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

-- | Adapted from [Linear.V2](https://hackage.haskell.org/package/linear-1.21.8/docs/Linear-V2.html)
module Nonlinear.V2 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.Vector (Vec (..), norm)

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

data V2 a = V2 {V2 a -> a
v2x :: !a, V2 a -> a
v2y :: !a}
  deriving stock (V2 a -> V2 a -> Bool
(V2 a -> V2 a -> Bool) -> (V2 a -> V2 a -> Bool) -> Eq (V2 a)
forall a. Eq a => V2 a -> V2 a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: V2 a -> V2 a -> Bool
$c/= :: forall a. Eq a => V2 a -> V2 a -> Bool
== :: V2 a -> V2 a -> Bool
$c== :: forall a. Eq a => V2 a -> V2 a -> Bool
Eq, Int -> V2 a -> ShowS
[V2 a] -> ShowS
V2 a -> String
(Int -> V2 a -> ShowS)
-> (V2 a -> String) -> ([V2 a] -> ShowS) -> Show (V2 a)
forall a. Show a => Int -> V2 a -> ShowS
forall a. Show a => [V2 a] -> ShowS
forall a. Show a => V2 a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [V2 a] -> ShowS
$cshowList :: forall a. Show a => [V2 a] -> ShowS
show :: V2 a -> String
$cshow :: forall a. Show a => V2 a -> String
showsPrec :: Int -> V2 a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> V2 a -> ShowS
Show, ReadPrec [V2 a]
ReadPrec (V2 a)
Int -> ReadS (V2 a)
ReadS [V2 a]
(Int -> ReadS (V2 a))
-> ReadS [V2 a]
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-> ReadPrec [V2 a]
-> Read (V2 a)
forall a. Read a => ReadPrec [V2 a]
forall a. Read a => ReadPrec (V2 a)
forall a. Read a => Int -> ReadS (V2 a)
forall a. Read a => ReadS [V2 a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
readListPrec :: ReadPrec [V2 a]
$creadListPrec :: forall a. Read a => ReadPrec [V2 a]
readPrec :: ReadPrec (V2 a)
$creadPrec :: forall a. Read a => ReadPrec (V2 a)
readList :: ReadS [V2 a]
$creadList :: forall a. Read a => ReadS [V2 a]
readsPrec :: Int -> ReadS (V2 a)
$creadsPrec :: forall a. Read a => Int -> ReadS (V2 a)
Read, V2 a
V2 a -> V2 a -> Bounded (V2 a)
forall a. a -> a -> Bounded a
forall a. Bounded a => V2 a
maxBound :: V2 a
$cmaxBound :: forall a. Bounded a => V2 a
minBound :: V2 a
$cminBound :: forall a. Bounded a => V2 a
Bounded, Eq (V2 a)
Eq (V2 a)
-> (V2 a -> V2 a -> Ordering)
-> (V2 a -> V2 a -> Bool)
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forall a.
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forall a. Ord a => Eq (V2 a)
forall a. Ord a => V2 a -> V2 a -> Bool
forall a. Ord a => V2 a -> V2 a -> Ordering
forall a. Ord a => V2 a -> V2 a -> V2 a
min :: V2 a -> V2 a -> V2 a
$cmin :: forall a. Ord a => V2 a -> V2 a -> V2 a
max :: V2 a -> V2 a -> V2 a
$cmax :: forall a. Ord a => V2 a -> V2 a -> V2 a
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compare :: V2 a -> V2 a -> Ordering
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(a -> b) -> V2 a -> V2 b
(forall a b. (a -> b) -> V2 a -> V2 b)
-> (forall a b. a -> V2 b -> V2 a) -> Functor V2
forall a b. a -> V2 b -> V2 a
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forall (f :: * -> *).
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forall a. Eq a => a -> V2 a -> Bool
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forall m. Monoid m => V2 m -> m
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forall m a. Monoid m => (a -> m) -> V2 a -> m
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-> (forall a b. (a -> b -> b) -> b -> t a -> b)
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product :: V2 a -> a
$cproduct :: forall a. Num a => V2 a -> a
sum :: V2 a -> a
$csum :: forall a. Num a => V2 a -> a
minimum :: V2 a -> a
$cminimum :: forall a. Ord a => V2 a -> a
maximum :: V2 a -> a
$cmaximum :: forall a. Ord a => V2 a -> a
elem :: a -> V2 a -> Bool
$celem :: forall a. Eq a => a -> V2 a -> Bool
length :: V2 a -> Int
$clength :: forall a. V2 a -> Int
null :: V2 a -> Bool
$cnull :: forall a. V2 a -> Bool
toList :: V2 a -> [a]
$ctoList :: forall a. V2 a -> [a]
foldl1 :: (a -> a -> a) -> V2 a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> V2 a -> a
foldr1 :: (a -> a -> a) -> V2 a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> V2 a -> a
foldl' :: (b -> a -> b) -> b -> V2 a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> V2 a -> b
foldl :: (b -> a -> b) -> b -> V2 a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> V2 a -> b
foldr' :: (a -> b -> b) -> b -> V2 a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> V2 a -> b
foldr :: (a -> b -> b) -> b -> V2 a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> V2 a -> b
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$cfoldMap' :: forall m a. Monoid m => (a -> m) -> V2 a -> m
