1 {-# OPTIONS -Wall -fno-warn-unused-binds #-}
3 -----------------------------------------------------------------------------
6 -- Copyright : (c) Ashley Yakeley 2005, 2006, 2009
7 -- License : BSD-style (see the file libraries/base/LICENSE)
9 -- Maintainer : Ashley Yakeley <ashley@semantic.org>
10 -- Stability : experimental
11 -- Portability : portable
13 -- This module defines a \"Fixed\" type for fixed-precision arithmetic.
14 -- The parameter to Fixed is any type that's an instance of HasResolution.
15 -- HasResolution has a single method that gives the resolution of the Fixed type.
17 -- This module also contains generalisations of div, mod, and divmod to work
18 -- with any Real instance.
20 -----------------------------------------------------------------------------
26 Fixed,HasResolution(..),
37 import Prelude -- necessary to get dependencies right
44 default () -- avoid any defaulting shenanigans
47 -- | generalisation of 'div' to any instance of Real
48 div' :: (Real a,Integral b) => a -> a -> b
49 div' n d = floor ((toRational n) / (toRational d))
51 -- | generalisation of 'divMod' to any instance of Real
52 divMod' :: (Real a,Integral b) => a -> a -> (b,a)
53 divMod' n d = (f,n - (fromIntegral f) * d) where
56 -- | generalisation of 'mod' to any instance of Real
57 mod' :: (Real a) => a -> a -> a
58 mod' n d = n - (fromInteger f) * d where
61 -- | The type parameter should be an instance of 'HasResolution'.
62 newtype Fixed a = MkFixed Integer
64 deriving (Eq,Ord,Typeable)
70 -- We do this because the automatically derived Data instance requires (Data a) context.
71 -- Our manual instance has the more general (Typeable a) context.
73 tyFixed = mkDataType "Data.Fixed.Fixed" [conMkFixed]
75 conMkFixed = mkConstr tyFixed "MkFixed" [] Prefix
76 instance (Typeable a) => Data (Fixed a) where
77 gfoldl k z (MkFixed a) = k (z MkFixed) a
78 gunfold k z _ = k (z MkFixed)
79 dataTypeOf _ = tyFixed
80 toConstr _ = conMkFixed
83 class HasResolution a where
84 resolution :: p a -> Integer
86 withType :: (p a -> f a) -> f a
87 withType foo = foo undefined
89 withResolution :: (HasResolution a) => (Integer -> f a) -> f a
90 withResolution foo = withType (foo . resolution)
92 instance Enum (Fixed a) where
93 succ (MkFixed a) = MkFixed (succ a)
94 pred (MkFixed a) = MkFixed (pred a)
95 toEnum = MkFixed . toEnum
96 fromEnum (MkFixed a) = fromEnum a
97 enumFrom (MkFixed a) = fmap MkFixed (enumFrom a)
98 enumFromThen (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromThen a b)
99 enumFromTo (MkFixed a) (MkFixed b) = fmap MkFixed (enumFromTo a b)
100 enumFromThenTo (MkFixed a) (MkFixed b) (MkFixed c) = fmap MkFixed (enumFromThenTo a b c)
102 instance (HasResolution a) => Num (Fixed a) where
103 (MkFixed a) + (MkFixed b) = MkFixed (a + b)
104 (MkFixed a) - (MkFixed b) = MkFixed (a - b)
105 fa@(MkFixed a) * (MkFixed b) = MkFixed (div (a * b) (resolution fa))
106 negate (MkFixed a) = MkFixed (negate a)
107 abs (MkFixed a) = MkFixed (abs a)
108 signum (MkFixed a) = fromInteger (signum a)
109 fromInteger i = withResolution (\res -> MkFixed (i * res))
111 instance (HasResolution a) => Real (Fixed a) where
112 toRational fa@(MkFixed a) = (toRational a) / (toRational (resolution fa))
114 instance (HasResolution a) => Fractional (Fixed a) where
115 fa@(MkFixed a) / (MkFixed b) = MkFixed (div (a * (resolution fa)) b)
116 recip fa@(MkFixed a) = MkFixed (div (res * res) a) where
118 fromRational r = withResolution (\res -> MkFixed (floor (r * (toRational res))))
120 instance (HasResolution a) => RealFrac (Fixed a) where
121 properFraction a = (i,a - (fromIntegral i)) where
123 truncate f = truncate (toRational f)
124 round f = round (toRational f)
125 ceiling f = ceiling (toRational f)
126 floor f = floor (toRational f)
128 chopZeros :: Integer -> String
130 chopZeros a | mod a 10 == 0 = chopZeros (div a 10)
133 -- only works for positive a
134 showIntegerZeros :: Bool -> Int -> Integer -> String
135 showIntegerZeros True _ 0 = ""
136 showIntegerZeros chopTrailingZeros digits a = replicate (digits - length s) '0' ++ s' where
138 s' = if chopTrailingZeros then chopZeros a else s
140 withDot :: String -> String
144 -- | First arg is whether to chop off trailing zeros
145 showFixed :: (HasResolution a) => Bool -> Fixed a -> String
146 showFixed chopTrailingZeros fa@(MkFixed a) | a < 0 = "-" ++ (showFixed chopTrailingZeros (asTypeOf (MkFixed (negate a)) fa))
147 showFixed chopTrailingZeros fa@(MkFixed a) = (show i) ++ (withDot (showIntegerZeros chopTrailingZeros digits fracNum)) where
150 -- enough digits to be unambiguous
151 digits = ceiling (logBase 10 (fromInteger res) :: Double)
153 fracNum = div (d * maxnum) res
155 instance (HasResolution a) => Show (Fixed a) where
156 show = showFixed False
163 instance HasResolution E0 where
165 -- | resolution of 1, this works the same as Integer
172 instance HasResolution E1 where
174 -- | resolution of 10^-1 = .1
181 instance HasResolution E2 where
183 -- | resolution of 10^-2 = .01, useful for many monetary currencies
184 type Centi = Fixed E2
190 instance HasResolution E3 where
192 -- | resolution of 10^-3 = .001
193 type Milli = Fixed E3
199 instance HasResolution E6 where
200 resolution _ = 1000000
201 -- | resolution of 10^-6 = .000001
202 type Micro = Fixed E6
208 instance HasResolution E9 where
209 resolution _ = 1000000000
210 -- | resolution of 10^-9 = .000000001
217 instance HasResolution E12 where
218 resolution _ = 1000000000000
219 -- | resolution of 10^-12 = .000000000001
220 type Pico = Fixed E12