Data/Floating/CMath/Instances.hs

   1 {-
   2  - Copyright (C) 2010 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 -- | Class instances for 'CFloat' and 'CDouble'.  As it is elsewhere in the
  10 -- library, it is assumed that 'CFloat' is identical to 'Float' and 'CDouble'
  11 -- is identical to 'Double'.
  12 module Data.Floating.CMath.Instances where
  13
  14 import Prelude (($), (.), const, undefined)
  15 import Data.Floating.Classes
  16 import Data.Floating.Types
  17 import Data.Floating.Types.Double
  18 import Data.Floating.Types.Float
  19 import Foreign.C
  20
  21 import Data.Poset
  22
  23 doubleLibm :: (Double -> Double) -> CDouble -> CDouble
  24 doubleLibm f a = toFloating $ f (toFloating a)
  25
  26 floatLibm :: (Float -> Float) -> CFloat -> CFloat
  27 floatLibm f a = toFloating $ f (toFloating a)
  28
  29 doubleLibm2 :: (Double -> Double -> Double) -> CDouble -> CDouble -> CDouble
  30 doubleLibm2 f a b = toFloating $ f (toFloating a) (toFloating b)
  31
  32 floatLibm2 :: (Float -> Float -> Float) -> CFloat -> CFloat -> CFloat
  33 floatLibm2 f a b = toFloating $ f (toFloating a) (toFloating b)
  34
  35 doubleLibm3 :: (Double -> Double -> Double -> Double)
  36     -> CDouble -> CDouble -> CDouble -> CDouble
  37 doubleLibm3 f a b c = toFloating
  38     $ f (toFloating a) (toFloating b) (toFloating c)
  39
  40 floatLibm3 :: (Float -> Float -> Float -> Float)
  41     -> CFloat -> CFloat -> CFloat -> CFloat
  42 floatLibm3 f a b c = toFloating
  43     $ f (toFloating a) (toFloating b) (toFloating c)
  44
  45 instance Floating CDouble where
  46     (**)  = doubleLibm2 (**)
  47     sqrt  = doubleLibm sqrt
  48     acos  = doubleLibm acos
  49     asin  = doubleLibm asin
  50     atan  = doubleLibm atan
  51     cos   = doubleLibm cos
  52     sin   = doubleLibm sin
  53     tan   = doubleLibm tan
  54     acosh = doubleLibm acosh
  55     asinh = doubleLibm asinh
  56     atanh = doubleLibm atanh
  57     cosh  = doubleLibm cosh
  58     sinh  = doubleLibm sinh
  59     tanh  = doubleLibm tanh
  60     exp   = doubleLibm exp
  61     log   = doubleLibm log
  62
  63 instance Floating CFloat where
  64     (**)  = floatLibm2 (**)
  65     sqrt  = floatLibm sqrt
  66     acos  = floatLibm acos
  67     asin  = floatLibm asin
  68     atan  = floatLibm atan
  69     cos   = floatLibm cos
  70     sin   = floatLibm sin
  71     tan   = floatLibm tan
  72     acosh = floatLibm acosh
  73     asinh = floatLibm asinh
  74     atanh = floatLibm atanh
  75     cosh  = floatLibm cosh
  76     sinh  = floatLibm sinh
  77     tanh  = floatLibm tanh
  78     exp   = floatLibm exp
  79     log   = floatLibm log
  80
  81 instance RealFloat CDouble where
  82     fma       = doubleLibm3 fma
  83     copysign  = doubleLibm2 copysign
  84     nextafter = doubleLibm2 nextafter
  85     atan2     = doubleLibm2 atan2
  86     fmod      = doubleLibm2 fmod
  87     frem      = doubleLibm2 frem
  88     hypot     = doubleLibm2 hypot
  89     cbrt      = doubleLibm cbrt
  90     exp2      = doubleLibm exp2
  91     expm1     = doubleLibm expm1
  92     log10     = doubleLibm log10
  93     log1p     = doubleLibm log1p
  94     log2      = doubleLibm log2
  95     erf       = doubleLibm erf
  96     erfc      = doubleLibm erfc
  97     gamma     = doubleLibm gamma
  98     lgamma    = doubleLibm lgamma
  99     rint      = doubleLibm rint
 100     nearbyint = doubleLibm nearbyint
 101
 102 instance RealFloat CFloat where
 103     fma       = floatLibm3 fma
