{-# LANGUAGE CPP #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE DerivingStrategies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}

-- | Adapted from [Linear.V3](https://hackage.haskell.org/package/linear-1.21.8/docs/Linear-V3.html)
module Nonlinear.V3 where

import Control.Applicative
import Data.Data (Data, Typeable)
import Data.Functor ((<&>))
import Data.Functor.Classes
import Foreign (Storable (..))
import Foreign.Ptr (castPtr)
import GHC.Generics (Generic, Generic1)
import Nonlinear.Internal (Lens')
import Nonlinear.V1 (R1 (..))
import Nonlinear.V2 (R2 (..), V2 (..))
import Nonlinear.Vector (Vec (..), dot)

#if MIN_VERSION_base(4,14,0)
import GHC.Ix (Ix (..))
#else
import Data.Ix (Ix (..))
#endif

data V3 a = V3 {V3 a -> a
v3x :: !a, V3 a -> a
v3y :: !a, V3 a -> a
v3z :: !a}
  deriving stock (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, 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, V3 a
V3 a -> V3 a -> Bounded (V3 a)
forall a. a -> a -> Bounded a
forall a. Bounded a => V3 a
maxBound :: V3 a
$cmaxBound :: forall a. Bounded a => V3 a
minBound :: V3 a
$cminBound :: forall a. Bounded a => V3 a
Bounded, 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
$cp1Ord :: forall a. Ord a => Eq (V3 a)
Ord, a -> V3 b -> V3 a
(a -> b) -> V3 a -> V3 b
(forall a b. (a -> b) -> V3 a -> V3 b)
-> (forall a b. a -> V3 b -> V3 a) -> Functor V3
forall a b. a -> V3 b -> V3 a
forall a b. (a -> b) -> V3 a -> V3 b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: a -> V3 b -> V3 a
$c<$ :: forall a b. a -> V3 b -> V3 a
fmap :: (a -> b) -> V3 a -> V3 b
$cfmap :: forall a b. (a -> b) -> V3 a -> V3 b
Functor, V3 a -> Bool
(a -> m) -> V3 a -> m
(a -> b -> b) -> b -> V3 a -> b
(forall m. Monoid m => V3 m -> m)
-> (forall m a. Monoid m => (a -> m) -> V3 a -> m)
-> (forall m a. Monoid m => (a -> m) -> V3 a -> m)
-> (forall a b. (a -> b -> b) -> b -> V3 a -> b)
-> (forall a b. (a -> b -> b) -> b -> V3 a -> b)
-> (forall b a. (b -> a -> b) -> b -> V3 a -> b)
-> (forall b a. (b -> a -> b) -> b -> V3 a -> b)
-> (forall a. (a -> a -> a) -> V3 a -> a)
-> (forall a. (a -> a -> a) -> V3 a -> a)
-> (forall a. V3 a -> [a])
-> (forall a. V3 a -> Bool)
-> (forall a. V3 a -> Int)
-> (forall a. Eq a => a -> V3 a -> Bool)
-> (forall a. Ord a => V3 a -> a)
-> (forall a. Ord a => V3 a -> a)
-> (forall a. Num a => V3 a -> a)
-> (forall a. Num a => V3 a -> a)
-> Foldable V3
forall a. Eq a => a -> V3 a -> Bool
forall a. Num a => V3 a -> a
forall a. Ord a => V3 a -> a
forall m. Monoid m => V3 m -> m
forall a. V3 a -> Bool
forall a. V3 a -> Int
forall a. V3 a -> [a]
forall a. (a -> a -> a) -> V3 a -> a
forall m a. Monoid m => (a -> m) -> V3 a -> m
forall b a. (b -> a -> b) -> b -> V3 a -> b
forall a b. (a -> b -> b) -> b -> V3 a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: V3 a -> a
$cproduct :: forall a. Num a => V3 a -> a
sum :: V3 a -> a
$csum :: forall a. Num a => V3 a -> a
minimum :: V3 a -> a
$cminimum :: forall a. Ord a => V3 a -> a
maximum :: V3 a -> a
$cmaximum :: forall a. Ord a => V3 a -> a
elem :: a -> V3 a -> Bool
$celem :: forall a. Eq a => a -> V3 a -> Bool
length :: V3 a -> Int
$clength :: forall a. V3 a -> Int
null :: V3 a -> Bool
$cnull :: forall a. V3 a -> Bool
toList :: V3 a -> [a]
$ctoList :: forall a. V3 a -> [a]
foldl1 :: (a -> a -> a) -> V3 a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> V3 a -> a
foldr1 :: (a -> a -> a) -> V3 a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> V3 a -> a
foldl' :: (b -> a -> b) -> b -> V3 a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> V3 a -> b
foldl :: (b -> a -> b) -> b -> V3 a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> V3 a -> b
foldr' :: (a -> b -> b) -> b -> V3 a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> V3 a -> b
foldr :: (a -> b -> b) -> b -> V3 a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> V3 a -> b
foldMap' :: (a -> m) -> V3 a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> V3 a -> m
foldMap :: (a -> m) -> V3 a -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> V3 a -> m
fold :: V3 m -> m
$cfold :: forall m. Monoid m => V3 m -> m
Foldable, Functor V3
Foldable V3
Functor V3
-> Foldable V3
-> (forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> V3 a -> f (V3 b))
-> (forall (f :: * -> *) a. Applicative f => V3 (f a) -> f (V3 a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> V3 a -> m (V3 b))
-> (forall (m :: * -> *) a. Monad m => V3 (m a) -> m (V3 a))
-> Traversable V3
(a -> f b) -> V3 a -> f (V3 b)
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a. Monad m => V3 (m a) -> m (V3 a)
forall (f :: * -> *) a. Applicative f => V3 (f a) -> f (V3 a)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> V3 a -> m (V3 b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> V3 a -> f (V3 b)
sequence :: V3 (m a) -> m (V3 a)
$csequence :: forall (m :: * -> *) a. Monad m => V3 (m a) -> m (V3 a)
mapM :: (a -> m b) -> V3 a -> m (V3 b)
$cmapM :: forall (m :: * -> *) a b. Monad m => (a -> m b) -> V3 a -> m (V3 b)
sequenceA :: V3 (f a) -> f (V3 a)
$csequenceA :: forall (f :: * -> *) a. Applicative f => V3 (f a) -> f (V3 a)
traverse :: (a -> f b) -> V3 a -> f (V3 b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> V3 a -> f (V3 b)
$cp2Traversable :: Foldable V3
$cp1Traversable :: Functor V3
Traversable, (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, 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, Typeable)

