X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=GHC%2FFloat.lhs;h=02aba8ca85f3fea261f8e8d3f22fa7f7787b37c0;hb=41e8fba828acbae1751628af50849f5352b27873;hp=1ca9638a336a74b2ac5ad9580ce0cd80ee2d6b30;hpb=80b3ca0899c2ae75f78c0060ece461538fd70017;p=ghc-base.git diff --git a/GHC/Float.lhs b/GHC/Float.lhs index 1ca9638..02aba8c 100644 --- a/GHC/Float.lhs +++ b/GHC/Float.lhs @@ -1,12 +1,21 @@ \begin{code} -{-# OPTIONS_GHC -XNoImplicitPrelude #-} +{-# LANGUAGE CPP + , NoImplicitPrelude + , MagicHash + , UnboxedTuples + , ForeignFunctionInterface + #-} +-- We believe we could deorphan this module, by moving lots of things +-- around, but we haven't got there yet: +{-# OPTIONS_GHC -fno-warn-orphans #-} {-# OPTIONS_HADDOCK hide #-} + ----------------------------------------------------------------------------- -- | -- Module : GHC.Float -- 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) @@ -23,6 +32,7 @@ module GHC.Float( module GHC.Float, Float(..), Double(..), Float#, Double# ) import Data.Maybe +import Data.Bits import GHC.Base import GHC.List import GHC.Enum @@ -55,6 +65,11 @@ class (Fractional a) => Floating a where sinh, cosh, tanh :: a -> a asinh, acosh, atanh :: a -> a + {-# INLINE (**) #-} + {-# INLINE logBase #-} + {-# INLINE sqrt #-} + {-# INLINE tan #-} + {-# INLINE tanh #-} x ** y = exp (log x * y) logBase x y = log y / log x sqrt x = x ** 0.5 @@ -122,13 +137,24 @@ class (RealFrac a, Floating a) => RealFloat a where significand x = encodeFloat m (negate (floatDigits x)) where (m,_) = decodeFloat x - scaleFloat k x = encodeFloat m (n+k) + scaleFloat k x = encodeFloat m (n + clamp b k) where (m,n) = decodeFloat x - + (l,h) = floatRange x + d = floatDigits x + b = h - l + 4*d + -- n+k may overflow, which would lead + -- to wrong results, hence we clamp the + -- scaling parameter. + -- If n + k would be larger than h, + -- n + clamp b k must be too, simliar + -- for smaller than l - d. + -- Add a little extra to keep clear + -- from the boundary cases. + atan2 y x | x > 0 = atan (y/x) | x == 0 && y > 0 = pi/2 - | x < 0 && y > 0 = pi + atan (y/x) + | x < 0 && y > 0 = pi + atan (y/x) |(x <= 0 && y < 0) || (x < 0 && isNegativeZero y) || (isNegativeZero x && isNegativeZero y) @@ -147,19 +173,6 @@ class (RealFrac a, Floating a) => RealFloat a where %********************************************************* \begin{code} -instance Eq Float where - (F# x) == (F# y) = x `eqFloat#` y - -instance Ord Float where - (F# x) `compare` (F# y) | x `ltFloat#` y = LT - | x `eqFloat#` y = EQ - | otherwise = GT - - (F# x) < (F# y) = x `ltFloat#` y - (F# x) <= (F# y) = x `leFloat#` y - (F# x) >= (F# y) = x `geFloat#` y - (F# x) > (F# y) = x `gtFloat#` y - instance Num Float where (+) x y = plusFloat x y (-) x y = minusFloat x y @@ -198,16 +211,22 @@ instance RealFrac Float where {-# INLINE floor #-} {-# INLINE truncate #-} - properFraction x - = case (decodeFloat x) of { (m,n) -> - let b = floatRadix x in - if n >= 0 then - (fromInteger m * fromInteger b ^ n, 0.0) - else - case (quotRem m (b^(negate n))) of { (w,r) -> - (fromInteger w, encodeFloat r n) - } - } +-- We assume that FLT_RADIX is 2 so that we can use more efficient code +#if FLT_RADIX != 2 +#error FLT_RADIX must be 2 +#endif + properFraction (F# x#) + = case decodeFloat_Int# x# of + (# m#, n# #) -> + let m = I# m# + n = I# n# + in + if n >= 0 + then (fromIntegral m * (2 ^ n), 0.0) + else let i = if m >= 0 then m `shiftR` negate n + else negate (negate m `shiftR` negate n) + f = m - (i `shiftL` negate n) + in (fromIntegral i, encodeFloat (fromIntegral f) n) truncate x = case properFraction x of (n,_) -> n @@ -247,15 +266,15 @@ instance Floating Float where asinh x = log (x + sqrt (1.0+x*x)) acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0))) - atanh