 104     copysign  = floatLibm2 copysign
 105     nextafter = floatLibm2 nextafter
 106     atan2     = floatLibm2 atan2
 107     fmod      = floatLibm2 fmod
 108     frem      = floatLibm2 frem
 109     hypot     = floatLibm2 hypot
 110     cbrt      = floatLibm cbrt
 111     exp2      = floatLibm exp2
 112     expm1     = floatLibm expm1
 113     log10     = floatLibm log10
 114     log1p     = floatLibm log1p
 115     log2      = floatLibm log2
 116     erf       = floatLibm erf
 117     erfc      = floatLibm erfc
 118     gamma     = floatLibm gamma
 119     lgamma    = floatLibm lgamma
 120     rint      = floatLibm rint
 121     nearbyint = floatLibm nearbyint
 122
 123 instance Poset CDouble where
 124     compare x y = compare (toFloating x :: Double) (toFloating y :: Double)
 125     x <==> y    = (toFloating x :: Double) <==> (toFloating y :: Double)
 126     x </=> y    = (toFloating x :: Double) </=> (toFloating y :: Double)
 127     x  <   y    = (toFloating x :: Double)  <   (toFloating y :: Double)
 128     x  <=  y    = (toFloating x :: Double)  <=  (toFloating y :: Double)
 129     x  >=  y    = (toFloating x :: Double)  >=  (toFloating y :: Double)
 130     x  >   y    = (toFloating x :: Double)  >   (toFloating y :: Double)
 131
 132 instance Poset CFloat where
 133     compare x y = compare (toFloating x :: Float) (toFloating y :: Float)
 134     x <==> y    = (toFloating x :: Float) <==> (toFloating y :: Float)
 135     x </=> y    = (toFloating x :: Float) </=> (toFloating y :: Float)
 136     x  <   y    = (toFloating x :: Float)  <   (toFloating y :: Float)
 137     x  <=  y    = (toFloating x :: Float)  <=  (toFloating y :: Float)
 138     x  >=  y    = (toFloating x :: Float)  >=  (toFloating y :: Float)
 139     x  >   y    = (toFloating x :: Float)  >   (toFloating y :: Float)
 140
 141 instance Sortable CDouble where
 142     isOrdered x = isOrdered (toFloating x :: Double)
 143     max = doubleLibm2 max
 144     min = doubleLibm2 min
 145
 146 instance Sortable CFloat where
 147     isOrdered x = isOrdered (toFloating x :: Float)
 148     max = floatLibm2 max
 149     min = floatLibm2 min
 150
 151 instance Roundable CDouble where
 152     toIntegral x = toIntegral (toFloating x :: Double)
 153     ceiling      = doubleLibm ceiling
 154     floor        = doubleLibm floor
 155     truncate     = doubleLibm truncate
 156     round        = doubleLibm round
 157
 158 instance Roundable CFloat where
 159     toIntegral x = toIntegral (toFloating x :: Float)
 160     ceiling      = floatLibm ceiling
 161     floor        = floatLibm floor
 162     truncate     = floatLibm truncate
 163     round        = floatLibm round
 164
 165 instance PrimFloat CDouble where
 166     floatRadix     = const $ floatRadix (undefined :: Double)
 167     floatPrecision = const $ floatPrecision (undefined :: Double)
 168     floatRange     = const $ floatRange (undefined :: Double)
 169     classify t     = classify (toFloating t :: Double)
 170     logb           = doubleLibm logb
 171     scalb x        = toFloating . scalb (toFloating x :: Double)
 172
 173 instance PrimFloat CFloat where
 174     floatRadix     = const $ floatRadix (undefined :: Float)
 175     floatPrecision = const $ floatPrecision (undefined :: Float)
 176     floatRange     = const $ floatRange (undefined :: Float)
 177     classify t     = classify (toFloating t :: Float)
 178     logb           = floatLibm logb
 179     scalb x        = toFloating . scalb (toFloating x :: Float)