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$cfoldMap :: forall m a. Monoid m => (a -> m) -> V2 a -> m
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Foldable, Functor V2
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    (a -> f b) -> V2 a -> f (V2 b))
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    (a -> m b) -> t a -> m (t b))
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-> Traversable t
forall (m :: * -> *) a. Monad m => V2 (m a) -> m (V2 a)
forall (f :: * -> *) a. Applicative f => V2 (f a) -> f (V2 a)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> V2 a -> m (V2 b)
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(a -> f b) -> V2 a -> f (V2 b)
sequence :: V2 (m a) -> m (V2 a)
$csequence :: forall (m :: * -> *) a. Monad m => V2 (m a) -> m (V2 a)
mapM :: (a -> m b) -> V2 a -> m (V2 b)
$cmapM :: forall (m :: * -> *) a b. Monad m => (a -> m b) -> V2 a -> m (V2 b)
sequenceA :: V2 (f a) -> f (V2 a)
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traverse :: (a -> f b) -> V2 a -> f (V2 b)
$ctraverse :: forall (f :: * -> *) a b.
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(a -> f b) -> V2 a -> f (V2 b)
$cp2Traversable :: Foldable V2
$cp1Traversable :: Functor V2
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-> (forall x. Rep (V2 a) x -> V2 a) -> Generic (V2 a)
forall x. Rep (V2 a) x -> V2 a
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Generic1, Typeable (V2 a)
DataType
Constr
Typeable (V2 a)
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    (forall d b. Data d => c (d -> b) -> d -> c b)
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    (forall b r. Data b => c (b -> r) -> c r)
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-> (forall r r'.
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-> (forall u. (forall d. Data d => d -> u) -> V2 a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> V2 a -> u)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> V2 a -> m (V2 a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> V2 a -> m (V2 a))
-> (forall (m :: * -> *).
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forall a u.
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a))
forall a.
Typeable a
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-> ((forall b. Data b => b -> b) -> a -> a)
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-> (forall r r'.
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-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
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    (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 :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> V2 a -> u
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forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
forall (c :: * -> *).
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-> (forall r. r -> c r) -> Constr -> c (V2 a)
forall (c :: * -> *).
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forall (t :: * -> *) (c :: * -> *).
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(forall d. Data d => c (t d)) -> Maybe (c (V2 a))
forall (t :: * -> * -> *) (c :: * -> *).
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$cV2 :: Constr
$tV2 :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
gmapMp :: (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
gmapM :: (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> V2 a -> m (V2 a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> V2 a -> u
gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u]
$cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> V2 a -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
$cgmapQl :: forall a r r'.
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(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r
gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a
$cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> V2 a -> V2 a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a))
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$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (V2 a))
dataTypeOf :: V2 a -> DataType
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toConstr :: V2 a -> Constr
$ctoConstr :: forall a. Data a => V2 a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V2 a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (V2 a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V2 a -> c (V2 a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> V2 a -> c (V2 a)
$cp1Data :: forall a. Data a => Typeable (V2 a)
Data, Typeable)

