X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=GHC%2FFloat.lhs;h=41ea69a8b9c9e9c1e75781c73210de9c009ea5a4;hb=e689c74ff37943db15ce9886f6361387a8f80e5f;hp=5c68de44149fba9f2f01051eb50240f6dcd65258;hpb=45afba05c6d0fca1e1b2d101c097a7738bb73b25;p=ghc-base.git diff --git a/GHC/Float.lhs b/GHC/Float.lhs index 5c68de4..41ea69a 100644 --- a/GHC/Float.lhs +++ b/GHC/Float.lhs @@ -38,6 +38,11 @@ infixr 8 ** %********************************************************* \begin{code} +-- | Trigonometric and hyperbolic functions and related functions. +-- +-- Minimal complete definition: +-- 'pi', 'exp', 'log', 'sin', 'cos', 'sinh', 'cosh' +-- 'asin', 'acos', 'atan', 'asinh', 'acosh' and 'atanh' class (Fractional a) => Floating a where pi :: a exp, log, sqrt :: a -> a @@ -53,17 +58,58 @@ class (Fractional a) => Floating a where tan x = sin x / cos x tanh x = sinh x / cosh x +-- | Efficient, machine-independent access to the components of a +-- floating-point number. +-- +-- Minimal complete definition: +-- all except 'exponent', 'significand', 'scaleFloat' and 'atan2' class (RealFrac a, Floating a) => RealFloat a where + -- | a constant function, returning the radix of the representation + -- (often @2@) floatRadix :: a -> Integer + -- | a constant function, returning the number of digits of + -- 'floatRadix' in the significand floatDigits :: a -> Int + -- | a constant function, returning the lowest and highest values + -- the exponent may assume floatRange :: a -> (Int,Int) + -- | The function 'decodeFloat' applied to a real floating-point + -- number returns the significand expressed as an 'Integer' and an + -- appropriately scaled exponent (an 'Int'). If @'decodeFloat' x@ + -- yields @(m,n)@, then @x@ is equal in value to @m*b^^n@, where @b@ + -- is the floating-point radix, and furthermore, either @m@ and @n@ + -- are both zero or else @b^(d-1) <= m < b^d@, where @d@ is the value + -- of @'floatDigits' x@. In particular, @'decodeFloat' 0 = (0,0)@. decodeFloat :: a -> (Integer,Int) + -- | 'encodeFloat' performs the inverse of 'decodeFloat' encodeFloat :: Integer -> Int -> a + -- | the second component of 'decodeFloat'. exponent :: a -> Int + -- | the first component of 'decodeFloat', scaled to lie in the open + -- interval (@-1@,@1@) significand :: a -> a + -- | multiplies a floating-point number by an integer power of the radix scaleFloat :: Int -> a -> a - isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE - :: a -> Bool + -- | 'True' if the argument is an IEEE \"not-a-number\" (NaN) value + isNaN :: a -> Bool + -- | 'True' if the argument is an IEEE infinity or negative infinity + isInfinite :: a -> Bool + -- | 'True' if the argument is too small to be represented in + -- normalized format + isDenormalized :: a -> Bool + -- | 'True' if the argument is an IEEE negative zero + isNegativeZero :: a -> Bool + -- | 'True' if the argument is an IEEE floating point number + isIEEE :: a -> Bool + -- | a version of arctangent taking two real floating-point arguments. + -- For real floating @x@ and @y@, @'atan2' y x@ computes the angle + -- (from the positive x-axis) of the vector from the origin to the + -- point @(x,y)@. @'atan2' y x@ returns a value in the range [@-pi@, + -- @pi@]. It follows the Common Lisp semantics for the origin when + -- signed zeroes are supported. @'atan2' y 1@, with @y@ in a type + -- that is 'RealFloat', should return the same value as @'atan' y@. + -- A default