    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE ScopedTypeVariables #-}
    {-# LANGUAGE PolyKinds #-}
    {-# LANGUAGE FlexibleInstances #-}

    -----------------------------------------------------------------------------
    -- |
    -- 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   :  stable
    -- 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 Data.Data
    import GHC.TypeLits (KnownNat, natVal)
    import GHC.Read
    import Text.ParserCombinators.ReadPrec
    import Text.Read.Lex

    default () -- avoid any defaulting shenanigans

    -- | Generalisation of 'div' to any instance of 'Real'
    div' :: (Real a,Integral b) => a -> a -> b
    div' :: forall a b. (Real a, Integral b) => a -> a -> b
    div' a
    n a
    d = Rational -> b
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    floor ((a -> Rational
    forall a. Real a => a -> Rational
    toRational a
    n) Rational -> Rational -> Rational
    forall a. Fractional a => a -> a -> a
    / (a -> Rational
    forall a. Real a => a -> Rational
    toRational a
    d))

    -- | Generalisation of 'divMod' to any instance of 'Real'
    divMod' :: (Real a,Integral b) => a -> a -> (b,a)
    divMod' :: forall a b. (Real a, Integral b) => a -> a -> (b, a)
    divMod' a
    n a
    d = (b
    f,a
    n a -> a -> a
    forall a. Num a => a -> a -> a
    - (b -> a
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral b
    f) a -> a -> a
    forall a. Num a => a -> a -> a
    * a
    d) where
        f :: b
    f = a -> a -> b
    forall a b. (Real a, Integral b) => a -> a -> b
    div' a
    n a
    d

    -- | Generalisation of 'mod' to any instance of 'Real'
    mod' :: (Real a) => a -> a -> a
    mod' :: forall a. Real a => a -> a -> a
    mod' a
    n a
    d = a
    n a -> a -> a
    forall a. Num a => a -> a -> a
    - (Integer -> a
    forall a. Num a => Integer -> a
    fromInteger Integer
    f) a -> a -> a
    forall a. Num a => a -> a -> a
    * a
    d where
        f :: Integer
    f = a -> a -> Integer
    forall a b. (Real a, Integral b) => a -> a -> b
    div' a
    n a
    d

    -- | The type parameter should be an instance of 'HasResolution'.
    newtype Fixed (a :: k) = MkFixed Integer
            deriving ( Fixed a -> Fixed a -> Bool
    (Fixed a -> Fixed a -> Bool)
    -> (Fixed a -> Fixed a -> Bool) -> Eq (Fixed a)
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    forall k (a :: k). Fixed a -> Fixed a -> Bool
    $c== :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    == :: Fixed a -> Fixed a -> Bool
    $c/= :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    /= :: Fixed a -> Fixed a -> Bool
    Eq  -- ^ @since 2.01
                     , Eq (Fixed a)
    Eq (Fixed a)
    -> (Fixed a -> Fixed a -> Ordering)
    -> (Fixed a -> Fixed a -> Bool)
    -> (Fixed a -> Fixed a -> Bool)
    -> (Fixed a -> Fixed a -> Bool)
    -> (Fixed a -> Fixed a -> Bool)
    -> (Fixed a -> Fixed a -> Fixed a)
    -> (Fixed a -> Fixed a -> Fixed a)
    -> Ord (Fixed a)
    Fixed a -> Fixed a -> Bool
    Fixed a -> Fixed a -> Ordering
    Fixed a -> Fixed a -> Fixed a
    forall a.
    Eq a
    -> (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    forall k (a :: k). Eq (Fixed a)
    forall k (a :: k). Fixed a -> Fixed a -> Bool
    forall k (a :: k). Fixed a -> Fixed a -> Ordering
    forall k (a :: k). Fixed a -> Fixed a -> Fixed a
    $ccompare :: forall k (a :: k). Fixed a -> Fixed a -> Ordering
    compare :: Fixed a -> Fixed a -> Ordering
    $c< :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    < :: Fixed a -> Fixed a -> Bool
    $c<= :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    <= :: Fixed a -> Fixed a -> Bool
    $c> :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    > :: Fixed a -> Fixed a -> Bool
    $c>= :: forall k (a :: k). Fixed a -> Fixed a -> Bool
    >= :: Fixed a -> Fixed a -> Bool
    $cmax :: forall k (a :: k). Fixed a -> Fixed a -> Fixed a
    max :: Fixed a -> Fixed a -> Fixed a
    $cmin :: forall k (a :: k). Fixed a -> Fixed a -> Fixed a
    min :: Fixed a -> Fixed a -> Fixed a
    Ord -- ^ @since 2.01
                     )

