base-4.18.1.0: Basic libraries

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.

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 :: 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 # | 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