\begin{code}
-{-# OPTIONS_GHC -fno-implicit-prelude #-}
+{-# OPTIONS_GHC -XNoImplicitPrelude #-}
{-# OPTIONS_HADDOCK hide #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.Real
--- Copyright : (c) The FFI Task Force, 1994-2002
+-- 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)
import GHC.List
import GHC.Enum
import GHC.Show
+import GHC.Err
infixr 8 ^, ^^
infixl 7 /, `quot`, `rem`, `div`, `mod`
infixl 7 %
-default () -- Double isn't available yet,
+default () -- Double isn't available yet,
-- and we shouldn't be using defaults anyway
\end{code}
infinity = 1 :% 0
notANumber = 0 :% 0
--- Use :%, not % for Inf/NaN; the latter would
--- immediately lead to a runtime error, because it normalises.
+-- Use :%, not % for Inf/NaN; the latter would
+-- immediately lead to a runtime error, because it normalises.
\end{code}
-- | conversion to 'Integer'
toInteger :: a -> Integer
+ {-# INLINE quot #-}
+ {-# INLINE rem #-}
+ {-# INLINE div #-}
+ {-# INLINE mod #-}
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
-- @('Fractional' a) => a@.
fromRational :: Rational -> a
+ {-# INLINE recip #-}
+ {-# INLINE (/) #-}
recip x = 1 / x
x / y = x * recip y
properFraction :: (Integral b) => a -> (b,a)
-- | @'truncate' x@ returns the integer nearest @x@ between zero and @x@
truncate :: (Integral b) => a -> b
- -- | @'round' x@ returns the nearest integer to @x@
+ -- | @'round' x@ returns the nearest integer to @x@;
+ -- the even integer if @x@ is equidistant between two integers
round :: (Integral b) => a -> b
-- | @'ceiling' x@ returns the least integer not less than @x@
ceiling :: (Integral b) => a -> b
-- | @'floor' x@ returns the greatest integer not greater than @x@
floor :: (Integral b) => a -> b
+ {-# INLINE truncate #-}
truncate x = m where (m,_) = properFraction x
-
+
round x = let (n,r) = properFraction x
m = if r < 0 then n - 1 else n + 1
in case signum (abs r - 0.5) of
-1 -> n
0 -> if even n then n else m
1 -> m
-
+ _ -> error "round default defn: Bad value"
+
ceiling x = if r > 0 then n + 1 else n
where (n,r) = properFraction x
-
+
floor x = if r < 0 then n - 1 else n
where (n,r) = properFraction x
\end{code}
\begin{code}
numericEnumFrom :: (Fractional a) => a -> [a]
-numericEnumFrom = iterate (+1)
+numericEnumFrom n = n `seq` (n : numericEnumFrom (n + 1))
numericEnumFromThen :: (Fractional a) => a -> a -> [a]
-numericEnumFromThen n m = iterate (+(m-n)) n
+numericEnumFromThen n m = n `seq` m `seq` (n : numericEnumFromThen m (m+m-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)
+numericEnumFromThenTo e1 e2 e3
+ = takeWhile predicate (numericEnumFromThen e1 e2)
where
mid = (e2 - e1) / 2
- pred | e2 >= e1 = (<= e3 + mid)
- | otherwise = (>= e3 + mid)
+ predicate | e2 >= e1 = (<= e3 + mid)
+ | otherwise = (>= e3 + mid)
\end{code}
instance Integral Integer where
toInteger n = n
- a `quot` 0 = divZeroError
+ _ `quot` 0 = divZeroError
n `quot` d = n `quotInteger` d
- a `rem` 0 = divZeroError
+ _ `rem` 0 = divZeroError
n `rem` d = n `remInteger` d
- a `divMod` 0 = divZeroError
+ _ `divMod` 0 = divZeroError
a `divMod` b = case a `divModInteger` b of
(# x, y #) -> (x, y)
- a `quotRem` 0 = divZeroError
+ _ `quotRem` 0 = divZeroError
a `quotRem` b = case a `quotRemInteger` b of
(# q, r #) -> (q, r)
instance (Integral a) => Fractional (Ratio a) where
{-# SPECIALIZE instance Fractional Rational #-}
(x:%y) / (x':%y') = (x*y') % (y*x')
- recip (x:%y) = y % x
+ recip (0:%_) = error "Ratio.%: zero denominator"
+ recip (x:%y)
+ | x < 0 = negate y :% negate x
+ | otherwise = y :% x
fromRational (x:%y) = fromInteger x :% fromInteger y
instance (Integral a) => Real (Ratio a) where
instance (Integral a) => Show (Ratio a) where
{-# SPECIALIZE instance Show Rational #-}
showsPrec p (x:%y) = showParen (p > ratioPrec) $
- showsPrec ratioPrec1 x .
