Data.Fixed

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.

Documentation

div' :: (Real a, Integral b) => a -> a -> b

Generalisation of div to any instance of Real

mod' :: Real a => a -> a -> a

Generalisation of mod to any instance of Real

divMod' :: (Real a, Integral b) => a -> a -> (b, a)

Generalisation of divMod to any instance of Real

newtype Fixed (a :: k)

The type parameter should be an instance of HasResolution.

Constructors

MkFixed Integer

Instances

(Typeable k, Typeable a) => Data (Fixed a)

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Fixed a -> c (Fixed a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Fixed a)

toConstr :: Fixed a -> Constr

dataTypeOf :: Fixed a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Fixed a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Fixed a))

gmapT :: (forall b. Data b => b -> b) -> Fixed a -> Fixed a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Fixed a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Fixed a -> r

gmapQ :: (forall d. Data d => d -> u) -> Fixed a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Fixed a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a)

Enum (Fixed a)

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) == 1.001

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.

Since: base-2.1

Defined in Data.Fixed

Methods

succ :: Fixed a -> Fixed a

pred :: Fixed a -> Fixed a

toEnum :: Int -> Fixed a

fromEnum :: Fixed a -> Int

enumFrom :: Fixed a -> [Fixed a]

enumFromThen :: Fixed a -> Fixed a -> [Fixed a]

enumFromTo :: Fixed a -> Fixed a -> [Fixed a]

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a]

HasResolution a => Num (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

(+) :: Fixed a -> Fixed a -> Fixed a

(-) :: Fixed a -> Fixed a -> Fixed a

(*) :: Fixed a -> Fixed a -> Fixed a

negate :: Fixed a -> Fixed a

abs :: Fixed a -> Fixed a

signum :: Fixed a -> Fixed a

fromInteger :: Integer -> Fixed a

HasResolution a => Read (Fixed a)

Since: base-4.3.0.0

Defined in Data.Fixed

Methods

readsPrec :: Int -> ReadS (Fixed a)

readList :: ReadS [Fixed a]

readPrec :: ReadPrec (Fixed a)

readListPrec :: ReadPrec [Fixed a]

HasResolution a => Fractional (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

(/) :: Fixed a -> Fixed a -> Fixed a

recip :: Fixed a -> Fixed a

fromRational :: Rational -> Fixed a

HasResolution a => Real (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

toRational :: Fixed a -> Rational

HasResolution a => RealFrac (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

properFraction :: Integral b => Fixed a -> (b, Fixed a)

truncate :: Integral b => Fixed a -> b

round :: Integral b => Fixed a -> b

ceiling :: Integral b => Fixed a -> b

floor :: Integral b => Fixed a -> b

HasResolution a => Show (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

showsPrec :: Int -> Fixed a -> ShowS

show :: Fixed a -> String

showList :: [Fixed a] -> ShowS

Eq (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

(==) :: Fixed a -> Fixed a -> Bool

(/=) :: Fixed a -> Fixed a -> Bool

Ord (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

compare :: 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

max :: Fixed a -> Fixed a -> Fixed a

min :: Fixed a -> Fixed a -> Fixed a

class HasResolution (a :: k) where

Methods

resolution :: p a -> Integer

Instances

KnownNat n => HasResolution (n :: Nat)

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.

Defined in Data.Fixed

Methods

resolution :: p n -> Integer

HasResolution E0

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E0 -> Integer

HasResolution E1

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E1 -> Integer

HasResolution E12

Since: base-2.1

Defined in Data.Fixed

Methods

resolution :: p E12 -> Integer

HasResolution E2

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E2 -> Integer

HasResolution E3

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E3 -> Integer

HasResolution E6

Since: base-2.1

Defined in Data.Fixed

Methods

resolution :: p E6 -> Integer

HasResolution E9

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E9 -> Integer

showFixed :: HasResolution a => Bool -> Fixed a -> String

First arg is whether to chop off trailing zeros

data E0

Instances

HasResolution E0

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E0 -> Integer

type Uni = Fixed E0

resolution of 1, this works the same as Integer

data E1

Instances

HasResolution E1

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E1 -> Integer

type Deci = Fixed E1

resolution of 10^-1 = .1

data E2

Instances

HasResolution E2

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E2 -> Integer

type Centi = Fixed E2

resolution of 10^-2 = .01, useful for many monetary currencies

data E3

Instances

HasResolution E3

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E3 -> Integer

type Milli = Fixed E3

resolution of 10^-3 = .001

data E6

Instances

HasResolution E6

Since: base-2.1

Defined in Data.Fixed

Methods

resolution :: p E6 -> Integer

type Micro = Fixed E6

resolution of 10^-6 = .000001

data E9

Instances

HasResolution E9

Since: base-4.1.0.0

Defined in Data.Fixed

Methods

resolution :: p E9 -> Integer

type Nano = Fixed E9

resolution of 10^-9 = .000000001

data E12

Instances

HasResolution E12

Since: base-2.1

Defined in Data.Fixed

Methods

resolution :: p E12 -> Integer

type Pico = Fixed E12

resolution of 10^-12 = .000000000001