| 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
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) :: Milli0.123
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
Instances
Instances details
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 #
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 #
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 * 0.5False
Since: base-2.1
Instance details
Defined in Data.Fixed
Instance details
Defined in Data.Fixed
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.
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
Resolution of 1, this works the same as Integer.
Instances
Instances details
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
Resolution of 10^-1 = .1
Instances
Instances details
Resolution of 10^-1 = .1
Examples
Expand
>>>show (MkFixed 12345 :: Fixed E1)"1234.5"
>>>show (MkFixed 12345 :: Deci)"1234.5"
1/100
Resolution of 10^-2 = .01, useful for many monetary currencies
Instances
Instances details
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
Resolution of 10^-3 = .001
Instances
Instances details
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
Resolution of 10^-6 = .000001
Instances
Instances details
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
Resolution of 10^-9 = .000000001
Instances
Instances details
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
Resolution of 10^-12 = .000000000001
Instances
Instances details
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"