Copyright	(c) Michal Konecny
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.Accuracy

Description

A type for measuring the accuracy of an enclosing set, roughly corresponding to the maximum absolute error in some distance metric approximately measured in bits.

Synopsis

data Accuracy
- = NoInformation
- | Exact
bits :: ConvertibleExactly t Accuracy => t -> Accuracy
fromAccuracy :: Accuracy -> Integer
class HasAccuracy a where
- getAccuracy :: a -> Accuracy
- getFiniteAccuracy :: a -> Accuracy
ac2prec :: Accuracy -> Precision
iterateUntilAccurate :: HasAccuracy t => Accuracy -> (Precision -> Maybe t) -> [(Precision, Maybe t)]
convergentList2seqByAccuracy :: HasAccuracy t => [t] -> Accuracy -> t
seqByPrecision2seqByAccuracy :: HasAccuracy t => (Precision -> t) -> Accuracy -> t
setPrecisionAtLeastAccuracy :: (HasPrecision t, CanSetPrecision t) => Accuracy -> t -> t
class ShowWithAccuracy t where
- showWithAccuracy :: Accuracy -> t -> String
class HasApproximate t where
- type Approximate t
- getApproximate :: Accuracy -> t -> Approximate t

Documentation

data Accuracy Source #

A non-negative Double value to serve as an error bound. Arithmetic is rounded towards +infinity.

Constructors

NoInformation
Exact

Instances

Instances details

Arbitrary Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

arbitrary :: Gen Accuracy #

shrink :: Accuracy -> [Accuracy] #

Bounded Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

minBound :: Accuracy #

maxBound :: Accuracy #

Enum Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

succ :: Accuracy -> Accuracy #

pred :: Accuracy -> Accuracy #

toEnum :: Int -> Accuracy #

fromEnum :: Accuracy -> Int #

enumFrom :: Accuracy -> [Accuracy] #

enumFromThen :: Accuracy -> Accuracy -> [Accuracy] #

enumFromTo :: Accuracy -> Accuracy -> [Accuracy] #

enumFromThenTo :: Accuracy -> Accuracy -> Accuracy -> [Accuracy] #

Show Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

showsPrec :: Int -> Accuracy -> ShowS #

show :: Accuracy -> String #

showList :: [Accuracy] -> ShowS #

Eq Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

(==) :: Accuracy -> Accuracy -> Bool #

(/=) :: Accuracy -> Accuracy -> Bool #

Ord Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

compare :: Accuracy -> Accuracy -> Ordering #

(<) :: Accuracy -> Accuracy -> Bool #

(<=) :: Accuracy -> Accuracy -> Bool #

(>) :: Accuracy -> Accuracy -> Bool #

(>=) :: Accuracy -> Accuracy -> Bool #

max :: Accuracy -> Accuracy -> Accuracy #

min :: Accuracy -> Accuracy -> Accuracy #

CanNeg Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type NegType Accuracy
Instance details Defined in AERN2.MP.Accuracy type NegType Accuracy = Accuracy

Methods

negate :: Accuracy -> NegType Accuracy #

CanAddAsymmetric Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type AddType Accuracy Accuracy
Instance details Defined in AERN2.MP.Accuracy type AddType Accuracy Accuracy = Accuracy

Methods

add :: Accuracy -> Accuracy -> AddType Accuracy Accuracy #

CanAddAsymmetric Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type AddType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type AddType Accuracy Integer = Accuracy

Methods

add :: Accuracy -> Integer -> AddType Accuracy Integer #

CanAddAsymmetric Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type AddType Integer Accuracy
Instance details Defined in AERN2.MP.Accuracy type AddType Integer Accuracy = Accuracy

Methods

add :: Integer -> Accuracy -> AddType Integer Accuracy #

CanSub Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type SubType Accuracy Accuracy
Instance details Defined in AERN2.MP.Accuracy type SubType Accuracy Accuracy = AddType Accuracy (NegType Accuracy)

Methods

sub :: Accuracy -> Accuracy -> SubType Accuracy Accuracy #

CanSub Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type SubType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type SubType Accuracy Integer = Accuracy

