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

Data.Fixed

Contents

The Fixed Type
Resolution / Scaling Factors
Generalized Functions on Real's

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

Synopsis

newtype Fixed (a :: k) = MkFixed Integer
class HasResolution (a :: k) where
- resolution :: p a -> Integer
showFixed :: forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String
data E0
type Uni = Fixed E0
data E1
type Deci = Fixed E1
data E2
type Centi = Fixed E2
data E3
type Milli = Fixed E3
data E6
type Micro = Fixed E6
data E9
type Nano = Fixed E9
data E12
type Pico = Fixed E12
div' :: (Real a, Integral b) => a -> a -> b
mod' :: Real a => a -> a -> a
divMod' :: (Real a, Integral b) => a -> a -> (b, a)

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

(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