    -- 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 :: DataType
    tyFixed = String -> [Constr] -> DataType
    mkDataType String
    "Data.Fixed.Fixed" [Constr
    conMkFixed]
    conMkFixed :: Constr
    conMkFixed :: Constr
    conMkFixed = DataType -> String -> [String] -> Fixity -> Constr
    mkConstr DataType
    tyFixed String
    "MkFixed" [] Fixity
    Prefix

    -- | @since 4.1.0.0
    instance (Typeable k,Typeable a) => Data (Fixed (a :: k)) where
        gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Fixed a -> c (Fixed a)
    gfoldl forall d b. Data d => c (d -> b) -> d -> c b
    k forall g. g -> c g
    z (MkFixed Integer
    a) = c (Integer -> Fixed a) -> Integer -> c (Fixed a)
    forall d b. Data d => c (d -> b) -> d -> c b
    k ((Integer -> Fixed a) -> c (Integer -> Fixed a)
    forall g. g -> c g
    z Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed) Integer
    a
        gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Fixed a)
    gunfold forall b r. Data b => c (b -> r) -> c r
    k forall r. r -> c r
    z Constr
    _ = c (Integer -> Fixed a) -> c (Fixed a)
    forall b r. Data b => c (b -> r) -> c r
    k ((Integer -> Fixed a) -> c (Integer -> Fixed a)
    forall r. r -> c r
    z Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed)
        dataTypeOf :: Fixed a -> DataType
    dataTypeOf Fixed a
    _ = DataType
    tyFixed
        toConstr :: Fixed a -> Constr
    toConstr Fixed a
    _ = Constr
    conMkFixed

    class HasResolution (a :: k) where
        resolution :: p a -> Integer

    -- | For example, @Fixed 1000@ will give you a 'Fixed' with a resolution of 1000.
    instance KnownNat n => HasResolution n where
        resolution :: forall (p :: Nat -> *). p n -> Integer
    resolution p n
    _ = Proxy n -> Integer
    forall (n :: Nat) (proxy :: Nat -> *).
    KnownNat n =>
    proxy n -> Integer
    natVal (Proxy n
    forall {k} (t :: k). Proxy t
    Proxy :: Proxy n)

    withType :: (Proxy a -> f a) -> f a
    withType :: forall {k} (a :: k) (f :: k -> *). (Proxy a -> f a) -> f a
    withType Proxy a -> f a
    foo = Proxy a -> f a
    foo Proxy a
    forall {k} (t :: k). Proxy t
    Proxy

    withResolution :: (HasResolution a) => (Integer -> f a) -> f a
    withResolution :: forall {k} (a :: k) (f :: k -> *).
    HasResolution a =>
    (Integer -> f a) -> f a
    withResolution Integer -> f a
    foo = (Proxy a -> f a) -> f a
    forall {k} (a :: k) (f :: k -> *). (Proxy a -> f a) -> f a
    withType (Integer -> f a
    foo (Integer -> f a) -> (Proxy a -> Integer) -> Proxy a -> f a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Proxy a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution)

