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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
Safe Haskell Trustworthy
Language Haskell2010

Description

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.

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

Generalisation of div to any instance of Real

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

Generalisation of mod to any instance of Real

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

Generalisation of divMod to any instance of Real

newtype Fixed (a :: k) Source

The type parameter should be an instance of HasResolution.

Constructors

MkFixed Integer
Instances
Instances details
(Typeable k, Typeable a) => Data (Fixed a) Source

Since: base-4.1.0.0
Instance details

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) Source

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

toConstr :: Fixed a -> Constr Source

dataTypeOf :: Fixed a -> DataType Source

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

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

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

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

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

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

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

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

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

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

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.

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

succ :: Fixed a -> Fixed a Source

pred :: Fixed a -> Fixed a Source

toEnum :: Int -> Fixed a Source

fromEnum :: Fixed a -> Int Source

enumFrom :: Fixed a -> [Fixed a] Source

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

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

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] Source
HasResolution a => Num (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

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

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

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

negate :: Fixed a -> Fixed a Source

abs :: Fixed a -> Fixed a Source

signum :: Fixed a -> Fixed a Source

fromInteger :: Integer -> Fixed a Source
HasResolution a => Read (Fixed a) Source

Since: base-4.3.0.0
Instance details

Defined in Data.Fixed

Methods

readsPrec :: Int -> ReadS (Fixed a) Source

readList :: ReadS [Fixed a] Source

readPrec :: ReadPrec (Fixed a) Source

readListPrec :: ReadPrec [Fixed a] Source
HasResolution a => Fractional (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

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

recip :: Fixed a -> Fixed a Source

fromRational :: Rational -> Fixed a Source
HasResolution a => Real (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

toRational :: Fixed a -> Rational Source
HasResolution a => RealFrac (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

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

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

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

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

floor :: Integral b => Fixed a -> b Source
HasResolution a => Show (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

showsPrec :: Int -> Fixed a -> ShowS Source

show :: Fixed a -> String Source

showList :: [Fixed a] -> ShowS Source
Eq (Fixed a) Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

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

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

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

compare :: Fixed a -> Fixed a -> Ordering Source

(<) :: Fixed a -> Fixed a -> Bool Source

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

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

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

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

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

class HasResolution (a :: k) where Source

Methods

resolution :: p a -> Integer Source

Instances
Instances details
KnownNat n => HasResolution (n :: Nat) Source

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

Defined in Data.Fixed

Methods

resolution :: p n -> Integer Source
HasResolution E0 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E0 -> Integer Source
HasResolution E1 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E1 -> Integer Source
HasResolution E12 Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

resolution :: p E12 -> Integer Source
HasResolution E2 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E2 -> Integer Source
HasResolution E3 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E3 -> Integer Source
HasResolution E6 Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

resolution :: p E6 -> Integer Source
HasResolution E9 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E9 -> Integer Source

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

First arg is whether to chop off trailing zeros

data E0 Source

Instances
Instances details
HasResolution E0 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E0 -> Integer Source

type Uni = Fixed E0 Source

resolution of 1, this works the same as Integer

data E1 Source

Instances
Instances details
HasResolution E1 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E1 -> Integer Source

type Deci = Fixed E1 Source

resolution of 10^-1 = .1

data E2 Source

Instances
Instances details
HasResolution E2 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E2 -> Integer Source

type Centi = Fixed E2 Source

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

data E3 Source

Instances
Instances details
HasResolution E3 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E3 -> Integer Source

type Milli = Fixed E3 Source

resolution of 10^-3 = .001

data E6 Source

Instances
Instances details
HasResolution E6 Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

resolution :: p E6 -> Integer Source

type Micro = Fixed E6 Source

resolution of 10^-6 = .000001

data E9 Source

Instances
Instances details
HasResolution E9 Source

Since: base-4.1.0.0
Instance details

Defined in Data.Fixed

Methods

resolution :: p E9 -> Integer Source

type Nano = Fixed E9 Source

resolution of 10^-9 = .000000001

data E12 Source

Instances
Instances details
HasResolution E12 Source

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

resolution :: p E12 -> Integer Source

type Pico = Fixed E12 Source

resolution of 10^-12 = .000000000001

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/Data-Fixed.html