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 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.

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

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

Documentation

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 #	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 #

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 :: forall {k} (a :: k). 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