    -- | @since 2.01
    --
    -- Recall that, for numeric types, 'succ' and 'pred' typically add and subtract
    -- @1@, respectively. This is not true in the case of 'Fixed', whose successor
    -- and predecessor functions intuitively return the "next" and "previous" values
    -- in the enumeration. The results of these functions thus depend on the
    -- resolution of the 'Fixed' value. For example, when enumerating values of
    -- resolution @10^-3@ of @type Milli = Fixed E3@,
    --
    -- @
    --   succ (0.000 :: Milli) == 0.001
    -- @
    --
    --
    -- and likewise
    --
    -- @
    --   pred (0.000 :: Milli) == -0.001
    -- @
    --
    --
    -- In other words, 'succ' and 'pred' increment and decrement a fixed-precision
    -- value by the least amount such that the value's resolution is unchanged.
    -- For example, @10^-12@ is the smallest (positive) amount that can be added to
    -- a value of @type Pico = Fixed E12@ without changing its resolution, and so
    --
    -- @
    --   succ (0.000000000000 :: Pico) == 0.000000000001
    -- @
    --
    --
    -- and similarly
    --
    -- @
    --   pred (0.000000000000 :: Pico) == -0.000000000001
    -- @
    --
    --
    -- This is worth bearing in mind when defining 'Fixed' arithmetic sequences. In
    -- particular, you may be forgiven for thinking the sequence
    --
    -- @
    --   [1..10] :: [Pico]
    -- @
    --
    --
    -- evaluates to @[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico]@.
    --
    -- However, this is not true. On the contrary, similarly to the above
    -- implementations of 'succ' and 'pred', @enumFromTo :: Pico -> Pico -> [Pico]@
    -- has a "step size" of @10^-12@. Hence, the list @[1..10] :: [Pico]@ has
    -- the form
    --
    -- @
    --   [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000]
    -- @
    --
    --
    -- and contains @9 * 10^12 + 1@ values.
    instance Enum (Fixed a) where
        succ :: Fixed a -> Fixed a
    succ (MkFixed Integer
    a) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer
    forall a. Enum a => a -> a
    succ Integer
    a)
        pred :: Fixed a -> Fixed a
    pred (MkFixed Integer
    a) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer
    forall a. Enum a => a -> a
    pred Integer
    a)
        toEnum :: Int -> Fixed a
    toEnum = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Fixed a) -> (Int -> Integer) -> Int -> Fixed a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Int -> Integer
    forall a. Enum a => Int -> a
    toEnum
        fromEnum :: Fixed a -> Int
    fromEnum (MkFixed Integer
    a) = Integer -> Int
    forall a. Enum a => a -> Int
    fromEnum Integer
    a
        enumFrom :: Fixed a -> [Fixed a]
    enumFrom (MkFixed Integer
    a) = (Integer -> Fixed a) -> [Integer] -> [Fixed a]
    forall a b. (a -> b) -> [a] -> [b]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> [Integer]
    forall a. Enum a => a -> [a]
    enumFrom Integer
    a)
        enumFromThen :: Fixed a -> Fixed a -> [Fixed a]
    enumFromThen (MkFixed Integer
    a) (MkFixed Integer
    b) = (Integer -> Fixed a) -> [Integer] -> [Fixed a]
    forall a b. (a -> b) -> [a] -> [b]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> [Integer]
    forall a. Enum a => a -> a -> [a]
    enumFromThen Integer
    a Integer
    b)
        enumFromTo :: Fixed a -> Fixed a -> [Fixed a]
    enumFromTo (MkFixed Integer
    a) (MkFixed Integer
    b) = (Integer -> Fixed a) -> [Integer] -> [Fixed a]
    forall a b. (a -> b) -> [a] -> [b]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> [Integer]
    forall a. Enum a => a -> a -> [a]
    enumFromTo Integer
    a Integer
    b)
        enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a]
    enumFromThenTo (MkFixed Integer
    a) (MkFixed Integer
    b) (MkFixed Integer
    c) = (Integer -> Fixed a) -> [Integer] -> [Fixed a]
    forall a b. (a -> b) -> [a] -> [b]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> Integer -> [Integer]
    forall a. Enum a => a -> a -> a -> [a]
    enumFromThenTo Integer
    a Integer
    b Integer
    c)

    -- | @since 2.01
    instance (HasResolution a) => Num (Fixed a) where
        (MkFixed Integer
    a) + :: Fixed a -> Fixed a -> Fixed a
    + (MkFixed Integer
    b) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer
    a Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    + Integer
    b)
        (MkFixed Integer
    a) - :: Fixed a -> Fixed a -> Fixed a
    - (MkFixed Integer
    b) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer
    a Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    - Integer
    b)
        fa :: Fixed a
    fa@(MkFixed Integer
    a) * :: Fixed a -> Fixed a -> Fixed a
    * (MkFixed Integer
    b) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    div (Integer
    a Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * Integer
    b) (Fixed a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution Fixed a
    fa))
        negate :: Fixed a -> Fixed a
    negate (MkFixed Integer
    a) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer
    forall a. Num a => a -> a
    negate Integer
    a)
        abs :: Fixed a -> Fixed a
    abs (MkFixed Integer
    a) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer
    forall a. Num a => a -> a
    abs Integer
    a)
        signum :: Fixed a -> Fixed a
    signum (MkFixed Integer
    a) = Integer -> Fixed a
    forall a. Num a => Integer -> a
    fromInteger (Integer -> Integer
    forall a. Num a => a -> a
    signum Integer
    a)
        fromInteger :: Integer -> Fixed a
    fromInteger Integer
    i = (Integer -> Fixed a) -> Fixed a
    forall {k} (a :: k) (f :: k -> *).
    HasResolution a =>
    (Integer -> f a) -> f a
    withResolution (\Integer
    res -> Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer
    i Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * Integer
    res))