instance Vec V2 where
  construct :: ((forall b. Lens' (V2 b) b) -> a) -> V2 a
construct (forall b. Lens' (V2 b) b) -> a
f = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 ((forall b. Lens' (V2 b) b) -> a
f forall b. Lens' (V2 b) b
forall (t :: * -> *) a. R1 t => Lens' (t a) a
_x) ((forall b. Lens' (V2 b) b) -> a
f forall b. Lens' (V2 b) b
forall (t :: * -> *) a. R2 t => Lens' (t a) a
_y)

instance Applicative V2 where
  {-# INLINE pure #-}
  {-# INLINE (<*>) #-}
  pure :: a -> V2 a
pure a
a = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a a
a
  V2 a -> b
fx a -> b
fy <*> :: V2 (a -> b) -> V2 a -> V2 b
<*> V2 a
x a
y = b -> b -> V2 b
forall a. a -> a -> V2 a
V2 (a -> b
fx a
x) (a -> b
fy a
y)

instance Monad V2 where
  {-# INLINE (>>=) #-}
  V2 a
x a
y >>= :: V2 a -> (a -> V2 b) -> V2 b
>>= a -> V2 b
f = b -> b -> V2 b
forall a. a -> a -> V2 a
V2 (V2 b -> b
forall a. V2 a -> a
v2x (V2 b -> b) -> V2 b -> b
forall a b. (a -> b) -> a -> b
$ a -> V2 b
f a
x) (V2 b -> b
forall a. V2 a -> a
v2y (V2 b -> b) -> V2 b -> b
forall a b. (a -> b) -> a -> b
$ a -> V2 b
f a
y)

instance Semigroup x => Semigroup (V2 x) where V2 x
x x
y <> :: V2 x -> V2 x -> V2 x
<> V2 x
x' x
y' = x -> x -> V2 x
forall a. a -> a -> V2 a
V2 (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')

instance Monoid a => Monoid (V2 a) where mempty :: V2 a
mempty = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
forall a. Monoid a => a
mempty a
forall a. Monoid a => a
mempty

instance Num a => Num (V2 a) where
  + :: V2 a -> V2 a -> V2 a
(+) = (a -> a -> a) -> V2 a -> V2 a -> V2 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) -> V2 a -> V2 a -> V2 a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (-)
  {-# INLINE (-) #-}
  * :: V2 a -> V2 a -> V2 a
(*) = (a -> a -> a) -> V2 a -> V2 a -> V2 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 :: V2 a -> V2 a
negate = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
abs = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
signum = (a -> a) -> V2 a -> V2 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 -> V2 a
fromInteger = a -> V2 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V2 a) -> (Integer -> a) -> Integer -> V2 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 (V2 a) where
  recip :: V2 a -> V2 a
recip = (a -> a) -> V2 a -> V2 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 #-}
  / :: V2 a -> V2 a -> V2 a
(/) = (a -> a -> a) -> V2 a -> V2 a -> V2 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 -> V2 a
fromRational = a -> V2 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> V2 a) -> (Rational -> a) -> Rational -> V2 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 (V2 a) where
  pi :: V2 a
pi = a -> V2 a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
forall a. Floating a => a
pi
  {-# INLINE pi #-}
  exp :: V2 a -> V2 a
exp = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
sqrt = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
log = (a -> a) -> V2 a -> V2 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 #-}
  ** :: V2 a -> V2 a -> V2 a
(**) = (a -> a -> a) -> V2 a -> V2 a -> V2 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 :: V2 a -> V2 a -> V2 a
logBase = (a -> a -> a) -> V2 a -> V2 a -> V2 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 :: V2 a -> V2 a
sin = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
tan = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
cos = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
asin = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
atan = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
acos = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
sinh = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
tanh = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
cosh = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
asinh = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
atanh = (a -> a) -> V2 a -> V2 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 :: V2 a -> V2 a
acosh = (a -> a) -> V2 a -> V2 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 V2 where
  liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool
liftEq a -> b -> Bool
f (V2 a
a a
b) (V2 b
c b
d) = a -> b -> Bool
f a
a b
c Bool -> Bool -> Bool
&& a -> b -> Bool
f a
b b
d

