module PrelNum where
-import PrelBase
-import Ix
import {-# SOURCE #-} PrelErr
+import PrelBase
+import PrelList
+import PrelEnum
+import PrelShow
infixr 8 ^, ^^, **
infixl 7 %, /, `quot`, `rem`, `div`, `mod`
+infixl 7 *
+infixl 6 +, -
+
\end{code}
%*********************************************************
%*********************************************************
\begin{code}
+class (Eq a, Show a) => Num a where
+ (+), (-), (*) :: a -> a -> a
+ negate :: a -> a
+ abs, signum :: a -> a
+ fromInteger :: Integer -> a
+ fromInt :: Int -> a -- partain: Glasgow extension
+
+ x - y = x + negate y
+ negate x = 0 - x
+ fromInt (I# i#) = fromInteger (S# i#)
+ -- Go via the standard class-op if the
+ -- non-standard one ain't provided
+
class (Num a, Ord a) => Real a where
toRational :: a -> Rational
%*********************************************************
\begin{code}
+instance Num Int where
+ (+) x y = plusInt x y
+ (-) x y = minusInt x y
+ negate x = negateInt x
+ (*) x y = timesInt x y
+ abs n = if n `geInt` 0 then n else (negateInt n)
+
+ signum n | n `ltInt` 0 = negateInt 1
+ | n `eqInt` 0 = 0
+ | otherwise = 1
+
+ fromInteger (S# i#) = I# i#
+ fromInteger (J# s# d#)
+ = case (integer2Int# s# d#) of { i# -> I# i# }
+
+ fromInt n = n
+
instance Real Int where
toRational x = toInteger x % 1
\begin{code}
instance Ord Integer where
- (J# a1 s1 d1) <= (J# a2 s2 d2)
- = (cmpInteger# a1 s1 d1 a2 s2 d2) <=# 0#
-
- (J# a1 s1 d1) < (J# a2 s2 d2)
- = (cmpInteger# a1 s1 d1 a2 s2 d2) <# 0#
-
- (J# a1 s1 d1) >= (J# a2 s2 d2)
- = (cmpInteger# a1 s1 d1 a2 s2 d2) >=# 0#
-
- (J# a1 s1 d1) > (J# a2 s2 d2)
- = (cmpInteger# a1 s1 d1 a2 s2 d2) ># 0#
-
- x@(J# a1 s1 d1) `max` y@(J# a2 s2 d2)
- = if ((cmpInteger# a1 s1 d1 a2 s2 d2) ># 0#) then x else y
-
- x@(J# a1 s1 d1) `min` y@(J# a2 s2 d2)
- = if ((cmpInteger# a1 s1 d1 a2 s2 d2) <# 0#) then x else y
-
- compare (J# a1 s1 d1) (J# a2 s2 d2)
- = case cmpInteger# a1 s1 d1 a2 s2 d2 of { res# ->
+ (S# i) <= (S# j) = i <=# j
+ (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
+ (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
+ (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
+
+ (S# i) > (S# j) = i ># j
+ (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
+ (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
+ (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
+
+ (S# i) < (S# j) = i <# j
+ (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
+ (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
+ (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
+
+ (S# i) >= (S# j) = i >=# j
+ (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
+ (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
+ (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
+
+ compare (S# i) (S# j)
+ | i ==# j = EQ
+ | i <=# j = LT
+ | otherwise = GT
+ compare (J# s d) (S# i)
+ = case cmpIntegerInt# s d i of { res# ->
+ if res# <# 0# then LT else
+ if res# ># 0# then GT else EQ