    -- | @since 2.01
    instance (HasResolution a) => Real (Fixed a) where
        toRational :: Fixed a -> Rational
    toRational fa :: Fixed a
    fa@(MkFixed Integer
    a) = (Integer -> Rational
    forall a. Real a => a -> Rational
    toRational Integer
    a) Rational -> Rational -> Rational
    forall a. Fractional a => a -> a -> a
    / (Integer -> Rational
    forall a. Real a => a -> Rational
    toRational (Fixed a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution Fixed a
    fa))

    -- | @since 2.01
    instance (HasResolution a) => Fractional (Fixed a) where
        fa :: Fixed a
    fa@(MkFixed Integer
    a) / :: Fixed a -> Fixed a -> Fixed a
    / (MkFixed Integer
    b) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    div (Integer
    a Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * (Fixed a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution Fixed a
    fa)) Integer
    b)
        recip :: Fixed a -> Fixed a
    recip fa :: Fixed a
    fa@(MkFixed Integer
    a) = Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    div (Integer
    res Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * Integer
    res) Integer
    a) where
            res :: Integer
    res = Fixed a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution Fixed a
    fa
        fromRational :: Rational -> Fixed a
    fromRational Rational
    r = (Integer -> Fixed a) -> Fixed a
    forall {k} (a :: k) (f :: k -> *).
    HasResolution a =>
    (Integer -> f a) -> f a
    withResolution (\Integer
    res -> Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Rational -> Integer
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    floor (Rational
    r Rational -> Rational -> Rational
    forall a. Num a => a -> a -> a
    * (Integer -> Rational
    forall a. Real a => a -> Rational
    toRational Integer
    res))))

    -- | @since 2.01
    instance (HasResolution a) => RealFrac (Fixed a) where
        properFraction :: forall b. Integral b => Fixed a -> (b, Fixed a)
    properFraction Fixed a
    a = (b
    i,Fixed a
    a Fixed a -> Fixed a -> Fixed a
    forall a. Num a => a -> a -> a
    - (b -> Fixed a
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral b
    i)) where
            i :: b
    i = Fixed a -> b
    forall b. Integral b => Fixed a -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    truncate Fixed a
    a
        truncate :: forall b. Integral b => Fixed a -> b
    truncate Fixed a
    f = Rational -> b
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    truncate (Fixed a -> Rational
    forall a. Real a => a -> Rational
    toRational Fixed a
    f)
        round :: forall b. Integral b => Fixed a -> b
    round Fixed a
    f = Rational -> b
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    round (Fixed a -> Rational
    forall a. Real a => a -> Rational
    toRational Fixed a
    f)
        ceiling :: forall b. Integral b => Fixed a -> b
    ceiling Fixed a
    f = Rational -> b
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    ceiling (Fixed a -> Rational
    forall a. Real a => a -> Rational
    toRational Fixed a
    f)
        floor :: forall b. Integral b => Fixed a -> b
    floor Fixed a
    f = Rational -> b
    forall b. Integral b => Rational -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    floor (Fixed a -> Rational
    forall a. Real a => a -> Rational
    toRational Fixed a
    f)

    chopZeros :: Integer -> String
    chopZeros :: Integer -> String
    chopZeros Integer
    0 = String
    ""
    chopZeros Integer
    a | Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    mod Integer
    a Integer
    10 Integer -> Integer -> Bool
    forall a. Eq a => a -> a -> Bool
    == Integer
    0 = Integer -> String
    chopZeros (Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    div Integer
    a Integer
    10)
    chopZeros Integer
    a = Integer -> String
    forall a. Show a => a -> String
    show Integer
    a

