X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=GHC%2FReal.lhs;h=17d04526ee0fc87abd546cdd9e10378dc1401b7b;hb=a07504ab09e4c63e7ef25c13e4e97466c36a651a;hp=9b6144583796e07bd4399dbc47abbafcf71b1061;hpb=72e4fe7801d2d8ab5b243cbb430272b45010f59d;p=ghc-base.git diff --git a/GHC/Real.lhs b/GHC/Real.lhs index 9b61445..17d0452 100644 --- a/GHC/Real.lhs +++ b/GHC/Real.lhs @@ -1,12 +1,12 @@ \begin{code} -{-# OPTIONS_GHC -fno-implicit-prelude #-} +{-# LANGUAGE CPP, NoImplicitPrelude, MagicHash, UnboxedTuples #-} {-# 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) @@ -24,12 +24,13 @@ import GHC.Num 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} @@ -57,8 +58,8 @@ infinity, notANumber :: Rational 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} @@ -132,10 +133,15 @@ class (Real a, Enum a) => Integral a where -- | 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 @@ -153,6 +159,8 @@ class (Num a) => Fractional a where -- @('Fractional' a) => a@. fromRational :: Rational -> a + {-# INLINE recip #-} + {-# INLINE (/) #-} recip x = 1 / x x / y = x * recip y @@ -173,25 +181,28 @@ class (Real a, Fractional a) => RealFrac a where 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} @@ -201,20 +212,21 @@ These 'numeric' enumerations come straight from the Report \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} @@ -233,32 +245,38 @@ instance Integral Int where a `quot` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `quotInt` b a `rem` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `remInt` b a `div` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `divInt` b a `mod` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `modInt` b a `quotRem` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `quotRemInt` b a `divMod` b | b == 0 = divZeroError - | a == minBound && b == (-1) = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `divModInt` b \end{code} @@ -276,17 +294,17 @@ instance Real Integer where 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) @@ -316,11 +334,15 @@ instance (Integral a) => Num (Ratio a) where signum (x:%_) = signum x :% 1 fromInteger x = fromInteger x :% 1 +{-# RULES "fromRational/id" fromRational = id :: Rational -> Rational #-} instance (Integral a) => Fractional (Ratio a) where {-# SPECIALIZE instance Fractional Rational #-} (x:%y) / (x':%y') = (x*y') % (y*x') - recip (x:%y) = y % x - fromRational (x:%y) = fromInteger x :% fromInteger y + 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 {-# SPECIALIZE instance Real Rational #-} @@ -334,9 +356,12 @@ instance (Integral a) => RealFrac (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 @@ -391,7 +416,7 @@ showSigned :: (Real a) -> 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 @@ -405,21 +430,94 @@ odd = not . even Integer -> Integer -> Integer, Integer -> Int -> Integer, Int -> Int -> Int #-} +{-# INLINABLE (^) #-} -- See Note [Inlining (^)] (^) :: (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 (^^) :: - Rational -> Int -> Rational #-} (^^) :: (Fractional a, Integral b) => a -> b -> a +{-# INLINABLE (^^) #-} -- See Note [Inlining (^) x ^^ n = if n >= 0 then x^n else recip (x^(negate n)) +{- Note [Inlining (^) + ~~~~~~~~~~~~~~~~~~~~~ + The INLINABLE pragma allows (^) to be specialised at its call sites. + If it is called repeatedly at the same type, that can make a huge + difference, because of those constants which can be repeatedly + calculated. + + Currently the fromInteger calls are not floated because we get + \d1 d2 x y -> blah + after the gentle round of simplification. -} + +------------------------------------------------------- +-- Special power functions for Rational +-- +-- see #4337 +-- +-- Rationale: +-- For a legitimate Rational (n :% d), the numerator and denominator are +-- coprime, i.e. they have no common prime factor. +-- Therefore all powers (n ^ a) and (d ^ b) are also coprime, so it is +-- not necessary to compute the greatest common divisor, which would be +-- done in the default implementation at each multiplication step. +-- Since exponentiation quickly leads to very large numbers and +-- calculation of gcds is generally very slow for large numbers, +-- avoiding the gcd leads to an order of magnitude speedup relatively +-- soon (and an asymptotic improvement overall). +-- +-- Note: +-- We cannot use these functions for general Ratio a because that would +-- change results in a multitude of cases. +-- The cause is that if a and b are coprime, their remainders by any +-- positive modulus generally aren't, so in the default implementation +-- reduction occurs. +-- +-- Example: +-- (17 % 3) ^ 3 :: Ratio Word8 +-- Default: +-- (17 % 3) ^ 3 = ((17 % 3) ^ 2) * (17 % 3) +-- = ((289 `mod` 256) % 9) * (17 % 3) +-- = (33 % 9) * (17 % 3) +-- = (11 % 3) * (17 % 3) +-- = (187 % 9) +-- But: +-- ((17^3) `mod` 256) % (3^3) = (4913 `mod` 256) % 27 +-- = 49 % 27 +-- +-- TODO: +-- Find out whether special-casing for numerator, denominator or +-- exponent = 1 (or -1, where that may apply) gains something. + +-- Special version of (^) for Rational base +{-# RULES "(^)/Rational" (^) = (^%^) #-} +(^%^) :: Integral a => Rational -> a -> Rational +(n :% d) ^%^ e + | e < 0 = error "Negative exponent" + | e == 0 = 1 :% 1 + | otherwise = (n ^ e) :% (d ^ e) + +-- Special version of (^^) for Rational base +{-# RULES "(^^)/Rational" (^^) = (^^%^^) #-} +(^^%^^) :: Integral a => Rational -> a -> Rational +(n :% d) ^^%^^ e + | e > 0 = (n ^ e) :% (d ^ e) + | e == 0 = 1 :% 1 + | n > 0 = (d ^ (negate e)) :% (n ^ (negate e)) + | n == 0 = error "Ratio.%: zero denominator" + | otherwise = let nn = d ^ (negate e) + dd = (negate n) ^ (negate e) + in if even e then (nn :% dd) else (negate nn :% dd) ------------------------------------------------------- -- | @'gcd' x y@ is the greatest (positive) integer that divides both @x@ @@ -438,6 +536,7 @@ lcm _ 0 = 0 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' @@ -448,6 +547,11 @@ 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)]