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 working with fixed-point arithmetic. Fixed-point arithmetic represents fractional numbers with a fixed number of digits for their fractional part. This is different to the behaviour of the floating-point number types Float and Double, because the number of digits of the fractional part of Float and Double numbers depends on the size of the number. Fixed point arithmetic is frequently used in financial mathematics, where they are used for representing decimal currencies.

The type Fixed is used for fixed-point fractional numbers, which are internally represented as an Integer. The type Fixed takes one parameter, which should implement the typeclass HasResolution, to specify the number of digits of the fractional part. This module provides instances of the HasResolution typeclass for arbitrary typelevel natural numbers, and for some canonical important fixed-point representations.

This module also contains generalisations of div, mod, and divMod to work with any Real instance.

Automatic conversion between different Fixed can be performed through realToFrac, bear in mind that converting to a fixed with a smaller resolution will truncate the number, losing information.

>>> realToFrac (0.123456 :: Pico) :: Milli
0.123

The Fixed Type

newtype Fixed (a :: k) Source

The type of fixed-point fractional numbers. The type parameter specifies the number of digits of the fractional part and should be an instance of the HasResolution typeclass.

Examples

Expand
 MkFixed 12345 :: Fixed E3

Constructors

MkFixed Integer
Instances
Instances details
Lift (Fixed a :: Type) Source

Since: base-4.21.0.0
Instance details

Defined in Data.Fixed

Methods

lift :: Quote m => Fixed a -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Fixed a -> Code m (Fixed a) Source

(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

Multiplication is not associative or distributive:

>>> (0.2 * 0.6 :: Deci) * 0.9 == 0.2 * (0.6 * 0.9)
False

>>> (0.1 + 0.1 :: Deci) * 0.5 == 0.1 * 0.5 + 0.1 * 0.5
False

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

Types which can be used as a resolution argument to the Fixed type constructor must implement the HasResolution typeclass.

Methods

resolution :: p a -> Integer Source

Provide the resolution for a fixed-point fractional number.

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 :: forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String Source

First arg is whether to chop off trailing zeros

Examples

Expand
>>> showFixed True  (MkFixed 10000 :: Fixed E3)
"10"

>>> showFixed False (MkFixed 10000 :: Fixed E3)
"10.000"

Resolution / Scaling Factors

The resolution or scaling factor determines the number of digits in the fractional part.

Resolution Scaling Factor Synonym for "Fixed EX" show (12345 :: Fixed EX)
E0 1/1 Uni 12345.0
E1 1/10 Deci 1234.5
E2 1/100 Centi 123.45
E3 1/1 000 Milli 12.345
E6 1/1 000 000 Micro 0.012345
E9 1/1 000 000 000 Nano 0.000012345
E12 1/1 000 000 000 000 Pico 0.000000012345

1/1

data E0 Source

Resolution of 1, this works the same as Integer.

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.

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E0)
"12345.0"

>>> show (MkFixed 12345 :: Uni)
"12345.0"

1/10

data E1 Source

Resolution of 10^-1 = .1

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E1)
"1234.5"

>>> show (MkFixed 12345 :: Deci)
"1234.5"

1/100

data E2 Source

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

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E2)
"123.45"

>>> show (MkFixed 12345 :: Centi)
"123.45"

1/1 000

data E3 Source

Resolution of 10^-3 = .001

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E3)
"12.345"

>>> show (MkFixed 12345 :: Milli)
"12.345"

1/1 000 000

data E6 Source

Resolution of 10^-6 = .000001

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E6)
"0.012345"

>>> show (MkFixed 12345 :: Micro)
"0.012345"

1/1 000 000 000

data E9 Source

Resolution of 10^-9 = .000000001

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E9)
"0.000012345"

>>> show (MkFixed 12345 :: Nano)
"0.000012345"

1/1 000 000 000 000

data E12 Source

Resolution of 10^-12 = .000000000001

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

Examples

Expand
>>> show (MkFixed 12345 :: Fixed E12)
"0.000000012345"

>>> show (MkFixed 12345 :: Pico)
"0.000000012345"

Generalized Functions on Real's

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

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/Data-Fixed.html