- showString "%" . -- H98 report has spaces round the %
- -- but we removed them [May 04]
+ showsPrec ratioPrec1 x .
+ showString " % " .
+ -- H98 report has spaces round the %
+ -- but we removed them [May 04]
+ -- and added them again for consistency with
+ -- Haskell 98 [Sep 08, #1920]
showsPrec ratioPrec1 y
instance (Integral a) => Enum (Ratio a) where
-> Int -- ^ the precedence of the enclosing context
-> a -- ^ the value to show
-> ShowS
-showSigned showPos p x
+showSigned showPos p x
| x < 0 = showParen (p > 6) (showChar '-' . showPos (-x))
| otherwise = showPos x
(^) :: (Num a, Integral b) => a -> b -> a
x0 ^ y0 | y0 < 0 = error "Negative exponent"
| y0 == 0 = 1
- | otherwise = f x0 y0 1
- where -- x0 ^ y0 = (x ^ y) * z
- f x y z | even y = f (x * x) (y `quot` 2) z
+ | otherwise = f x0 y0
+ where -- f : x0 ^ y0 = x ^ y
+ f x y | even y = f (x * x) (y `quot` 2)
+ | y == 1 = x
+ | otherwise = g (x * x) ((y - 1) `quot` 2) x
+ -- g : x0 ^ y0 = (x ^ y) * z
+ g x y z | even y = g (x * x) (y `quot` 2) z
| y == 1 = x * z
- | otherwise = f (x * x) ((y - 1) `quot` 2) (x * z)
+ | otherwise = g (x * x) ((y - 1) `quot` 2) (x * z)
-- | raise a number to an integral power
{-# SPECIALISE (^^) ::
lcm 0 _ = 0
lcm x y = abs ((x `quot` (gcd x y)) * y)
+#ifdef OPTIMISE_INTEGER_GCD_LCM
{-# RULES
"gcd/Int->Int->Int" gcd = gcdInt
+"gcd/Integer->Integer->Integer" gcd = gcdInteger'
+"lcm/Integer->Integer->Integer" lcm = lcmInteger
#-}
--- XXX these optimisation rules are disabled for now to make it easier
--- to experiment with other Integer implementations
--- "gcd/Integer->Integer->Integer" gcd = gcdInteger'
--- "lcm/Integer->Integer->Integer" lcm = lcmInteger
---
--- gcdInteger' :: Integer -> Integer -> Integer
--- gcdInteger' 0 0 = error "GHC.Real.gcdInteger': gcd 0 0 is undefined"
--- gcdInteger' a b = gcdInteger a b
+gcdInteger' :: Integer -> Integer -> Integer
+gcdInteger' 0 0 = error "GHC.Real.gcdInteger': gcd 0 0 is undefined"
+gcdInteger' a b = gcdInteger a b
+
+gcdInt :: Int -> Int -> Int
+gcdInt 0 0 = error "GHC.Real.gcdInt: gcd 0 0 is undefined"
+gcdInt a b = fromIntegral (gcdInteger (fromIntegral a) (fromIntegral b))
+#endif
integralEnumFrom :: (Integral a, Bounded a) => a -> [a]
integralEnumFrom n = map fromInteger [toInteger n .. toInteger (maxBound `asTypeOf` n)]
projects / ghc-base.git / blobdiff