module Numeric.Group.Additive
(
AdditiveGroup(..)
) where
import Data.Int
import Data.Word
import Prelude hiding ((+), (), negate, subtract)
import qualified Prelude
import Numeric.Semigroup.Additive
import Numeric.Monoid.Additive
import Numeric.Module.Class
infixl 6
infixl 7 `times`
class (LeftModule Integer r, RightModule Integer r, AdditiveMonoid r) => AdditiveGroup r where
() :: r -> r -> r
negate :: r -> r
subtract :: r -> r -> r
times :: Integral n => n -> r -> r
times y0 x0 = case compare y0 0 of
LT -> f (negate x0) (Prelude.negate y0)
EQ -> zero
GT -> f x0 y0
where
f x y
| even y = f (x + x) (y `quot` 2)
| y == 1 = x
| otherwise = g (x + x) ((y Prelude.- 1) `quot` 2) x
g x y z
| even y = g (x + x) (y `quot` 2) z
| y == 1 = x + z
| otherwise = g (x + x) ((y Prelude.- 1) `quot` 2) (x + z)
negate a = zero a
a b = a + negate b
subtract a b = negate a + b
instance AdditiveGroup r => AdditiveGroup (e -> r) where
f g = \x -> f x g x
negate f x = negate (f x)
subtract f g x = subtract (f x) (g x)
times n f e = times n (f e)
instance AdditiveGroup Integer where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Int where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Int8 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Int16 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Int32 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Int64 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Word where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Word8 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Word16 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Word32 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup Word64 where
() = (Prelude.-)
negate = Prelude.negate
subtract = Prelude.subtract
times n r = fromIntegral n * r
instance AdditiveGroup () where
_ _ = ()
negate _ = ()
subtract _ _ = ()
times _ _ = ()
instance (AdditiveGroup a, AdditiveGroup b) => AdditiveGroup (a,b) where
negate (a,b) = (negate a, negate b)
(a,b) (i,j) = (ai, bj)
subtract (a,b) (i,j) = (subtract a i, subtract b j)
times n (a,b) = (times n a,times n b)
instance (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c) => AdditiveGroup (a,b,c) where
negate (a,b,c) = (negate a, negate b, negate c)
(a,b,c) (i,j,k) = (ai, bj, ck)
subtract (a,b,c) (i,j,k) = (subtract a i, subtract b j, subtract c k)
times n (a,b,c) = (times n a,times n b, times n c)
instance (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c, AdditiveGroup d) => AdditiveGroup (a,b,c,d) where
negate (a,b,c,d) = (negate a, negate b, negate c, negate d)
(a,b,c,d) (i,j,k,l) = (ai, bj, ck, dl)
subtract (a,b,c,d) (i,j,k,l) = (subtract a i, subtract b j, subtract c k, subtract d l)
times n (a,b,c,d) = (times n a,times n b, times n c, times n d)
instance (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c, AdditiveGroup d, AdditiveGroup e) => AdditiveGroup (a,b,c,d,e) where
negate (a,b,c,d,e) = (negate a, negate b, negate c, negate d, negate e)
(a,b,c,d,e) (i,j,k,l,m) = (ai, bj, ck, dl, em)
subtract (a,b,c,d,e) (i,j,k,l,m) = (subtract a i, subtract b j, subtract c k, subtract d l, subtract e m)
times n (a,b,c,d,e) = (times n a,times n b, times n c, times n d, times n e)