    -- only works for positive a
    showIntegerZeros :: Bool -> Int -> Integer -> String
    showIntegerZeros :: Bool -> Int -> Integer -> String
    showIntegerZeros Bool
    True Int
    _ Integer
    0 = String
    ""
    showIntegerZeros Bool
    chopTrailingZeros Int
    digits Integer
    a = Int -> Char -> String
    forall a. Int -> a -> [a]
    replicate (Int
    digits Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - String -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length String
    s) Char
    '0' String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    s' where
        s :: String
    s = Integer -> String
    forall a. Show a => a -> String
    show Integer
    a
        s' :: String
    s' = if Bool
    chopTrailingZeros then Integer -> String
    chopZeros Integer
    a else String
    s

    withDot :: String -> String
    withDot :: String -> String
    withDot String
    "" = String
    ""
    withDot String
    s = Char
    '.'Char -> String -> String
    forall a. a -> [a] -> [a]
    :String
    s

    -- | First arg is whether to chop off trailing zeros
    showFixed :: (HasResolution a) => Bool -> Fixed a -> String
    showFixed :: forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String
    showFixed Bool
    chopTrailingZeros fa :: Fixed a
    fa@(MkFixed Integer
    a) | Integer
    a Integer -> Integer -> Bool
    forall a. Ord a => a -> a -> Bool
    < Integer
    0 = String
    "-" String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ (Bool -> Fixed a -> String
    forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String
    showFixed Bool
    chopTrailingZeros (Fixed a -> Fixed a -> Fixed a
    forall a. a -> a -> a
    asTypeOf (Integer -> Fixed a
    forall k (a :: k). Integer -> Fixed a
    MkFixed (Integer -> Integer
    forall a. Num a => a -> a
    negate Integer
    a)) Fixed a
    fa))
    showFixed Bool
    chopTrailingZeros fa :: Fixed a
    fa@(MkFixed Integer
    a) = (Integer -> String
    forall a. Show a => a -> String
    show Integer
    i) String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ (String -> String
    withDot (Bool -> Int -> Integer -> String
    showIntegerZeros Bool
    chopTrailingZeros Int
    digits Integer
    fracNum)) where
        res :: Integer
    res = Fixed a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution Fixed a
    fa
        (Integer
    i,Integer
    d) = Integer -> Integer -> (Integer, Integer)
    forall a. Integral a => a -> a -> (a, a)
    divMod Integer
    a Integer
    res
        -- enough digits to be unambiguous
        digits :: Int
    digits = Double -> Int
    forall b. Integral b => Double -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    ceiling (Double -> Double -> Double
    forall a. Floating a => a -> a -> a
    logBase Double
    10 (Integer -> Double
    forall a. Num a => Integer -> a
    fromInteger Integer
    res) :: Double)
        maxnum :: Integer
    maxnum = Integer
    10 Integer -> Int -> Integer
    forall a b. (Num a, Integral b) => a -> b -> a
    ^ Int
    digits
        -- read floors, so show must ceil for `read . show = id` to hold. See #9240
        fracNum :: Integer
    fracNum = Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    divCeil (Integer
    d Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * Integer
    maxnum) Integer
    res
        divCeil :: a -> a -> a
    divCeil a
    x a
    y = (a
    x a -> a -> a
    forall a. Num a => a -> a -> a
    + a
    y a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    1) a -> a -> a
    forall a. Integral a => a -> a -> a
    `div` a
    y

    -- | @since 2.01
    instance (HasResolution a) => Show (Fixed a) where
        showsPrec :: Int -> Fixed a -> String -> String
    showsPrec Int
    p Fixed a
    n = Bool -> (String -> String) -> String -> String
    showParen (Int
    p Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    6 Bool -> Bool -> Bool
    && Fixed a
    n Fixed a -> Fixed a -> Bool
    forall a. Ord a => a -> a -> Bool
    < Fixed a
    0) ((String -> String) -> String -> String)
    -> (String -> String) -> String -> String
    forall a b. (a -> b) -> a -> b
    $ String -> String -> String
    showString (String -> String -> String) -> String -> String -> String
    forall a b. (a -> b) -> a -> b
    $ Bool -> Fixed a -> String
    forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String
    showFixed Bool
    False Fixed a
    n

