
a a
b a
c) = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (b -> b -> b -> V3 b) -> f b -> f (b -> b -> V3 b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> E V3 -> a -> f b
f E V3
forall (t :: * -> *). R1 t => E t
ex a
a f (b -> b -> V3 b) -> f b -> f (b -> V3 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> E V3 -> a -> f b
f E V3
forall (t :: * -> *). R2 t => E t
ey a
b f (b -> V3 b) -> f b -> f (V3 b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> E V3 -> a -> f b
f E V3
forall (t :: * -> *). R3 t => E t
ez a
c
{-# INLINE itraverse #-}
#if !MIN_VERSION_lens(5,0,0)
instance Lens.FunctorWithIndex (E V3) V3 where imap = WithIndex.imap
instance Lens.FoldableWithIndex (E V3) V3 where ifoldMap = WithIndex.ifoldMap
instance Lens.TraversableWithIndex (E V3) V3 where itraverse = WithIndex.itraverse
#endif
type instance Index (V3 a) = E V3
type instance IxValue (V3 a) = a
instance Ixed (V3 a) where
ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a))
ix Index (V3 a)
i = E V3 -> forall a. Lens' (V3 a) a
forall (t :: * -> *). E t -> forall x. Lens' (t x) x
el Index (V3 a)
E V3
i
{-# INLINE ix #-}
instance Each (V3 a) (V3 b) a b where
each :: (a -> f b) -> V3 a -> f (V3 b)
each = (a -> f b) -> V3 a -> f (V3 b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse
{-# INLINE each #-}
data instance U.Vector (V3 a) = V_V3 {-# UNPACK #-} !Int !(U.Vector a)
data instance U.MVector s (V3 a) = MV_V3 {-# UNPACK #-} !Int !(U.MVector s a)
instance U.Unbox a => U.Unbox (V3 a)
instance U.Unbox a => M.MVector U.MVector (V3 a) where
{-# INLINE basicLength #-}
{-# INLINE basicUnsafeSlice #-}
{-# INLINE basicOverlaps #-}
{-# INLINE basicUnsafeNew #-}
{-# INLINE basicUnsafeRead #-}
{-# INLINE basicUnsafeWrite #-}
basicLength :: MVector s (V3 a) -> Int
basicLength (MV_V3 n _) = Int
n
basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a)
basicUnsafeSlice Int
m Int
n (MV_V3 _ v) = Int -> MVector s a -> MVector s (V3 a)
forall s a. Int -> MVector s a -> MVector s (V3 a)
MV_V3 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
3Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
m) (Int
3Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n) MVector s a
v)
basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool
basicOverlaps (MV_V3 _ v) (MV_V3 _ 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) (V3 a))
basicUnsafeNew Int
n = (MVector (PrimState m) a -> MVector (PrimState m) (V3 a))
-> m (MVector (PrimState m) a) -> m (MVector (PrimState m) (V3 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (Int -> MVector (PrimState m) a -> MVector (PrimState m) (V3 a)
forall s a. Int -> MVector s a -> MVector s (V3 a)
MV_V3 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
3Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n))
basicUnsafeRead :: MVector (PrimState m) (V3 a) -> Int -> m (V3 a)
basicUnsafeRead (MV_V3 _ v) Int
i =
do let o :: Int
o = Int
3Int -> 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)
V3 a -> m (V3 a)
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y a
z)
basicUnsafeWrite :: MVector (PrimState m) (V3 a) -> Int -> V3 a -> m ()
basicUnsafeWrite (MV_V3 _ v) Int
i (V3 a
x a
y a
z) =
do let o :: Int
o = Int
3Int -> 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
basicInitialize :: MVector (PrimState m) (V3 a) -> m ()
basicInitialize (MV_V3 _ 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
{-# INLINE basicInitialize #-}
instance U.Unbox a => G.Vector U.Vector (V3 a) where
{-# INLINE basicUnsafeFreeze #-}
{-# INLINE basicUnsafeThaw #-}
{-# INLINE basicLength #-}
{-# INLINE basicUnsafeSlice #-}
{-# INLINE basicUnsafeIndexM #-}
basicUnsafeFreeze :: Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a))
basicUnsafeFreeze (MV_V3 n v) = (Vector a -> Vector (V3 a)) -> m (Vector a) -> m (Vector (V3 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM ( Int -> Vector a -> Vector (V3 a)
forall a. Int -> Vector a -> Vector (V3 a)
V_V3 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 (V3 a) -> m (Mutable Vector (PrimState m) (V3 a))
basicUnsafeThaw ( V_V3 n v) = (MVector (PrimState m) a -> MVector (PrimState m) (V3 a))
-> m (MVector (PrimState m) a) -> m (MVector (PrimState m) (V3 a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (Int -> MVector (PrimState m) a -> MVector (PrimState m) (V3 a)
forall s a. Int -> MVector s a -> MVector s (V3 a)
MV_V3 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 (V3 a) -> Int
basicLength ( V_V3 n _) = Int
n
basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a)
basicUnsafeSlice Int
m Int
n (V_V3 _ v) = Int -> Vector a -> Vector (V3 a)
forall a. Int -> Vector a -> Vector (V3 a)
V_V3 Int
n (Int -> Int -> Vector a -> Vector a
forall (v :: * -> *) a. Vector v a => Int -> Int -> v a -> v a
G.basicUnsafeSlice (Int
3Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
m) (Int
3Int -> Int -> Int
forall a. Num a => a -> a -> a
