    {-# OPTIONS -Wall -fno-warn-unused-binds #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Fixed
    -- Copyright   :  (c) Ashley Yakeley 2005, 2006, 2009
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  Ashley Yakeley <ashley@semantic.org>
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- This module defines a \"Fixed\" type for fixed-precision arithmetic.
    -- The parameter to Fixed is any type that's an instance of HasResolution.
    -- HasResolution has a single method that gives the resolution of the Fixed type.
    --
    -- This module also contains generalisations of div, mod, and divmod to work
    -- with any Real instance.
    --
    -----------------------------------------------------------------------------

    module Data.Fixed
    (
        div',mod',divMod',

        Fixed,HasResolution(..),
        showFixed,
        E0,Uni,
        E1,Deci,
        E2,Centi,
        E3,Milli,
        E6,Micro,
        E9,Nano,
        E12,Pico
    ) where

    import Prelude -- necessary to get dependencies right
    #ifndef __NHC__
    import Data.Typeable
    import Data.Data
    #endif

    #ifndef __NHC__
    default () -- avoid any defaulting shenanigans
    #endif

    -- | generalisation of 'div' to any instance of Real
    div' :: (Real a,Integral b) => a -> a -> b
    div' n d = floor ((toRational n) / (toRational d))

    -- | 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

    -- | 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

    -- | The type parameter should be an instance of 'HasResolution'.
    newtype Fixed a = MkFixed Integer
    #ifndef __NHC__
            deriving (Eq,Ord,Typeable)
    #else
            deriving (Eq,Ord)
    #endif

    #ifndef __NHC__
    -- We do this because the automatically derived Data instance requires (Data a) context.
    -- Our manual instance has the more general (Typeable a) context.
    tyFixed :: DataType
    tyFixed = mkDataType "Data.Fixed.Fixed" [conMkFixed]
    conMkFixed :: Constr
    conMkFixed = mkConstr tyFixed "MkFixed" [] Prefix
    instance (Typeable a) => Data (Fixed a) where
        gfoldl k z (MkFixed a) = k (z MkFixed) a
        gunfold k z _ = k (z MkFixed)
        dataTypeOf _ = tyFixed
        toConstr _ = conMkFixed
    #endif

    class HasResolution a where
        resolution :: p a -> Integer

    withType :: (p a -> f a) -> f a
    withType foo = foo undefined

    withResolution :: (HasResolution a) => (Integer -> f a) -> f a
    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)

    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) (resolution 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 (resolution fa))

    instance (HasResolution a) => Fractional (Fixed a) where
        fa@(MkFixed a) / (MkFixed b) = MkFixed (div (a * (resolution fa)) b)
        recip fa@(MkFixed a) = MkFixed (div (res * res) a) where
            res = resolution 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)

    chopZeros :: Integer -> String
    chopZeros 0 = ""
    chopZeros a | mod a 10 == 0 = chopZeros (div a 10)
    chopZeros a = show a

    -- only works for positive a
    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

    withDot :: String -> String
    withDot "" = ""
    withDot s = '.':s

    -- | First arg is whether to chop off trailing zeros
    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 = resolution 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

    data E0 = E0
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E0 where
        resolution _ = 1
    -- | resolution of 1, this works the same as Integer
    type Uni = Fixed E0

    data E1 = E1
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E1 where
        resolution _ = 10
    -- | resolution of 10^-1 = .1
    type Deci = Fixed E1

    data E2 = E2
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E2 where
        resolution _ = 100
    -- | resolution of 10^-2 = .01, useful for many monetary currencies
    type Centi = Fixed E2

    data E3 = E3
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E3 where
        resolution _ = 1000
    -- | resolution of 10^-3 = .001
    type Milli = Fixed E3

    data E6 = E6
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E6 where
        resolution _ = 1000000
    -- | resolution of 10^-6 = .000001
    type Micro = Fixed E6

    data E9 = E9
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E9 where
        resolution _ = 1000000000
    -- | resolution of 10^-9 = .000000001
    type Nano = Fixed E9

    data E12 = E12
    #ifndef __NHC__
         deriving (Typeable)
    #endif
    instance HasResolution E12 where
        resolution _ = 1000000000000
    -- | resolution of 10^-12 = .000000000001
    type Pico = Fixed E12