    -- | @since 4.3.0.0
    instance (HasResolution a) => Read (Fixed a) where
        readPrec :: ReadPrec (Fixed a)
    readPrec     = (Lexeme -> ReadPrec (Fixed a)) -> ReadPrec (Fixed a)
    forall a. Num a => (Lexeme -> ReadPrec a) -> ReadPrec a
    readNumber Lexeme -> ReadPrec (Fixed a)
    forall {k} (a :: k).
    HasResolution a =>
    Lexeme -> ReadPrec (Fixed a)
    convertFixed
        readListPrec :: ReadPrec [Fixed a]
    readListPrec = ReadPrec [Fixed a]
    forall a. Read a => ReadPrec [a]
    readListPrecDefault
        readList :: ReadS [Fixed a]
    readList     = ReadS [Fixed a]
    forall a. Read a => ReadS [a]
    readListDefault

    convertFixed :: forall a . HasResolution a => Lexeme -> ReadPrec (Fixed a)
    convertFixed :: forall {k} (a :: k).
    HasResolution a =>
    Lexeme -> ReadPrec (Fixed a)
    convertFixed (Number Number
    n)
     | Just (Integer
    i, Integer
    f) <- Integer -> Number -> Maybe (Integer, Integer)
    numberToFixed Integer
    e Number
    n =
        Fixed a -> ReadPrec (Fixed a)
    forall a. a -> ReadPrec a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (Integer -> Fixed a
    forall a. Num a => Integer -> a
    fromInteger Integer
    i Fixed a -> Fixed a -> Fixed a
    forall a. Num a => a -> a -> a
    + (Integer -> Fixed a
    forall a. Num a => Integer -> a
    fromInteger Integer
    f Fixed a -> Fixed a -> Fixed a
    forall a. Fractional a => a -> a -> a
    / (Fixed a
    10 Fixed a -> Integer -> Fixed a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^ Integer
    e)))
        where r :: Integer
    r = Proxy a -> Integer
    forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
    forall (p :: k -> *). p a -> Integer
    resolution (Proxy a
    forall {k} (t :: k). Proxy t
    Proxy :: Proxy a)
              -- round 'e' up to help make the 'read . show == id' property
              -- possible also for cases where 'resolution' is not a
              -- power-of-10, such as e.g. when 'resolution = 128'
              e :: Integer
    e = Double -> Integer
    forall b. Integral b => Double -> b
    forall a b. (RealFrac a, Integral b) => a -> b
    ceiling (Double -> Double -> Double
    forall a. Floating a => a -> a -> a
    logBase Double
    10 (Integer -> Double
    forall a. Num a => Integer -> a
    fromInteger Integer
    r) :: Double)
    convertFixed Lexeme
    _ = ReadPrec (Fixed a)
    forall a. ReadPrec a
    pfail

    data E0

    -- | @since 4.1.0.0
    instance HasResolution E0 where
        resolution :: forall (p :: * -> *). p E0 -> Integer
    resolution p E0
    _ = Integer
    1
    -- | resolution of 1, this works the same as Integer
    type Uni = Fixed E0

    data E1

    -- | @since 4.1.0.0
    instance HasResolution E1 where
        resolution :: forall (p :: * -> *). p E1 -> Integer
    resolution p E1
    _ = Integer
    10
    -- | resolution of 10^-1 = .1
    type Deci = Fixed E1

    data E2

    -- | @since 4.1.0.0
    instance HasResolution E2 where
        resolution :: forall (p :: * -> *). p E2 -> Integer
    resolution p E2
    _ = Integer
    100
    -- | resolution of 10^-2 = .01, useful for many monetary currencies
    type Centi = Fixed E2

    data E3

    -- | @since 4.1.0.0
    instance HasResolution E3 where
        resolution :: forall (p :: * -> *). p E3 -> Integer
    resolution p E3
    _ = Integer
    1000
    -- | resolution of 10^-3 = .001
    type Milli = Fixed E3

    data E6

    -- | @since 2.01
    instance HasResolution E6 where
        resolution :: forall (p :: * -> *). p E6 -> Integer
    resolution p E6
    _ = Integer
    1000000
    -- | resolution of 10^-6 = .000001
    type Micro = Fixed E6

    data E9

    -- | @since 4.1.0.0
    instance HasResolution E9 where
        resolution :: forall (p :: * -> *). p E9 -> Integer
    resolution p E9
    _ = Integer
    1000000000
    -- | resolution of 10^-9 = .000000001
    type Nano = Fixed E9

    data E12

    -- | @since 2.01
    instance HasResolution E12 where
        resolution :: forall (p :: * -> *). p E12 -> Integer
    resolution p E12
    _ = Integer
    1000000000000
    -- | resolution of 10^-12 = .000000000001
    type Pico = Fixed E12