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\begin{code}
{-# OPTIONS -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  GHC.Real
-- Copyright   :  (c) The FFI Task Force, 1994-2002
-- License     :  see libraries/base/LICENSE
-- 
-- Maintainer  :  cvs-ghc@haskell.org
-- Stability   :  internal
-- Portability :  non-portable (GHC Extensions)
--
-- The types 'Ratio' and 'Rational', and the classes 'Real', 'Fractional',
-- 'Integral', and 'RealFrac'.
--
-----------------------------------------------------------------------------

module GHC.Real where

import {-# SOURCE #-} GHC.Err
import GHC.Base
import GHC.Num
import GHC.List
import GHC.Enum
import GHC.Show

infixr 8  ^, ^^
infixl 7  /, `quot`, `rem`, `div`, `mod`
infixl 7  %

default ()		-- Double isn't available yet, 
			-- and we shouldn't be using defaults anyway
\end{code}


%*********************************************************
%*							*
\subsection{The @Ratio@ and @Rational@ types}
%*							*
%*********************************************************

\begin{code}
data  (Integral a)	=> Ratio a = !a :% !a  deriving (Eq)

-- | Arbitrary-precision rational numbers, represented as a ratio of
-- two 'Integer' values.  A rational number may be constructed using
-- the '%' operator.
type  Rational		=  Ratio Integer

ratioPrec, ratioPrec1 :: Int
ratioPrec  = 7 	-- Precedence of ':%' constructor
ratioPrec1 = ratioPrec + 1

infinity, notANumber :: Rational
infinity   = 1 :% 0
notANumber = 0 :% 0

-- Use :%, not % for Inf/NaN; the latter would 
-- immediately lead to a runtime error, because it normalises. 
\end{code}


\begin{code}
{-# SPECIALISE (%) :: Integer -> Integer -> Rational #-}
(%)			:: (Integral a) => a -> a -> Ratio a
numerator, denominator	:: (Integral a) => Ratio a -> a
\end{code}

\tr{reduce} is a subsidiary function used only in this module .
It normalises a ratio by dividing both numerator and denominator by
their greatest common divisor.

\begin{code}
reduce ::  (Integral a) => a -> a -> Ratio a
{-# SPECIALISE reduce :: Integer -> Integer -> Rational #-}
reduce _ 0		=  error "Ratio.%: zero denominator"
reduce x y		=  (x `quot` d) :% (y `quot` d)
			   where d = gcd x y
\end{code}

\begin{code}
x % y			=  reduce (x * signum y) (abs y)

numerator   (x :% _)	=  x
denominator (_ :% y)	=  y
\end{code}


%*********************************************************
%*							*
\subsection{Standard numeric classes}
%*							*
%*********************************************************

\begin{code}
class  (Num a, Ord a) => Real a  where
    toRational		::  a -> Rational

class  (Real a, Enum a) => Integral a  where
    quot, rem, div, mod	:: a -> a -> a
    quotRem, divMod	:: a -> a -> (a,a)
    toInteger		:: a -> Integer

    n `quot` d		=  q  where (q,_) = quotRem n d
    n `rem` d		=  r  where (_,r) = quotRem n d
    n `div` d		=  q  where (q,_) = divMod n d
    n `mod` d		=  r  where (_,r) = divMod n d
    divMod n d 		=  if signum r == negate (signum d) then (q-1, r+d) else qr
			   where qr@(q,r) = quotRem n d

class  (Num a) => Fractional a  where
    (/)			:: a -> a -> a
    recip		:: a -> a
    fromRational	:: Rational -> a

    recip x		=  1 / x
    x / y		= x * recip y