x = log ((x+1.0) / sqrt (1.0-x*x)) + atanh x = 0.5 * log ((1.0+x) / (1.0-x)) instance RealFloat Float where floatRadix _ = FLT_RADIX -- from float.h floatDigits _ = FLT_MANT_DIG -- ditto floatRange _ = (FLT_MIN_EXP, FLT_MAX_EXP) -- ditto - decodeFloat (F# f#) = case decodeFloatInteger f# of - (# i, e #) -> (i, I# e) + decodeFloat (F# f#) = case decodeFloat_Int# f# of + (# i, e #) -> (smallInteger i, I# e) encodeFloat i (I# e) = F# (encodeFloatInteger i e) @@ -266,7 +285,9 @@ instance RealFloat Float where (m,_) -> encodeFloat m (negate (floatDigits x)) scaleFloat k x = case decodeFloat x of - (m,n) -> encodeFloat m (n+k) + (m,n) -> encodeFloat m (n + clamp bf k) + where bf = FLT_MAX_EXP - (FLT_MIN_EXP) + 4*FLT_MANT_DIG + isNaN x = 0 /= isFloatNaN x isInfinite x = 0 /= isFloatInfinite x isDenormalized x = 0 /= isFloatDenormalized x @@ -275,7 +296,7 @@ instance RealFloat Float where instance Show Float where showsPrec x = showSignedFloat showFloat x - showList = showList__ (showsPrec 0) + showList = showList__ (showsPrec 0) \end{code} %********************************************************* @@ -285,19 +306,6 @@ instance Show Float where %********************************************************* \begin{code} -instance Eq Double where - (D# x) == (D# y) = x ==## y - -instance Ord Double where - (D# x) `compare` (D# y) | x <## y = LT - | x ==## y = EQ - | otherwise = GT - - (D# x) < (D# y) = x <## y - (D# x) <= (D# y) = x <=## y - (D# x) >= (D# y) = x >=## y - (D# x) > (D# y) = x >## y - instance Num Double where (+) x y = plusDouble x y (-) x y = minusDouble x y @@ -342,7 +350,7 @@ instance Floating Double where asinh x = log (x + sqrt (1.0+x*x)) acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0))) - atanh x = log ((x+1.0) / sqrt (1.0-x*x)) + atanh x = 0.5 * log ((1.0+x) / (1.0-x)) {-# RULES "truncate/Double->Int" truncate = double2Int #-} instance RealFrac Double where @@ -406,7 +414,8 @@ instance RealFloat Double where (m,_) -> encodeFloat m (negate (floatDigits x)) scaleFloat k x = case decodeFloat x of - (m,n) -> encodeFloat m (n+k) + (m,n) -> encodeFloat m (n + clamp bd k) + where bd = DBL_MAX_EXP - (DBL_MIN_EXP) + 4*DBL_MANT_DIG isNaN x = 0 /= isDoubleNaN x isInfinite x = 0 /= isDoubleInfinite x @@ -416,7 +425,7 @@ instance RealFloat Double where instance Show Double where showsPrec x = showSignedFloat showFloat x - showList = showList__ (showsPrec 0) + showList = showList__ (showsPrec 0) \end{code} %********************************************************* @@ -434,7 +443,7 @@ how 0.1 is represented. NOTE: The instances for Float and Double do not make use of the default methods for @enumFromTo@ and @enumFromThenTo@, as these rely on there being -a `non-lossy' conversion to and from Ints. Instead we make use of the +a `non-lossy' conversion to and from Ints. Instead we make use of the 1.2 default methods (back in the days when Enum had Ord as a superclass) for these (@numericEnumFromTo@ and @numericEnumFromThenTo@ below.) @@ -470,7 +479,7 @@ instance Enum Double where \begin{code} -- | Show a signed 'RealFloat' value to full precision --- using standard decimal notation for arguments whose absolute value lies +-- using standard decimal notation for arguments whose absolute value lies -- between @0.1@ and @9,999,999@, and scientific notation otherwise. showFloat :: (RealFloat a) => a -> ShowS showFloat x = showString (formatRealFloat FFGeneric Nothing x) @@ -485,7 +494,7 @@ formatRealFloat fmt decs x | isInfinite x = if x < 0 then "-Infinity" else "Infinity" | x < 0 || isNegativeZero x = '-':doFmt fmt (floatToDigits (toInteger base) (-x)) | otherwise = doFmt fmt (floatToDigits (toInteger base) x) - where + where base = 10 doFmt format (is, e) = @@ -566,7 +575,7 @@ roundTo base d is = -- This version uses a much slower logarithm estimator. It should be improved. -- | 'floatToDigits' takes a base and a non-negative 'RealFloat' number, --- and returns a list of digits and an exponent. +-- and returns a list of digits and an exponent. -- In particular, if @x>=0@, and -- -- > floatToDigits base x = ([d1,d2,...,dn], e) @@ -582,7 +591,7 @@ roundTo base d is = floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int) floatToDigits _ 0 = ([0], 0) floatToDigits base x = - let + let (f0, e0) = decodeFloat x (minExp0, _) = floatRange x p = floatDigits x @@ -590,34 +599,52 @@ floatToDigits base x = minExp = minExp0 - p -- the real minimum exponent -- Haskell requires that f be adjusted so denormalized numbers -- will have an impossibly low exponent. Adjust for this. - (f, e) = + (f, e) = let n = minExp - e0 in - if n > 0 then (f0 `div` (b^n), e0+n) else (f0, e0) + if n > 0 then (f0 `quot` (expt b n), e0+n) else (f0, e0) (r, s, mUp, mDn) = if e >= 0 then - let be = b^ e in - if f == b^(p-1) then - (f*be*b*2, 2*b, be*b, b) + let be = expt b e in + if f == expt b (p-1) then + (f*be*b*2, 2*b, be*b, be) -- according to Burger and Dybvig else (f*be*2, 2, be, be) else - if e > minExp && f == b^(p-1) then - (f*b*2, b^(-e+1)*2, b, 1) + if e > minExp && f == expt b (p-1) then + (f*b*2, expt b (-e+1)*2, b, 1) else - (f*2, b^(-e)*2, 1, 1) + (f*2, expt b (-e)*2, 1, 1) k :: Int k = - let + let k0 :: Int k0 = if b == 2 && base == 10 then - -- logBase 10 2 is slightly bigger than 3/10 so - -- the following will err on the low side. Ignoring - -- the fraction will make it err even more. - -- Haskell promises that p-1 <= logBase b f < p. - (p - 1 + e0) * 3 `div` 10 + -- logBase 10 2 is very slightly larger than 8651/28738 + -- (about 5.3558e-10), so if log x >= 0, the approximation + -- k1 is too small, hence we add one and need one fixup step less. + -- If log x < 0, the approximation errs rather on the high side. + -- That is usually more than compensated for by ignoring the + -- fractional part of logBase 2 x, but when x is a power of 1/2 + -- or slightly larger and the exponent is a multiple of the + -- denominator of the rational approximation to logBase 10 2, + -- k1 is larger than logBase 10 x. If k1 > 1 + logBase 10 x, + -- we get a leading zero-digit we don't want. + -- With the approximation 3/10, this happened for + -- 0.5^1030, 0.5^1040, ..., 0.5^1070 and values close above. + -- The approximation 8651/28738 guarantees k1 < 1 + logBase 10 x + -- for IEEE-ish floating point types with exponent fields + -- <= 17 bits and mantissae of several thousand bits, earlier + -- convergents to logBase 10 2 would fail for long double. + -- Using quot instead of div is a little faster and requires + -- fewer fixup steps for negative lx. + let lx = p - 1 + e0 + k1 = (lx * 8651) `quot` 28738 + in if lx >= 0 then k1 + 1 else k1 else - ceiling ((log (fromInteger (f+1)) + + -- f :: Integer, log :: Float -> Float, + -- ceiling :: Float -> Int + ceiling ((log (fromInteger (f+1) :: Float) + fromIntegral e * log (fromInteger b)) / log (fromInteger base)) --WAS: fromInt e * log (fromInteger b)) @@ -632,7 +659,7 @@ floatToDigits base x = gen ds rn sN mUpN mDnN = let - (dn, rn') = (rn * base) `divMod` sN + (dn, rn') = (rn * base) `quotRem` sN mUpN' = mUpN * base mDnN' = mDnN * base in @@ -641,8 +668,8 @@ floatToDigits base x = (False, True) -> dn+1 : ds (True, True) -> if rn' * 2 < sN then dn : ds else dn+1 : ds (False, False) -> gen (dn:ds) rn' sN mUpN' mDnN' - - rds = + + rds = if k >= 0 then gen [] r (s * expt base k) mUp mDn else @@ -685,7 +712,7 @@ fromRat :: (RealFloat a) => Rational -> a fromRat x = x' where x' = f e --- If the exponent of the nearest floating-point