{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
-----------------------------------------------------------------------------
-- |
-- Copyright   :  (c) Edward Kmett 2010-2015
-- Maintainer  :  ekmett@gmail.com
-- Stability   :  experimental
-- Portability :  GHC only
--
-----------------------------------------------------------------------------

(
Mode(..)
) where

import Numeric.Natural
import Data.Complex
import Data.Int
import Data.Ratio
import Data.Word

infixr 7 *^
infixl 7 ^*
infixr 7 ^/

class (Num t, Num (Scalar t)) => Mode t where
type Scalar t
-- | allowed to return False for items with a zero derivative, but we'll give more NaNs than strictly necessary
isKnownConstant :: t -> Bool
isKnownConstant _ = False

-- | allowed to return False for zero, but we give more NaN's than strictly necessary
isKnownZero :: t -> Bool
isKnownZero _ = False

-- | Embed a constant
auto  :: Scalar t -> t

-- | Scalar-vector multiplication
(*^) :: Scalar t -> t -> t
a *^ b = auto a * b

-- | Vector-scalar multiplication
(^*) :: t -> Scalar t -> t
a ^* b = a * auto b

-- | Scalar division
(^/) :: Fractional (Scalar t) => t -> Scalar t -> t
a ^/ b = a ^* recip b

-- |
-- @'zero' = 'lift' 0@
zero :: t
zero = auto 0

instance Mode Double where
type Scalar Double = Double
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Float where
type Scalar Float = Float
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Int where
type Scalar Int = Int
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Integer where
type Scalar Integer = Integer
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Int8 where
type Scalar Int8 = Int8
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Int16 where
type Scalar Int16 = Int16
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Int32 where
type Scalar Int32 = Int32
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Int64 where
type Scalar Int64 = Int64
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Natural where
type Scalar Natural = Natural
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Word where
type Scalar Word = Word
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Word8 where
type Scalar Word8 = Word8
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Word16 where
type Scalar Word16 = Word16
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Word32 where
type Scalar Word32 = Word32
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Mode Word64 where
type Scalar Word64 = Word64
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance RealFloat a => Mode (Complex a) where
type Scalar (Complex a) = Complex a
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)

instance Integral a => Mode (Ratio a) where
type Scalar (Ratio a) = Ratio a
isKnownConstant _ = True
isKnownZero x = 0 == x
auto = id
(^/) = (/)