module Numeric.Log
( Log(..)
) where
import Data.Function (on)
import Numeric.Algebra
import Prelude hiding ((*),(^),(/),recip,negate,subtract)
newtype Log r = Log { runLog :: r }
instance Multiplicative r => Additive (Log r) where
Log a + Log b = Log (a * b)
sumWith1 f = Log . productWith1 (runLog . f)
replicate1p n (Log m) = Log (pow1p m n)
instance Unital r => LeftModule Natural (Log r) where
n .* Log m = Log (pow m n)
instance Unital r => RightModule Natural (Log r) where
Log m *. n = Log (pow m n)
instance Unital r => Monoidal (Log r) where
zero = Log one
replicate n (Log m) = Log (pow m n)
sumWith f = Log . productWith (runLog . f)
instance Division r => LeftModule Integer (Log r) where
n .* Log m = Log (m ^ n)
instance Division r => RightModule Integer (Log r) where
Log m *. n = Log (m ^ n)
instance Division r => Group (Log r) where
Log a Log b = Log (a / b)
negate (Log a) = Log (recip a)
subtract (Log a) (Log b) = Log (a \\ b)
times n (Log m) = Log (m ^ n)
instance Commutative r => Abelian (Log r)
instance Band r => Idempotent (Log r)
instance Factorable r => Partitionable (Log r) where
partitionWith f = factorWith (f `on` Log) . runLog