Data/Floating/Classes.hs

   1 {-
   2  - Copyright (C) 2009 Nick Bowler.
   3  -
   4  - License BSD2:  2-clause BSD license.  See LICENSE for full terms.
   5  - This is free software: you are free to change and redistribute it.
   6  - There is NO WARRANTY, to the extent permitted by law.
   7  -}
   8
   9 -- | Generic classes for floating point types.  The interface is loosely based
  10 -- off of the C math library.
  11 module Data.Floating.Classes where
  12
  13 import Prelude hiding (Floating(..), RealFloat(..), RealFrac(..), Ord(..))
  14 import Data.Ratio
  15 import Data.Poset
  16
  17 -- | Classification of floating point values.
  18 data FPClassification = FPInfinite | FPNaN | FPNormal | FPSubNormal | FPZero
  19     deriving (Show, Read, Eq, Enum, Bounded)
  20
  21 -- | Class for types which can be rounded to integers.
  22 --
  23 -- Minimal complete definition: 'toIntegral' and 'round'.
  24 class (Fractional a, Poset a) => Roundable a where
  25     -- | Discards the fractional component from a value.  Results in 'Nothing'
  26     -- if the result cannot be represented as an integer, such as if the input
  27     -- is infinite or NaN.
  28     toIntegral :: Integral b => a -> Maybe b
  29     ceiling    :: a -> a
  30     floor      :: a -> a
  31     truncate   :: a -> a
  32     round      :: a -> a
  33
  34     floor x
  35         | round x == x = x
  36         | otherwise = round $ x - fromRational (1%2)
  37     ceiling x
  38         | round x == x = x
  39         | otherwise = round $ x + fromRational (1%2)
  40     truncate x
  41         | x < 0 = ceiling x
  42         | x > 0 = floor x
  43         | otherwise = x
  44
  45 -- | Class for floating point types (real or complex-valued).
  46 --
  47 -- Minimal complete definition: everything.
  48 class Fractional a => Floating a where
  49     (**)  :: a -> a -> a
  50     sqrt  :: a -> a
  51     acos  :: a -> a
  52     asin  :: a -> a
  53     atan  :: a -> a
  54     cos   :: a -> a
  55     sin   :: a -> a
  56     tan   :: a -> a
  57     acosh :: a -> a
  58     asinh :: a -> a
  59     atanh :: a -> a
  60     cosh  :: a -> a
  61     sinh  :: a -> a
  62     tanh  :: a -> a
  63     exp   :: a -> a
  64     log   :: a -> a
  65
  66 -- | Class for real-valued floating point types.
  67 --
  68 -- Minimal complete definition: all except 'pi', 'infinity' and 'nan'.
  69 class Floating a => RealFloat a where
  70     fma       :: a -> a -> a -> a
  71     copysign  :: a -> a -> a
  72     nextafter :: a -> a -> a
  73     atan2     :: a -> a -> a
  74     fmod      :: a -> a -> a
  75     frem      :: a -> a -> a
  76     fquotRem  :: a -> a -> (Int, a)
  77     hypot     :: a -> a -> a
  78     cbrt      :: a -> a
  79     exp2      :: a -> a
  80     expm1     :: a -> a
  81     log10     :: a -> a
  82     log1p     :: a -> a
  83     log2      :: a -> a
  84     logb      :: a -> a
  85     erf       :: a -> a
  86     erfc      :: a -> a
  87     lgamma    :: a -> a
  88     tgamma    :: a -> a
  89     classify  :: a -> FPClassification
  90     infinity  :: a
  91     nan       :: a
  92     pi        :: a
  93
  94     infinity = 1/0
  95     nan      = 0/0
  96     pi       = 4 * atan 1