module Data.Fixed
(
- div',mod',divMod',
+ div',mod',divMod',
- Fixed,HasResolution(..),
- showFixed,
- E6,Micro,
- E12,Pico
+ Fixed,HasResolution(..),
+ showFixed,
+ E6,Micro,
+ E12,Pico
) where
import Prelude -- necessary to get dependencies right
-- | generalisation of 'divMod' to any instance of Real
divMod' :: (Real a,Integral b) => a -> a -> (b,a)
divMod' n d = (f,n - (fromIntegral f) * d) where
- f = div' n d
+ f = div' n d
-- | generalisation of 'mod' to any instance of Real
mod' :: (Real a) => a -> a -> a
mod' n d = n - (fromInteger f) * d where
- f = div' n d
+ f = div' n d
newtype Fixed a = MkFixed Integer deriving (Eq,Ord)
class HasResolution a where
- resolution :: a -> Integer
+ resolution :: a -> Integer
fixedResolution :: (HasResolution a) => Fixed a -> Integer
fixedResolution fa = resolution (uf fa) where
- uf :: Fixed a -> a
- uf _ = undefined
+ uf :: Fixed a -> a
+ uf _ = undefined
withType :: (a -> f a) -> f a
withType foo = foo undefined
withResolution foo = withType (foo . resolution)
instance Enum (Fixed a) where
- succ (MkFixed a) = MkFixed (succ a)
- pred (MkFixed a) = MkFixed (pred a)
- toEnum = MkFixed . toEnum
- fromEnum (MkFixed a) = fromEnum a
- enumFrom (MkFixed a) = fmap MkFixed (enumFrom a)
- enumFromThen (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromThen a b)
- enumFromTo (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromTo a b)
- enumFromThenTo (MkFixed a) (MkFixed b) (MkFixed c) = fmap MkFixed (enumFromThenTo a b c)
+ succ (MkFixed a) = MkFixed (succ a)
+ pred (MkFixed a) = MkFixed (pred a)
+ toEnum = MkFixed . toEnum
+ fromEnum (MkFixed a) = fromEnum a
+ enumFrom (MkFixed a) = fmap MkFixed (enumFrom a)
+ enumFromThen (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromThen a b)
+ enumFromTo (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromTo a b)
+ enumFromThenTo (MkFixed a) (MkFixed b) (MkFixed c) = fmap MkFixed (enumFromThenTo a b c)
instance (HasResolution a) => Num (Fixed a) where
- (MkFixed a) + (MkFixed b) = MkFixed (a + b)
- (MkFixed a) - (MkFixed b) = MkFixed (a - b)
- fa@(MkFixed a) * (MkFixed b) = MkFixed (div (a * b) (fixedResolution fa))
- negate (MkFixed a) = MkFixed (negate a)
- abs (MkFixed a) = MkFixed (abs a)
- signum (MkFixed a) = fromInteger (signum a)
- fromInteger i = withResolution (\res -> MkFixed (i * res))
+ (MkFixed a) + (MkFixed b) = MkFixed (a + b)
+ (MkFixed a) - (MkFixed b) = MkFixed (a - b)
+ fa@(MkFixed a) * (MkFixed b) = MkFixed (div (a * b) (fixedResolution fa))
+ negate (MkFixed a) = MkFixed (negate a)
+ abs (MkFixed a) = MkFixed (abs a)
+ signum (MkFixed a) = fromInteger (signum a)
+ fromInteger i = withResolution (\res -> MkFixed (i * res))
instance (HasResolution a) => Real (Fixed a) where
- toRational fa@(MkFixed a) = (toRational a) / (toRational (fixedResolution fa))
+ toRational fa@(MkFixed a) = (toRational a) / (toRational (fixedResolution fa))
instance (HasResolution a) => Fractional (Fixed a) where
- fa@(MkFixed a) / (MkFixed b) = MkFixed (div (a * (fixedResolution fa)) b)
- recip fa@(MkFixed a) = MkFixed (div (res * res) a) where
- res = fixedResolution fa
- fromRational r = withResolution (\res -> MkFixed (floor (r * (toRational res))))
+ fa@(MkFixed a) / (MkFixed b) = MkFixed (div (a * (fixedResolution fa)) b)
+ recip fa@(MkFixed a) = MkFixed (div (res * res) a) where
+ res = fixedResolution fa
+ fromRational r = withResolution (\res -> MkFixed (floor (r * (toRational res))))
instance (HasResolution a) => RealFrac (Fixed a) where
- properFraction a = (i,a - (fromIntegral i)) where
- i = truncate a
- truncate f = truncate (toRational f)
- round f = round (toRational f)
- ceiling f = ceiling (toRational f)
- floor f = floor (toRational f)
+ properFraction a = (i,a - (fromIntegral i)) where
+ i = truncate a
+ truncate f = truncate (toRational f)
+ round f = round (toRational f)
+ ceiling f = ceiling (toRational f)
+ floor f = floor (toRational f)
chopZeros :: Integer -> String
chopZeros 0 = ""
showIntegerZeros :: Bool -> Int -> Integer -> String
showIntegerZeros True _ 0 = ""
showIntegerZeros chopTrailingZeros digits a = replicate (digits - length s) '0' ++ s' where
- s = show a
- s' = if chopTrailingZeros then chopZeros a else s
+ s = show a
+ s' = if chopTrailingZeros then chopZeros a else s
withDot :: String -> String
withDot "" = ""
showFixed :: (HasResolution a) => Bool -> Fixed a -> String
showFixed chopTrailingZeros fa@(MkFixed a) | a < 0 = "-" ++ (showFixed chopTrailingZeros (asTypeOf (MkFixed (negate a)) fa))
showFixed chopTrailingZeros fa@(MkFixed a) = (show i) ++ (withDot (showIntegerZeros chopTrailingZeros digits fracNum)) where
- res = fixedResolution fa
- (i,d) = divMod a res
- -- enough digits to be unambiguous
- digits = ceiling (logBase 10 (fromInteger res) :: Double)
- maxnum = 10 ^ digits
- fracNum = div (d * maxnum) res
+ res = fixedResolution fa
+ (i,d) = divMod a res
+ -- enough digits to be unambiguous
+ digits = ceiling (logBase 10 (fromInteger res) :: Double)
+ maxnum = 10 ^ digits
+ fracNum = div (d * maxnum) res
instance (HasResolution a) => Show (Fixed a) where
- show = showFixed False
+ show = showFixed False
data E6 = E6
instance HasResolution E6 where
- resolution _ = 1000000
+ resolution _ = 1000000
type Micro = Fixed E6
data E12 = E12
instance HasResolution E12 where
- resolution _ = 1000000000000
+ resolution _ = 1000000000000
type Pico = Fixed E12