GHC/Num.hs

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE NoImplicitPrelude, MagicHash, UnboxedTuples #-}
    {-# OPTIONS_HADDOCK hide #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Num
    -- Copyright   :  (c) The University of Glasgow 1994-2002
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC Extensions)
    --
    -- The 'Num' class and the 'Integer' type.
    --
    -----------------------------------------------------------------------------

    module GHC.Num (module GHC.Num, module GHC.Integer) where

    import GHC.Base
    import GHC.Integer

    infixl 7  *
    infixl 6  +, -

    default ()              -- Double isn't available yet,
                            -- and we shouldn't be using defaults anyway

    -- | Basic numeric class.
    class  Num a  where
        {-# MINIMAL (+), (*), abs, signum, fromInteger, (negate | (-)) #-}

        (+), (-), (*)       :: a -> a -> a
        -- | Unary negation.
        negate              :: a -> a
        -- | Absolute value.
        abs                 :: a -> a
        -- | Sign of a number.
        -- The functions 'abs' and 'signum' should satisfy the law:
        --
        -- > abs x * signum x == x
        --
        -- For real numbers, the 'signum' is either @-1@ (negative), @0@ (zero)
        -- or @1@ (positive).
        signum              :: a -> a
        -- | Conversion from an 'Integer'.
        -- An integer literal represents the application of the function
        -- 'fromInteger' to the appropriate value of type 'Integer',
        -- so such literals have type @('Num' a) => a@.
        fromInteger         :: Integer -> a

        {-# INLINE (-) #-}
        {-# INLINE negate #-}
        x - y               = x + negate y
        negate x            = 0 - x

    -- | the same as @'flip' ('-')@.
    --
    -- Because @-@ is treated specially in the Haskell grammar,
    -- @(-@ /e/@)@ is not a section, but an application of prefix negation.
    -- However, @('subtract'@ /exp/@)@ is equivalent to the disallowed section.
    {-# INLINE subtract #-}
    subtract :: (Num a) => a -> a -> a
    subtract x y = y - x

    -- | @since 2.01
    instance  Num Int  where
        I# x + I# y = I# (x +# y)
        I# x - I# y = I# (x -# y)
        negate (I# x) = I# (negateInt# x)
        I# x * I# y = I# (x *# y)
        abs n  = if n `geInt` 0 then n else negate n

        signum n | n `ltInt` 0 = negate 1
                 | n `eqInt` 0 = 0
                 | otherwise   = 1

        {-# INLINE fromInteger #-}   -- Just to be sure!
        fromInteger i = I# (integerToInt i)

    -- | @since 2.01
    instance Num Word where
        (W# x#) + (W# y#)      = W# (x# `plusWord#` y#)
        (W# x#) - (W# y#)      = W# (x# `minusWord#` y#)
        (W# x#) * (W# y#)      = W# (x# `timesWord#` y#)
        negate (W# x#)         = W# (int2Word# (negateInt# (word2Int# x#)))
        abs x                  = x
        signum 0               = 0
        signum _               = 1
        fromInteger i          = W# (integerToWord i)

    -- | @since 2.01
    instance  Num Integer  where
        (+) = plusInteger
        (-) = minusInteger
        (*) = timesInteger
        negate         = negateInteger
        fromInteger x  =  x

        abs = absInteger
        signum = signumInteger