+ }
+ compare (S# i) (J# s d)
+ = case cmpIntegerInt# s d i of { res# ->
+ if res# ># 0# then LT else
+ if res# <# 0# then GT else EQ
+ }
+ compare (J# s1 d1) (J# s2 d2)
+ = case cmpInteger# s1 d1 s2 d2 of { res# ->
if res# <# 0# then LT else
if res# ># 0# then GT else EQ
}
-instance Num Integer where
- (+) (J# a1 s1 d1) (J# a2 s2 d2)
- = case plusInteger# a1 s1 d1 a2 s2 d2 of (# a, s, d #) -> J# a s d
-
- (-) (J# a1 s1 d1) (J# a2 s2 d2)
- = case minusInteger# a1 s1 d1 a2 s2 d2 of (# a, s, d #) -> J# a s d
-
- negate (J# a s d)
- = case negateInteger# a s d of (# a1, s1, d1 #) -> J# a1 s1 d1
+toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
+toBig i@(J# _ _) = i
- (*) (J# a1 s1 d1) (J# a2 s2 d2)
- = case timesInteger# a1 s1 d1 a2 s2 d2 of (# a, s, d #) -> J# a s d
+instance Num Integer where
+ (+) i1@(S# i) i2@(S# j)
+ = case addIntC# i j of { (# r, c #) ->
+ if c ==# 0# then S# r
+ else toBig i1 + toBig i2 }
+ (+) i1@(J# _ _) i2@(S# _) = i1 + toBig i2
+ (+) i1@(S# _) i2@(J# _ _) = toBig i1 + i2
+ (+) (J# s1 d1) (J# s2 d2)
+ = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
+
+ (-) i1@(S# i) i2@(S# j)
+ = case subIntC# i j of { (# r, c #) ->
+ if c ==# 0# then S# r
+ else toBig i1 - toBig i2 }
+ (-) i1@(J# _ _) i2@(S# _) = i1 - toBig i2
+ (-) i1@(S# _) i2@(J# _ _) = toBig i1 - i2
+ (-) (J# s1 d1) (J# s2 d2)
+ = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
+
+ (*) i1@(S# i) i2@(S# j)
+ = case mulIntC# i j of { (# r, c #) ->
+ if c ==# 0# then S# r
+ else toBig i1 * toBig i2 }
+ (*) i1@(J# _ _) i2@(S# _) = i1 * toBig i2
+ (*) i1@(S# _) i2@(J# _ _) = toBig i1 * i2
+ (*) (J# s1 d1) (J# s2 d2)
+ = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
+
+ negate (S# (-2147483648#)) = 2147483648
+ negate (S# i) = S# (negateInt# i)
+ negate (J# s d) = J# (negateInt# s) d
-- ORIG: abs n = if n >= 0 then n else -n
- abs n@(J# a1 s1 d1)
- = case 0 of { J# a2 s2 d2 ->
- if (cmpInteger# a1 s1 d1 a2 s2 d2) >=# 0#
+ abs (S# i) = case abs (I# i) of I# j -> S# j
+ abs n@(J# s d)
+ = if (cmpIntegerInt# s d 0#) >=# 0#
then n
- else case negateInteger# a1 s1 d1 of (# a, s, d #) -> J# a s d
- }
+ else J# (negateInt# s) d
- signum (J# a1 s1 d1)
- = case 0 of { J# a2 s2 d2 ->
- let
- cmp = cmpInteger# a1 s1 d1 a2 s2 d2
+ signum (S# i) = case signum (I# i) of I# j -> S# j
+ signum (J# s d)
+ = let
+ cmp = cmpIntegerInt# s d 0#
in
- if cmp ># 0# then 1
- else if cmp ==# 0# then 0
- else (negate 1)
- }
+ if cmp ># 0# then S# 1#
+ else if cmp ==# 0# then S# 0#
+ else S# (negateInt# 1#)
fromInteger x = x
- fromInt (I# i) = int2Integer i
+ fromInt (I# i) = S# i
instance Real Integer where
toRational x = x % 1
instance Integral Integer where
- quotRem (J# a1 s1 d1) (J# a2 s2 d2)
- = case (quotRemInteger# a1 s1 d1 a2 s2 d2) of
- (# a3, s3, d3, a4, s4, d4 #)
- -> (J# a3 s3 d3, J# a4 s4 d4)
+ -- ToDo: a `rem` b returns a small integer if b is small,
+ -- a `quot` b returns a small integer if a is small.
