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\begin{code}
{-# 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
\end{code}
%*********************************************************
%* *
\subsection{Standard numeric class}
%* *
%*********************************************************
\begin{code}
-- | Basic numeric class.
--
-- Minimal complete definition: all except 'negate' or @(-)@
class Num a where
(+), (-), (*) :: 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
{-# MINIMAL (+), (*), abs, signum, fromInteger, (negate | (-)) #-}
-- | 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
\end{code}
%*********************************************************
%* *
\subsection{Instances for @Int@}
%* *
%*********************************************************
\begin{code}
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)
\end{code}
%*********************************************************
%* *
\subsection{Instances for @Word@}
%* *
%*********************************************************
\begin{code}
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)
\end{code}
%*********************************************************
%* *
\subsection{The @Integer@ instances for @Num@}
%* *
%*********************************************************
\begin{code}
instance Num Integer where
(+) = plusInteger
(-) = minusInteger
(*) = timesInteger
negate = negateInteger
fromInteger x = x
abs = absInteger
signum = signumInteger
\end{code}
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