definition of 'atan2' is provided, but implementors + -- can provide a more accurate implementation. atan2 :: a -> a -> a @@ -98,14 +144,15 @@ class (RealFrac a, Floating a) => RealFloat a where %********************************************************* \begin{code} +-- | Single-precision floating point numbers. +-- It is desirable that this type be at least equal in range and precision +-- to the IEEE single-precision type. data Float = F# Float# -data Double = D# Double# -instance CCallable Float -instance CReturnable Float - -instance CCallable Double -instance CReturnable Double +-- | Double-precision floating point numbers. +-- It is desirable that this type be at least equal in range and precision +-- to the IEEE double-precision type. +data Double = D# Double# \end{code} @@ -161,14 +208,14 @@ instance RealFrac Float where {-# SPECIALIZE properFraction :: Float -> (Int, Float) #-} {-# SPECIALIZE round :: Float -> Int #-} - {-# SPECIALIZE ceiling :: Float -> Int #-} - {-# SPECIALIZE floor :: Float -> Int #-} - {-# SPECIALIZE properFraction :: Float -> (Integer, Float) #-} - {-# SPECIALIZE truncate :: Float -> Integer #-} + {-# SPECIALIZE properFraction :: Float -> (Integer, Float) #-} {-# SPECIALIZE round :: Float -> Integer #-} - {-# SPECIALIZE ceiling :: Float -> Integer #-} - {-# SPECIALIZE floor :: Float -> Integer #-} + + -- ceiling, floor, and truncate are all small + {-# INLINE ceiling #-} + {-# INLINE floor #-} + {-# INLINE truncate #-} properFraction x = case (decodeFloat x) of { (m,n) -> @@ -325,14 +372,14 @@ instance RealFrac Double where {-# SPECIALIZE properFraction :: Double -> (Int, Double) #-} {-# SPECIALIZE round :: Double -> Int #-} - {-# SPECIALIZE ceiling :: Double -> Int #-} - {-# SPECIALIZE floor :: Double -> Int #-} {-# SPECIALIZE properFraction :: Double -> (Integer, Double) #-} - {-# SPECIALIZE truncate :: Double -> Integer #-} {-# SPECIALIZE round :: Double -> Integer #-} - {-# SPECIALIZE ceiling :: Double -> Integer #-} - {-# SPECIALIZE floor :: Double -> Integer #-} + + -- ceiling, floor, and truncate are all small + {-# INLINE ceiling #-} + {-# INLINE floor #-} + {-# INLINE truncate #-} properFraction x = case (decodeFloat x) of { (m,n) -> @@ -446,6 +493,9 @@ instance Enum Double where \begin{code} +-- | Show a signed 'RealFloat' value to full precision +-- 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) @@ -537,14 +587,19 @@ roundTo base d is = -- by R.G. Burger and R.K. Dybvig in PLDI 96. -- This version uses a much slower logarithm estimator. It should be improved. --- floatToDigits takes a base and a non-negative RealFloat number, +-- | 'floatToDigits' takes a base and a non-negative 'RealFloat' number, -- and returns a list of digits and an exponent. --- In particular, if x>=0, and --- floatToDigits base x = ([d1,d2,...,dn], e) +-- In particular, if @x>=0@, and +-- +-- > floatToDigits base x = ([d1,d2,...,dn], e) +-- -- then --- (a) n >= 1 --- (b) x = 0.d1d2...dn * (base**e) --- (c) 0 <= di <= base-1 +-- +-- (1) @n >= 1@ +-- +-- (2) @x = 0.d1d2...dn * (base**e)@ +-- +-- (3) @0 <= di <= base-1@ floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int) floatToDigits _ 0 = ([0], 0) @@ -675,6 +730,7 @@ fromRat x = x' Now, here's Lennart's code (which works) \begin{code} +-- | Converts a 'Rational' value into any type in class 'RealFloat'. {-# SPECIALISE fromRat :: Rational -> Double, Rational -> Float #-} fromRat :: (RealFloat a) => Rational -> a