number to x +-- If the exponent of the nearest floating-point number to x -- is e, then the significand is the integer nearest xb^(-e), -- where b is the floating-point radix. We start with a good -- guess for e, and if it is correct, the exponent of the @@ -748,7 +775,7 @@ fromRat' x = r -- Scale x until xMin <= x < xMax, or p (the exponent) <= minExp. scaleRat :: Rational -> Int -> Rational -> Rational -> Int -> Rational -> (Rational, Int) -scaleRat b minExp xMin xMax p x +scaleRat b minExp xMin xMax p x | p <= minExp = (x, p) | x >= xMax = scaleRat b minExp xMin xMax (p+1) (x/b) | x < xMin = scaleRat b minExp xMin xMax (p-1) (x*b) @@ -764,11 +791,20 @@ expt base n = if base == 2 && n >= minExpt && n <= maxExpt then expts!n else - base^n + if base == 10 && n <= maxExpt10 then + expts10!n + else + base^n expts :: Array Int Integer expts = array (minExpt,maxExpt) [(n,2^n) | n <- [minExpt .. maxExpt]] +maxExpt10 :: Int +maxExpt10 = 324 + +expts10 :: Array Int Integer +expts10 = array (minExpt,maxExpt10) [(n,10^n) | n <- [minExpt .. maxExpt10]] + -- Compute the (floor of the) log of i in base b. -- Simplest way would be just divide i by b until it's smaller then b, but that would -- be very slow! We are just slightly more clever. @@ -895,21 +931,12 @@ powerDouble (D# x) (D# y) = D# (x **## y) \end{code} \begin{code} -foreign import ccall unsafe "__encodeFloat" - encodeFloat# :: Int# -> ByteArray# -> Int -> Float -foreign import ccall unsafe "__int_encodeFloat" - int_encodeFloat# :: Int# -> Int -> Float - - foreign import ccall unsafe "isFloatNaN" isFloatNaN :: Float -> Int foreign import ccall unsafe "isFloatInfinite" isFloatInfinite :: Float -> Int foreign import ccall unsafe "isFloatDenormalized" isFloatDenormalized :: Float -> Int foreign import ccall unsafe "isFloatNegativeZero" isFloatNegativeZero :: Float -> Int -foreign import ccall unsafe "__encodeDouble" - encodeDouble# :: Int# -> ByteArray# -> Int -> Double - foreign import ccall unsafe "isDoubleNaN" isDoubleNaN :: Double -> Int foreign import ccall unsafe "isDoubleInfinite" isDoubleInfinite :: Double -> Int foreign import ccall unsafe "isDoubleDenormalized" isDoubleDenormalized :: Double -> Int @@ -940,36 +967,36 @@ Note [realToFrac int-to-float] Don found that the RULES for realToFrac/Int->Double and simliarly Float made a huge difference to some stream-fusion programs. Here's an example - + import Data.Array.Vector - + n = 40000000 - + main = do let c = replicateU n (2::Double) a = mapU realToFrac (enumFromToU 0 (n-1) ) :: UArr Double print (sumU (zipWithU (*) c a)) - + Without the RULE we get this loop body: - + case $wtoRational sc_sY4 of ww_aM7 { (# ww1_aM9, ww2_aMa #) -> case $wfromRat ww1_aM9 ww2_aMa of tpl_X1P { D# ipv_sW3 -> Main.$s$wfold (+# sc_sY4 1) (+# wild_X1i 1) (+## sc2_sY6 (*## 2.0 ipv_sW3)) - + And with the rule: - + Main.$s$wfold (+# sc_sXT 1) (+# wild_X1h 1) (+## sc2_sXV (*## 2.0 (int2Double# sc_sXT))) - + The running time of the program goes from 120 seconds to 0.198 seconds with the native backend, and 0.143 seconds with the C backend. - -A few more details in Trac #2251, and the patch message + +A few more details in Trac #2251, and the patch message "Add RULES for realToFrac from Int". %********************************************************* @@ -989,3 +1016,12 @@ showSignedFloat showPos p x = showParen (p > 6) (showChar '-' . showPos (-x)) | otherwise = showPos x \end{code} + +We need to prevent over/underflow of the exponent in encodeFloat when +called from scaleFloat, hence we clamp the scaling parameter. +We must have a large enough range to cover the maximum difference of +exponents returned by decodeFloat. +\begin{code} +clamp :: Int -> Int -> Int +clamp bd k = max (-bd) (min bd k) +\end{code}