\begin{code}
-{-# OPTIONS_GHC -fno-implicit-prelude #-}
+{-# OPTIONS_GHC -XNoImplicitPrelude #-}
{-# OPTIONS_HADDOCK hide #-}
-----------------------------------------------------------------------------
-- |
import GHC.List
import GHC.Enum
import GHC.Show
+import GHC.Err
infixr 8 ^, ^^
infixl 7 /, `quot`, `rem`, `div`, `mod`
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
-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
\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}
toRational x = toInteger x % 1
instance Integral Int where
- toInteger i = int2Integer i -- give back a full-blown Integer
+ toInteger (I# i) = smallInteger i
a `quot` b
| b == 0 = divZeroError
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
- a `divMod` b = a `divModInteger` b
+ _ `divMod` 0 = divZeroError
+ a `divMod` b = case a `divModInteger` b of
+ (# x, y #) -> (x, y)
- a `quotRem` 0 = divZeroError
- a `quotRem` b = a `quotRemInteger` b
+ _ `quotRem` 0 = divZeroError
+ a `quotRem` b = case a `quotRemInteger` b of
+ (# q, r #) -> (q, r)
-- use the defaults for div & mod
\end{code}
{-# 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]
+ 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
succ x = x + 1
pred x = x - 1
- toEnum n = fromInteger (int2Integer n) :% 1
+ toEnum n = fromIntegral n :% 1
fromEnum = fromInteger . truncate
enumFrom = numericEnumFrom
Integer -> Integer -> Integer,
Integer -> Int -> Integer,
Int -> Int -> Int #-}
-(^) :: (Num a, Integral b) => a -> b -> a
-_ ^ 0 = 1
-x ^ n | n > 0 = f x (n-1) x
- where f _ 0 y = y
- f a d y = g a d where
- g b i | even i = g (b*b) (i `quot` 2)
- | otherwise = f b (i-1) (b*y)
-_ ^ _ = error "Prelude.^: negative exponent"
+(^) :: (Num a, Integral b) => a -> b -> a
+x0 ^ y0 | y0 < 0 = error "Negative exponent"
+ | y0 == 0 = 1
+ | 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 = 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)
-
{-# RULES
"gcd/Int->Int->Int" gcd = gcdInt
-"gcd/Integer->Integer->Integer" gcd = gcdInteger
+"gcd/Integer->Integer->Integer" gcd = gcdInteger'
"lcm/Integer->Integer->Integer" lcm = lcmInteger
#-}
+-- XXX to use another Integer implementation, you might need to disable
+-- the gcd/Integer and lcm/Integer RULES above
+--
+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))
+
integralEnumFrom :: (Integral a, Bounded a) => a -> [a]
integralEnumFrom n = map fromInteger [toInteger n .. toInteger (maxBound `asTypeOf` n)]
projects / ghc-base.git / blobdiff