{-# LANGUAGE MultiParamTypeClasses #-}
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