instance Vec V3 where
  construct :: ((forall b. Lens' (V3 b) b) -> a) -> V3 a
construct (forall b. Lens' (V3 b) b) -> a
f = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 ((forall b. Lens' (V3 b) b) -> a
f forall b. Lens' (V3 b) b
forall (t :: * -> *) a. R1 t => Lens' (t a) a
_x) ((forall b. Lens' (V3 b) b) -> a
f forall b. Lens' (V3 b) b
forall (t :: * -> *) a. R2 t => Lens' (t a) a
_y) ((forall b. Lens' (V3 b) b) -> a
f forall b. Lens' (V3 b) b
forall (t :: * -> *) a. R3 t => Lens' (t a) a
_z)

instance Applicative V3 where
  {-# INLINE pure #-}
  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 (<*>) #-}
  V3 a -> b
fx a -> b
fy a -> b
fz <*> :: V3 (a -> b) -> V3 a -> V3 b
<*> V3 a
x a
y a
z = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (a -> b
fx a
x) (a -> b
fy a
y) (a -> b
fz a
z)

instance Monad V3 where
  {-# INLINE (>>=) #-}
  V3 a
x a
y a
z >>= :: V3 a -> (a -> V3 b) -> V3 b
>>= a -> V3 b
f = b -> b -> b -> V3 b
forall a. a -> a -> a -> V3 a
V3 (V3 b -> b
forall a. V3 a -> a
v3x (V3 b -> b) -> V3 b -> b
forall a b. (a -> b) -> a -> b
$ a -> V3 b
f a
x) (V3 b -> b
forall a. V3 a -> a
v3y (V3 b -> b) -> V3 b -> b
forall a b. (a -> b) -> a -> b
$ a -> V3 b
f a
y) (V3 b -> b
forall a. V3 a -> a
v3z (V3 b -> b) -> V3 b -> b
forall a b. (a -> b) -> a -> b
$ a -> V3 b
f a
z)

