{-# LANGUAGE Trustworthy #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE DeriveDataTypeable #-} {-# 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 import Data.Typeable import Data.Data 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' 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 -- ^ /Since: 4.7.0.0/ deriving (Eq,Ord,Typeable) -- 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 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 instance (HasResolution a) => Read (Fixed a) where readPrec = readNumber convertFixed readListPrec = readListPrecDefault readList = readListDefault convertFixed :: forall a . HasResolution a => Lexeme -> ReadPrec (Fixed a) convertFixed (Number n) | Just (i, f) <- numberToFixed r n = return (fromInteger i + (fromInteger f / (10 ^ r))) where r = resolution (undefined :: Fixed a) convertFixed _ = pfail data E0 = E0 deriving (Typeable) instance HasResolution E0 where resolution _ = 1 -- | resolution of 1, this works the same as Integer type Uni = Fixed E0 data E1 = E1 deriving (Typeable) instance HasResolution E1 where resolution _ = 10 -- | resolution of 10^-1 = .1 type Deci = Fixed E1 data E2 = E2 deriving (Typeable) instance HasResolution E2 where resolution _ = 100 -- | resolution of 10^-2 = .01, useful for many monetary currencies type Centi = Fixed E2 data E3 = E3 deriving (Typeable) instance HasResolution E3 where resolution _ = 1000 -- | resolution of 10^-3 = .001 type Milli = Fixed E3 data E6 = E6 deriving (Typeable) instance HasResolution E6 where resolution _ = 1000000 -- | resolution of 10^-6 = .000001 type Micro = Fixed E6 data E9 = E9 deriving (Typeable) instance HasResolution E9 where resolution _ = 1000000000 -- | resolution of 10^-9 = .000000001 type Nano = Fixed E9 data E12 = E12 deriving (Typeable) instance HasResolution E12 where resolution _ = 1000000000000 -- | resolution of 10^-12 = .000000000001 type Pico = Fixed E12