+% ------------------------------------------------------------------------------
+% $Id: PrelReal.lhs,v 1.10 2001/02/28 00:01:03 qrczak Exp $
%
-% (c) The AQUA Project, Glasgow University, 1994-1996
+% (c) The University of Glasgow, 1994-2000
%
\section[PrelReal]{Module @PrelReal@}
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
\end{code}
+These 'numeric' enumerations come straight from the Report
+
+\begin{code}
+numericEnumFrom :: (Fractional a) => a -> [a]
+numericEnumFrom = iterate (+1)
+
+numericEnumFromThen :: (Fractional a) => a -> a -> [a]
+numericEnumFromThen n m = iterate (+(m-n)) n
+
+numericEnumFromTo :: (Ord a, Fractional a) => a -> a -> [a]
+numericEnumFromTo n m = takeWhile (<= m + 1/2) (numericEnumFrom n)
+
+numericEnumFromThenTo :: (Ord a, Fractional a) => a -> a -> a -> [a]
+numericEnumFromThenTo e1 e2 e3 = takeWhile pred (numericEnumFromThen e1 e2)
+ where
+ mid = (e2 - e1) / 2
+ pred | e2 > e1 = (<= e3 + mid)
+ | otherwise = (>= e3 + mid)
+\end{code}
+
+
%*********************************************************
%* *
\subsection{Instances for @Int@}
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
\begin{code}
instance (Integral a) => Ord (Ratio a) where
+ {-# SPECIALIZE instance Ord Rational #-}
(x:%y) <= (x':%y') = x * y' <= x' * y
(x:%y) < (x':%y') = x * y' < x' * y
instance (Integral a) => Num (Ratio a) where
+ {-# SPECIALIZE instance Num Rational #-}
(x:%y) + (x':%y') = reduce (x*y' + x'*y) (y*y')
(x:%y) - (x':%y') = reduce (x*y' - x'*y) (y*y')
(x:%y) * (x':%y') = reduce (x * x') (y * y')
fromInteger x = fromInteger x :% 1
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
fromRational (x:%y) = fromInteger x :% fromInteger y
instance (Integral a) => Real (Ratio a) where
+ {-# SPECIALIZE instance Real Rational #-}
toRational (x:%y) = toInteger x :% toInteger y
instance (Integral a) => RealFrac (Ratio a) where
+ {-# SPECIALIZE instance RealFrac Rational #-}
properFraction (x:%y) = (fromInteger (toInteger q), r:%y)
where (q,r) = quotRem x y
instance (Integral a) => Show (Ratio a) where
+ {-# SPECIALIZE instance Show Rational #-}
showsPrec p (x:%y) = showParen (p > ratio_prec)
(shows x . showString " % " . shows y)
ratio_prec = 7
instance (Integral a) => Enum (Ratio a) where
+ {-# SPECIALIZE instance Enum Rational #-}
succ x = x + 1
pred x = x - 1
- toEnum n = fromInt n :% 1
+ toEnum n = fromInteger (int2Integer n) :% 1
fromEnum = fromInteger . truncate
- enumFrom = bounded_iterator True (1)
- enumFromThen n m = bounded_iterator (diff >= 0) diff n
- where diff = m - n
-
-bounded_iterator :: (Ord a, Num a) => Bool -> a -> a -> [a]
-bounded_iterator inc step v
- | inc && v > new_v = [v] -- oflow
- | not inc && v < new_v = [v] -- uflow
- | otherwise = v : bounded_iterator inc step new_v
- where
- new_v = v + step
+ enumFrom = numericEnumFrom
+ enumFromThen = numericEnumFromThen
+ enumFromTo = numericEnumFromTo
+ enumFromThenTo = numericEnumFromThenTo
\end{code}
%*********************************************************
%* *
+\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}
%* *
%*********************************************************
| otherwise = f b (i-1) (b*y)
_ ^ _ = error "Prelude.^: negative exponent"
-{- SPECIALISE (^^) ::
+{-# SPECIALISE (^^) ::
Rational -> Int -> Rational #-}
(^^) :: (Fractional a, Integral b) => a -> b -> a
x ^^ n = if n >= 0 then x^n else recip (x^(negate n))
{-# RULES
-"Int.gcd" forall a b . gcd a b = gcdInt a b
-"Integer.gcd" forall a b . gcd a b = gcdInteger a b
-"Integer.lcm" forall a b . lcm a b = lcmInteger a b
+"gcd/Int->Int->Int" gcd = gcdInt
+"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
\end{code}
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