% ------------------------------------------------------------------------------
-% $Id: PrelReal.lhs,v 1.7 2000/12/16 17:46:57 qrczak Exp $
+% $Id: PrelReal.lhs,v 1.16 2001/09/26 16:27:04 simonpj Exp $
%
% (c) The University of Glasgow, 1994-2000
%
\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
quot, rem, div, mod :: a -> a -> a
quotRem, divMod :: a -> a -> (a,a)
toInteger :: a -> Integer
- toInt :: a -> Int -- partain: Glasgow extension
n `quot` d = q where (q,_) = quotRem n d
n `rem` d = r where (_,r) = quotRem n d
instance Integral Int where
toInteger i = int2Integer i -- give back a full-blown Integer
- toInt x = x
-- Following chks for zero divisor are non-standard (WDP)
a `quot` b = if b /= 0
instance Integral Integer where
toInteger n = n
- toInt n = integer2Int n
n `quot` d = n `quotInteger` d
n `rem` d = n `remInteger` d
instance (Integral a) => Fractional (Ratio a) where
{-# SPECIALIZE instance Fractional Rational #-}
(x:%y) / (x':%y') = (x*y') % (y*x')
- recip (x:%y) = if x < 0 then (-y) :% (-x) else y :% x
+ recip (x:%y) = y % x
fromRational (x:%y) = fromInteger x :% fromInteger y
instance (Integral a) => Real (Ratio a) where
succ x = x + 1
pred x = x - 1
- toEnum n = fromInt n :% 1
+ toEnum n = fromInteger (int2Integer n) :% 1
fromEnum = fromInteger . truncate
enumFrom = numericEnumFrom
%*********************************************************
%* *
+\subsection{Coercions}
+%* *
+%*********************************************************
+
+\begin{code}
+fromIntegral :: (Integral a, Num b) => a -> b
+fromIntegral = fromInteger . toInteger
+
+{-# RULES
+"fromIntegral/Int->Int" fromIntegral = id :: Int -> Int
+ #-}
+
+realToFrac :: (Real a, Fractional b) => a -> b
+realToFrac = fromRational . toRational
+
+{-# RULES
+"realToFrac/Int->Int" realToFrac = id :: Int -> Int
+ #-}
+
+-- For backward compatibility
+{-# DEPRECATED fromInt "use fromIntegral instead" #-}
+fromInt :: Num a => Int -> a
+fromInt = fromIntegral
+
+-- For backward compatibility
+{-# DEPRECATED toInt "use fromIntegral instead" #-}
+toInt :: Integral a => a -> Int
+toInt = fromIntegral
+\end{code}
+
+%*********************************************************
+%* *
\subsection{Overloaded numeric functions}
%* *
%*********************************************************
"gcd/Integer->Integer->Integer" gcd = gcdInteger
"lcm/Integer->Integer->Integer" lcm = lcmInteger
#-}
+
+integralEnumFrom :: (Integral a, Bounded a) => a -> [a]
+integralEnumFrom n = map fromInteger [toInteger n .. toInteger (maxBound `asTypeOf` n)]
+
+integralEnumFromThen :: (Integral a, Bounded a) => a -> a -> [a]
+integralEnumFromThen n1 n2
+ | i_n2 >= i_n1 = map fromInteger [i_n1, i_n2 .. toInteger (maxBound `asTypeOf` n1)]
+ | otherwise = map fromInteger [i_n1, i_n2 .. toInteger (minBound `asTypeOf` n1)]
+ where
+ i_n1 = toInteger n1
+ i_n2 = toInteger n2
+
+integralEnumFromTo :: Integral a => a -> a -> [a]
+integralEnumFromTo n m = map fromInteger [toInteger n .. toInteger m]
+
+integralEnumFromThenTo :: Integral a => a -> a -> a -> [a]
+integralEnumFromThenTo n1 n2 m
+ = map fromInteger [toInteger n1, toInteger n2 .. toInteger m]
\end{code}