module Numeric.Quadrance.Class
( Quadrance(..)
) where
import Data.Int
import Data.Word
import Numeric.Additive.Class
import Numeric.Algebra.Class
import Numeric.Algebra.Unital
import Numeric.Rig.Class
import Numeric.Natural.Internal
import Prelude hiding ((+),(*))
class Additive r => Quadrance r m where
quadrance :: m -> r
instance Quadrance () a where
quadrance _ = ()
instance Monoidal r => Quadrance r () where
quadrance _ = zero
instance (Quadrance r a, Quadrance r b) => Quadrance r (a,b) where
quadrance (a,b) = quadrance a + quadrance b
instance (Quadrance r a, Quadrance r b, Quadrance r c) => Quadrance r (a,b,c) where
quadrance (a,b,c) = quadrance a + quadrance b + quadrance c
instance (Quadrance r a, Quadrance r b, Quadrance r c, Quadrance r d) => Quadrance r (a,b,c,d) where
quadrance (a,b,c,d) = quadrance a + quadrance b + quadrance c + quadrance d
instance (Quadrance r a, Quadrance r b, Quadrance r c, Quadrance r d, Quadrance r e) => Quadrance r (a,b,c,d,e) where
quadrance (a,b,c,d,e) = quadrance a + quadrance b + quadrance c + quadrance d + quadrance e
instance Rig r => Quadrance r Bool where
quadrance False = zero
quadrance True = one
sq :: Multiplicative r => r -> r
sq r = r * r
instance Rig r => Quadrance r Int where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Word where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Natural where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Integer where
quadrance = fromNatural . Natural . fromInteger . sq
instance Rig r => Quadrance r Int8 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Int16 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Int32 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Int64 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Word8 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Word16 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Word32 where
quadrance = fromNatural . Natural . sq . toInteger
instance Rig r => Quadrance r Word64 where
quadrance = fromNatural . Natural . sq . toInteger