instance Ord1 V2 where
  liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering
liftCompare a -> b -> Ordering
f (V2 a
a a
b) (V2 b
c b
d) = a -> b -> Ordering
f a
a b
c Ordering -> Ordering -> Ordering
forall a. Monoid a => a -> a -> a
`mappend` a -> b -> Ordering
f a
b b
d

instance Read1 V2 where
  liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a)
liftReadsPrec Int -> ReadS a
f ReadS [a]
_ = (String -> ReadS (V2 a)) -> Int -> ReadS (V2 a)
forall a. (String -> ReadS a) -> Int -> ReadS a
readsData ((String -> ReadS (V2 a)) -> Int -> ReadS (V2 a))
-> (String -> ReadS (V2 a)) -> Int -> ReadS (V2 a)
forall a b. (a -> b) -> a -> b
$ (Int -> ReadS a)
-> (Int -> ReadS a)
-> String
-> (a -> a -> V2 a)
-> String
-> ReadS (V2 a)
forall a b t.
(Int -> ReadS a)
-> (Int -> ReadS b) -> String -> (a -> b -> t) -> String -> ReadS t
readsBinaryWith Int -> ReadS a
f Int -> ReadS a
f String
"V2" a -> a -> V2 a
forall a. a -> a -> V2 a
V2

instance Show1 V2 where
  liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS
liftShowsPrec Int -> a -> ShowS
f [a] -> ShowS
_ Int
d (V2 a
a a
b) = (Int -> a -> ShowS)
-> (Int -> a -> ShowS) -> String -> Int -> a -> a -> ShowS
forall a b.
(Int -> a -> ShowS)
-> (Int -> b -> ShowS) -> String -> Int -> a -> b -> ShowS
showsBinaryWith Int -> a -> ShowS
f Int -> a -> ShowS
f String
"V2" Int
d a
a a
b

-- | the counter-clockwise perpendicular vector
--
-- >>> perp $ V2 10 20
-- V2 (-20) 10
perp :: Num a => V2 a -> V2 a
perp :: V2 a -> V2 a
perp (V2 a
a a
b) = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 (a -> a
forall a. Num a => a -> a
negate a
b) a
a
{-# INLINE perp #-}

angle :: Floating a => a -> V2 a
angle :: a -> V2 a
angle a
a = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 (a -> a
forall a. Floating a => a -> a
cos a
a) (a -> a
forall a. Floating a => a -> a
sin a
a)

unangle :: (Floating a, Ord a) => V2 a -> a
unangle :: V2 a -> a
unangle a :: V2 a
a@(V2 a
ax a
ay) =
  let alpha :: a
alpha = a -> a
forall a. Floating a => a -> a
asin (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ a
ay a -> a -> a
forall a. Fractional a => a -> a -> a
/ V2 a -> a
forall (f :: * -> *) a. (Vec f, Floating a) => f a -> a
norm V2 a
a
   in if a
ax a -> a -> Bool
forall a. Ord a => a -> a -> Bool
< a
0
        then a
forall a. Floating a => a
pi a -> a -> a
forall a. Num a => a -> a -> a
- a
alpha
        else a
alpha

-- | The Z-component of the cross product of two vectors in the XY-plane.
--
-- >>> crossZ (V2 1 0) (V2 0 1)
-- 1
crossZ :: Num a => V2 a -> V2 a -> a
crossZ :: V2 a -> V2 a -> a
crossZ (V2 a
x1 a
y1) (V2 a
x2 a
y2) = a
x1 a -> a -> a
forall a. Num a => a -> a -> a
* a
y2 a -> a -> a
forall a. Num a => a -> a -> a
- a
y1 a -> a -> a
forall a. Num a => a -> a -> a
* a
x2
{-# INLINE crossZ #-}

class R1 t => R2 t where
  _y :: Lens' (t a) a
  _xy :: Lens' (t a) (V2 a)

instance R1 V2 where
  {-# INLINE _x #-}
  _x :: (a -> m a) -> V2 a -> m (V2 a)
_x a -> m a
f (V2 a
x a
y) = (\a
x' -> a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
x' a
y) (a -> V2 a) -> m a -> m (V2 a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m a
f a
x

instance R2 V2 where
  {-# INLINE _y #-}
  _y :: (a -> m a) -> V2 a -> m (V2 a)
_y a -> m a
f (V2 a
x a
y) = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
x (a -> V2 a) -> m a -> m (V2 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)) -> V2 a -> m (V2 a)
_xy = (V2 a -> m (V2 a)) -> V2 a -> m (V2 a)
forall a. a -> a
id