+ quotRem (S# i) (S# j)
+ = case quotRem (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
+ quotRem i1@(J# _ _) i2@(S# _) = quotRem i1 (toBig i2)
+ quotRem i1@(S# _) i2@(J# _ _) = quotRem (toBig i1) i2
+ quotRem (J# s1 d1) (J# s2 d2)
+ = case (quotRemInteger# s1 d1 s2 d2) of
+ (# s3, d3, s4, d4 #)
+ -> (J# s3 d3, J# s4 d4)
{- USING THE UNDERLYING "GMP" CODE IS DUBIOUS FOR NOW:
-> (J# a3 s3 d3, J# a4 s4 d4)
-}
toInteger n = n
- toInt (J# a s d) = case (integer2Int# a s d) of { n# -> I# n# }
+ toInt (S# i) = I# i
+ toInt (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
-- the rest are identical to the report default methods;
-- you get slightly better code if you let the compiler
-- see them right here:
+ (S# n) `quot` (S# d) = S# (n `quotInt#` d)
n `quot` d = if d /= 0 then q else
error "Prelude.Integral.quot{Integer}: divide by 0"
where (q,_) = quotRem n d
+
+ (S# n) `rem` (S# d) = S# (n `remInt#` d)
n `rem` d = if d /= 0 then r else
error "Prelude.Integral.rem{Integer}: divide by 0"
where (_,r) = quotRem n d
+
n `div` d = q where (q,_) = divMod n d
n `mod` d = r where (_,r) = divMod n d
if signum r == negate (signum d) then (q - 1, r+d) else qr }
-- Case-ified by WDP 94/10
+------------------------------------------------------------------------
instance Enum Integer where
succ x = x + 1
pred x = x - 1
toEnum n = toInteger n
fromEnum n = toInt n
- enumFrom n = n : enumFrom (n + 1)
- enumFromThen e1 e2 = en' e1 (e2 - e1)
- where en' a b = a : en' (a + b) b
- enumFromTo n m
- | n <= m = takeWhile (<= m) (enumFrom n)
- | otherwise = takeWhile (>= m) (enumFromThen n (n-1))
- enumFromThenTo n m p = takeWhile pred (enumFromThen n m)
- where
- pred | m >= n = (<= p)
- | otherwise = (>= p)
+
+ {-# INLINE enumFrom #-}
+ {-# INLINE enumFromThen #-}
+ {-# INLINE enumFromTo #-}
+ {-# INLINE enumFromThenTo #-}
+ enumFrom x = build (\c _ -> enumDeltaIntegerFB c x 1)
+ enumFromThen x y = build (\c _ -> enumDeltaIntegerFB c x (y-x))
+ enumFromTo x lim = build (\c n -> enumDeltaToIntegerFB c n x 1 lim)
+ enumFromThenTo x y lim = build (\c n -> enumDeltaToIntegerFB c n x (y-x) lim)
+
+enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
+enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
+
+enumDeltaIntegerList :: Integer -> Integer -> [Integer]
+enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
+
+enumDeltaToIntegerFB c n x delta lim
+ | delta >= 0 = up_fb c n x delta lim
+ | otherwise = dn_fb c n x delta lim
+
+enumDeltaToIntegerList x delta lim
+ | delta >= 0 = up_list x delta lim
+ | otherwise = dn_list x delta lim
+
+up_fb c n x delta lim = go (x::Integer)
+ where
+ go x | x > lim = n
+ | otherwise = x `c` go (x+delta)
+dn_fb c n x delta lim = go (x::Integer)
+ where
+ go x | x < lim = n
+ | otherwise = x `c` go (x+delta)
+
+up_list x delta lim = go (x::Integer)
+ where
+ go x | x > lim = []
+ | otherwise = x : go (x+delta)
+dn_list x delta lim = go (x::Integer)
+ where
+ go x | x < lim = []
+ | otherwise = x : go (x+delta)
+
+{-# RULES
+"enumDeltaInteger" enumDeltaIntegerFB (:) = enumDeltaIntegerList
+"enumDeltaToInteger" enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
+ #-}
+
+------------------------------------------------------------------------
instance Show Integer where
showsPrec x = showSignedInteger x
showList = showList__ (showsPrec 0)
-instance Ix Integer where
- range (m,n) = [m..n]
- index b@(m,_) i
- | inRange b i = fromInteger (i - m)
- | otherwise = indexIntegerError i b
- inRange (m,n) i = m <= i && i <= n
-
--- Sigh, really want to use helper function in Ix, but
--- module deps. are too painful.
-{-# NOINLINE indexIntegerError #-}
-indexIntegerError :: Integer -> (Integer,Integer) -> a
-indexIntegerError i rng
- = error (showString "Ix{Integer}.index: Index " .
- showParen True (showsPrec 0 i) .
- showString " out of range " $
- showParen True (showsPrec 0 rng) "")
-
showSignedInteger :: Int -> Integer -> ShowS
showSignedInteger p n r
| n < 0 && p > 6 = '(':jtos n (')':r)
| otherwise = jtos' q (chr (toInt r + (ord_0::Int)) : cs)
where
(q,r) = n `quotRem` 10
+
+ord_0 :: Num a => a
+ord_0 = fromInt (ord '0')
\end{code}
%*********************************************************
%*********************************************************
\begin{code}
+
+{-# SPECIALISE subtract :: Int -> Int -> Int #-}
+subtract :: (Num a) => a -> a -> a
+subtract x y = y - x
+
even, odd :: (Integral a) => a -> Bool
even n = n `rem` 2 == 0
odd = not . even
Rational -> Int -> Rational #-}
(^^) :: (Fractional a, Integral b) => a -> b -> a
x ^^ n = if n >= 0 then x^n else recip (x^(negate n))
-
\end{code}
projects / ghc-hetmet.git / blobdiff