\begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
+{-# OPTIONS_GHC -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.Float
%*********************************************************
\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
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
\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#
-- | 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}
\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)
-- 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
+-- In particular, if @x>=0@, and
--
--- @
--- floatToDigits base x = ([d1,d2,...,dn], e)
--- @
+-- > floatToDigits base x = ([d1,d2,...,dn], e)
--
-- then
--
--- (1) n >= 1
+-- (1) @n >= 1@
--
--- (2) x = 0.d1d2...dn * (base**e)
+-- (2) @x = 0.d1d2...dn * (base**e)@
--
--- (3) 0 <= di <= base-1
+-- (3) @0 <= di <= base-1@
floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int)
floatToDigits _ 0 = ([0], 0)
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
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