Num.hs

{-# LANGUAGE DataKinds             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeFamilies          #-}

{-# OPTIONS_HADDOCK show-extensions #-}

{-|
Copyright  :  (C) 2013-2015, University of Twente
License    :  BSD2 (see the file LICENSE)
Maintainer :  Christiaan Baaij <christiaan.baaij@gmail.com>
-}
module CLaSH.Class.Num
  ( -- * Arithmetic functions for arguments and results of different precision
    ExtendingNum (..)
    -- * Saturating arithmetic functions
  , SaturationMode (..)
  , SaturatingNum (..)
  , boundedPlus
  , boundedMin
  , boundedMult
  )
where

-- * Arithmetic functions for arguments and results of different precision

-- | Adding, subtracting, and multiplying values of two different (sub-)types.
class ExtendingNum a b where
  -- | Type of the result of the addition or subtraction
  type AResult a b
  -- | Add values of different (sub-)types, return a value of a (sub-)type
  -- that is potentially different from either argument.
  plus  :: a -> b -> AResult a b
  -- | Subtract values of different (sub-)types, return a value of a (sub-)type
  -- that is potentially different from either argument.
  minus :: a -> b -> AResult a b
  -- | Type of the result of the multiplication
  type MResult a b
  -- | Multiply values of different (sub-)types, return a value of a (sub-)type
  -- that is potentially different from either argument.
  times :: a -> b -> MResult a b

-- * Saturating arithmetic functions

-- | Determine how overflow and underflow are handled by the functions in
-- 'SaturatingNum'
data SaturationMode
  = SatWrap  -- ^ Wrap around on overflow and underflow
  | SatBound -- ^ Become 'maxBound' on overflow, and 'minBound' on underflow
  | SatZero  -- ^ Become @0@ on overflow and underflow
  | SatSymmetric -- ^ Become 'maxBound' on overflow, and (@'minBound' - 1@) on
                 -- underflow for signed numbers, and 'minBound' for unsigned
                 -- numbers.
  deriving Eq

-- | 'Num' operators in which overflow and underflow behaviour can be specified
-- using 'SaturationMode'.
class (Bounded a, Num a) => SaturatingNum a where
  -- | Addition with parametrisable over- and underflow behaviour
  satPlus :: SaturationMode -> a -> a -> a
  -- | Subtraction with parametrisable over- and underflow behaviour
  satMin  :: SaturationMode -> a -> a -> a
  -- | Multiplication with parametrisable over- and underflow behaviour
  satMult :: SaturationMode -> a -> a -> a

{-# INLINE boundedPlus #-}
-- | Addition that clips to 'maxBound' on overflow, and 'minBound' on underflow
boundedPlus :: SaturatingNum a => a -> a -> a
boundedPlus = satPlus SatBound

{-# INLINE boundedMin #-}
-- | Subtraction that clips to 'maxBound' on overflow, and 'minBound' on
-- underflow
boundedMin  :: SaturatingNum a => a -> a -> a
boundedMin = satMin SatBound

{-# INLINE boundedMult #-}
-- | Multiplication that clips to 'maxBound' on overflow, and 'minBound' on
-- underflow
boundedMult :: SaturatingNum a => a -> a -> a
boundedMult = satMult SatBound