*Int
n) Vector a
v)
basicUnsafeIndexM :: Vector (V3 a) -> Int -> m (V3 a)
basicUnsafeIndexM (V_V3 _ v) Int
i =
do let o :: Int
o = Int
3Int -> 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)
V3 a -> m (V3 a)
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y a
z)
instance MonadZip V3 where
mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c
mzipWith = (a -> b -> c) -> V3 a -> V3 b -> V3 c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
instance MonadFix V3 where
mfix :: (a -> V3 a) -> V3 a
mfix a -> V3 a
f = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (let V3 a
a a
_ a
_ = a -> V3 a
f a
a in a
a)
(let V3 a
_ a
a a
_ = a -> V3 a
f a
a in a
a)
(let V3 a
_ a
_ a
a = a -> V3 a
f a
a in a
a)
instance Bounded a => Bounded (V3 a) where
minBound :: V3 a
minBound = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Bounded a => a
minBound
{-# INLINE minBound #-}
maxBound :: V3 a
maxBound = a -> V3 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Bounded a => a
maxBound
{-# INLINE maxBound #-}
instance NFData a => NFData (V3 a) where
rnf :: V3 a -> ()
rnf (V3 a
a a
b a
c) = 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
instance Serial1 V3 where
serializeWith :: (a -> m ()) -> V3 a -> m ()
serializeWith = (a -> m ()) -> V3 a -> m ()
forall (t :: * -> *) (f :: * -> *) a b.
(Foldable t, Applicative f) =>
(a -> f b) -> t a -> f ()
traverse_
deserializeWith :: m a -> m (V3 a)
deserializeWith m a
k = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a -> a -> a -> V3 a) -> m a -> m (a -> a -> V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m a
k m (a -> a -> V3 a) -> m a -> m (a -> V3 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> m a
k m (a -> V3 a) -> m a -> m (V3 a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> m a
k
instance Serial a => Serial (V3 a) where
serialize :: V3 a -> m ()
serialize = (a -> m ()) -> V3 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 (V3 a)
deserialize = m a -> m (V3 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 (V3 a) where
put :: V3 a -> Put
put = (a -> Put) -> V3 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 (V3 a)
get = Get a -> Get (V3 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 (V3 a) where
put :: Putter (V3 a)
put = (a -> PutM ()) -> Putter (V3 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 (V3 a)
get = Get a -> Get (V3 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
instance Eq1 V3 where
liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool
liftEq a -> b -> Bool
k (V3 a
a a
b a
c) (V3 b
d b
e b
f) = a -> b -> Bool
k a
a b
d Bool -> Bool -> Bool
&& a -> b -> Bool
k a
b b
e Bool -> Bool -> Bool
&& a -> b -> Bool
k a
c b
f
instance Ord1 V3 where
liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering
liftCompare a -> b -> Ordering
k (V3 a
a a
b a
c) (V3 b
d b
e b
f) = a -> b -> Ordering
k a
a b
d Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
k a
b b
e Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
k a
c b
f
instance Read1 V3 where
liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a)
liftReadsPrec Int -> ReadS a
k ReadS [a]
_ Int
d = Bool -> ReadS (V3 a) -> ReadS (V3 a)
forall a. Bool -> ReadS a -> ReadS a
readParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (ReadS (V3 a) -> ReadS (V3 a)) -> ReadS (V3 a) -> ReadS (V3 a)
forall a b. (a -> b) -> a -> b
$ \String
r ->
[ (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b a
c, String
r4)
| (String
"V3",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
]
instance Show1 V3 where
liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS
liftShowsPrec Int -> a -> ShowS
f [a] -> ShowS
_ Int
d (V3 a
a a
b a
c) = Bool -> ShowS -> ShowS
showParen (Int
d 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
"V3 " 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
instance Field1 (V3 a) (V3 a) a a where
_1 :: (a -> f a) -> V3 a -> f (V3 a)
_1 a -> f a
f (V3 a
x a
y a
z) = a -> f a
f a
x f a -> (a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
x' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x' a
y a
z
instance Field2 (V3 a) (V3 a) a a where
_2 :: (a -> f a) -> V3 a -> f (V3 a)
_2 a -> f a
f (V3 a
x a
y a
z) = a -> f a
f a
y f a -> (a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
y' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y' a
z
instance Field3 (V3 a) (V3 a) a a where
_3 :: (a -> f a) -> V3 a -> f (V3 a)
_3 a -> f a
f (V3 a
x a
y a
z) = a -> f a
f a
z f a -> (a -> V3 a) -> f (V3 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
z' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y a
z'
instance Semigroup a => Semigroup (V3 a) where
<> :: V3 a -> V3 a -> V3 a
(<>) = (a -> a -> a) -> V3 a -> V3 a -> V3 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 (V3 a) where
mempty :: V3 a
mempty = a -> V3 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