instance Semigroup x => Semigroup (V3 x) where V3 x
x x
y x
z <> :: V3 x -> V3 x -> V3 x
<> V3 x
x' x
y' x
z' = x -> x -> x -> V3 x
forall a. a -> a -> a -> V3 a
V3 (x
x x -> x -> x
forall a. Semigroup a => a -> a -> a
<> x
x') (x
y x -> x -> x
forall a. Semigroup a => a -> a -> a
<> x
y') (x
z x -> x -> x
forall a. Semigroup a => a -> a -> a
<> x
z')

instance Monoid a => Monoid (V3 a) where mempty :: V3 a
mempty = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
forall a. Monoid a => a
mempty a
forall a. Monoid a => a
mempty a
forall a. Monoid a => a
mempty

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 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

-- | cross product
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
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
e) (a
c a -> a -> a
forall a. Num a => a -> a -> a
* a
d a -> a -> a
forall a. Num a => a -> a -> a
- a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
f) (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
d)
{-# INLINEABLE cross #-}

-- | scalar triple product
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. (Vec 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 #-}

class R2 t => R3 t where
  _z :: Lens' (t a) a
  _xyz :: Lens' (t a) (V3 a)

instance R1 V3 where
  {-# INLINE _x #-}
  _x :: (a -> m a) -> V3 a -> m (V3 a)
_x a -> m a
f (V3 a
x a
y a
z) = (\a
x' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x' a
y a
z) (a -> V3 a) -> m a -> m (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m a
f a
x

instance R2 V3 where
  {-# INLINE _y #-}
  _y :: (a -> m a) -> V3 a -> m (V3 a)
_y a -> m a
f (V3 a
x a
y a
z) = (\a
y' -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y' a
z) (a -> V3 a) -> m a -> m (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m a
f a
y
  {-# INLINE _xy #-}
  _xy :: (V2 a -> m (V2 a)) -> V3 a -> m (V3 a)
_xy V2 a -> m (V2 a)
f (V3 a
x a
y a
z) = (\(V2 a
x' a
y') -> a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x' a
y' a
z) (V2 a -> V3 a) -> m (V2 a) -> m (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
x a
y)

instance R3 V3 where
  {-# INLINE _z #-}
  _z :: (a -> m a) -> V3 a -> m (V3 a)
_z a -> m a
f (V3 a
x a
y a
z) = a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
x a
y (a -> V3 a) -> m a -> m (V3 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m a
f a
z
  {-# INLINE _xyz #-}
  _xyz :: (V3 a -> m (V3 a)) -> V3 a -> m (V3 a)
_xyz = (V3 a -> m (V3 a)) -> V3 a -> m (V3 a)
forall a. a -> a
id

_xz, _yz, _zx, _zy :: R3 t => Lens' (t a) (V2 a)
_xz :: Lens' (t a) (V2 a)
_xz V2 a -> m (V2 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a a
c) m (V2 a) -> (V2 a -> V3 a) -> m (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 -> m (V2 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
b a
c) m (V2 a) -> (V2 a -> V3 a) -> m (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 -> m (V2 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
c a
a) m (V2 a) -> (V2 a -> V3 a) -> m (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 -> m (V2 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
c a
b) m (V2 a) -> (V2 a -> V3 a) -> m (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 -> m (V3 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> m (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
c a
b) m (V3 a) -> (V3 a -> V3 a) -> m (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 -> m (V3 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> m (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
a a
c) m (V3 a) -> (V3 a -> V3 a) -> m (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 -> m (V3 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> m (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
b a
c a
a) m (V3 a) -> (V3 a -> V3 a) -> m (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 -> m (V3 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> m (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
a a
b) m (V3 a) -> (V3 a -> V3 a) -> m (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 -> m (V3 a)
f = (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V3 a
a a
b a
c) -> V3 a -> m (V3 a)
f (a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
c a
b a
a) m (V3 a) -> (V3 a -> V3 a) -> m (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 #-}

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 #-}

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

  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 #-}

#if MIN_VERSION_base(4,14,0)
  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 #-}
#else
  index (V3 l1 l2 l3, V3 u1 u2 u3) (V3 i1 i2 i3) =
    index (l3, u3) i3 + rangeSize (l3, u3)
      * ( index (l2, u2) i2 + rangeSize (l2, u2)
            * index (l1, u1) i1
        )
  {-# INLINE index #-}
#endif