-- |
-- >>> V2 1 2 ^. _yx
-- V2 2 1
_yx :: R2 t => Lens' (t a) (V2 a)
_yx :: Lens' (t a) (V2 a)
_yx V2 a -> m (V2 a)
f = (V2 a -> m (V2 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy ((V2 a -> m (V2 a)) -> t a -> m (t a))
-> (V2 a -> m (V2 a)) -> t a -> m (t a)
forall a b. (a -> b) -> a -> b
$ \(V2 a
a a
b) -> V2 a -> m (V2 a)
f (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
b a
a) m (V2 a) -> (V2 a -> V2 a) -> m (V2 a)
forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \(V2 a
b' a
a') -> a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
a' a
b'
{-# INLINE _yx #-}

instance Storable a => Storable (V2 a) where
  sizeOf :: V2 a -> Int
sizeOf V2 a
_ = Int
2 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 :: V2 a -> Int
alignment V2 a
_ = a -> Int
forall a. Storable a => a -> Int
alignment (a
forall a. HasCallStack => a
undefined :: a)
  {-# INLINE alignment #-}
  poke :: Ptr (V2 a) -> V2 a -> IO ()
poke Ptr (V2 a)
ptr (V2 a
x a
y) = Ptr a -> a -> IO ()
forall a. Storable a => Ptr a -> a -> IO ()
poke Ptr a
forall b. Ptr b
ptr' a
x IO () -> IO () -> IO ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> Ptr a -> Int -> a -> IO ()
forall a. Storable a => Ptr a -> Int -> a -> IO ()
pokeElemOff Ptr a
forall b. Ptr b
ptr' Int
1 a
y
    where
      ptr' :: Ptr b
ptr' = Ptr (V2 a) -> Ptr b
forall a b. Ptr a -> Ptr b
castPtr Ptr (V2 a)
ptr
  {-# INLINE poke #-}
  peek :: Ptr (V2 a) -> IO (V2 a)
peek Ptr (V2 a)
ptr = a -> a -> V2 a
forall a. a -> a -> V2 a
V2 (a -> a -> V2 a) -> IO a -> IO (a -> V2 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
forall b. Ptr b
ptr' IO (a -> V2 a) -> IO a -> IO (V2 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
forall b. Ptr b
ptr' Int
1
    where
      ptr' :: Ptr b
ptr' = Ptr (V2 a) -> Ptr b
forall a b. Ptr a -> Ptr b
castPtr Ptr (V2 a)
ptr
  {-# INLINE peek #-}

instance Ix a => Ix (V2 a) where
  {-# SPECIALIZE instance Ix (V2 Int) #-}

  range :: (V2 a, V2 a) -> [V2 a]
range (V2 a
l1 a
l2, V2 a
u1 a
u2) =
    [a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
i1 a
i2 | 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)]
  {-# INLINE range #-}

  inRange :: (V2 a, V2 a) -> V2 a -> Bool
inRange (V2 a
l1 a
l2, V2 a
u1 a
u2) (V2 a
i1 a
i2) =
    (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
  {-# INLINE inRange #-}

#if MIN_VERSION_base(4,14,0)
  unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int
unsafeIndex (V2 a
l1 a
l2, V2 a
u1 a
u2) (V2 a
i1 a
i2) =
    (a, a) -> a -> Int
forall a. Ix a => (a, a) -> a -> Int
unsafeIndex (a
l1, a
u1) a
i1 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
l2, a
u2) a
i2
  {-# INLINE unsafeIndex #-}
#else
  index (V2 l1 l2, V2 u1 u2) (V2 i1 i2) =
    index (l1, u1) i1 * rangeSize (l2, u2) + index (l2, u2) i2
  {-# INLINE index #-}
#endif