Methods

sub :: Accuracy -> Integer -> SubType Accuracy Integer #

HasEqAsymmetric Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type EqCompareType Accuracy Accuracy
Instance details Defined in AERN2.MP.Accuracy type EqCompareType Accuracy Accuracy = Bool

Methods

equalTo :: Accuracy -> Accuracy -> EqCompareType Accuracy Accuracy #

notEqualTo :: Accuracy -> Accuracy -> EqCompareType Accuracy Accuracy #

HasEqAsymmetric Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type EqCompareType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type EqCompareType Accuracy Integer = Bool

Methods

equalTo :: Accuracy -> Integer -> EqCompareType Accuracy Integer #

notEqualTo :: Accuracy -> Integer -> EqCompareType Accuracy Integer #

HasEqAsymmetric Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type EqCompareType Accuracy Int
Instance details Defined in AERN2.MP.Accuracy type EqCompareType Accuracy Int = Bool

Methods

equalTo :: Accuracy -> Int -> EqCompareType Accuracy Int #

notEqualTo :: Accuracy -> Int -> EqCompareType Accuracy Int #

HasEqAsymmetric Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type EqCompareType Integer Accuracy
Instance details Defined in AERN2.MP.Accuracy type EqCompareType Integer Accuracy = Bool

Methods

equalTo :: Integer -> Accuracy -> EqCompareType Integer Accuracy #

notEqualTo :: Integer -> Accuracy -> EqCompareType Integer Accuracy #

HasEqAsymmetric Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type EqCompareType Int Accuracy
Instance details Defined in AERN2.MP.Accuracy type EqCompareType Int Accuracy = Bool

Methods

equalTo :: Int -> Accuracy -> EqCompareType Int Accuracy #

notEqualTo :: Int -> Accuracy -> EqCompareType Int Accuracy #

ConvertibleExactly Precision Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

safeConvertExactly :: Precision -> ConvertResult Accuracy #

ConvertibleExactly NormLog Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

safeConvertExactly :: NormLog -> ConvertResult Accuracy #

ConvertibleExactly Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

safeConvertExactly :: Integer -> ConvertResult Accuracy #

ConvertibleExactly Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

safeConvertExactly :: Int -> ConvertResult Accuracy #

CanMinMaxAsymmetric Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MinMaxType Accuracy Accuracy
Instance details Defined in AERN2.MP.Accuracy type MinMaxType Accuracy Accuracy = Accuracy

Methods

min :: Accuracy -> Accuracy -> MinMaxType Accuracy Accuracy #

max :: Accuracy -> Accuracy -> MinMaxType Accuracy Accuracy #

CanMinMaxAsymmetric Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MinMaxType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type MinMaxType Accuracy Integer = Accuracy

Methods

min :: Accuracy -> Integer -> MinMaxType Accuracy Integer #

max :: Accuracy -> Integer -> MinMaxType Accuracy Integer #

CanMinMaxAsymmetric Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MinMaxType Accuracy Int
Instance details Defined in AERN2.MP.Accuracy type MinMaxType Accuracy Int = Accuracy

Methods

min :: Accuracy -> Int -> MinMaxType Accuracy Int #

max :: Accuracy -> Int -> MinMaxType Accuracy Int #

CanMinMaxAsymmetric Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MinMaxType Integer Accuracy
Instance details Defined in AERN2.MP.Accuracy type MinMaxType Integer Accuracy = Accuracy

Methods

min :: Integer -> Accuracy -> MinMaxType Integer Accuracy #

max :: Integer -> Accuracy -> MinMaxType Integer Accuracy #

CanMinMaxAsymmetric Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MinMaxType Int Accuracy
Instance details Defined in AERN2.MP.Accuracy type MinMaxType Int Accuracy = Accuracy

Methods

min :: Int -> Accuracy -> MinMaxType Int Accuracy #

max :: Int -> Accuracy -> MinMaxType Int Accuracy #

CanMulAsymmetric Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MulType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type MulType Accuracy Integer = Accuracy

Methods

mul :: Accuracy -> Integer -> MulType Accuracy Integer #

CanMulAsymmetric Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type MulType Integer Accuracy
Instance details Defined in AERN2.MP.Accuracy type MulType Integer Accuracy = Accuracy

Methods

mul :: Integer -> Accuracy -> MulType Integer Accuracy #

HasOrderAsymmetric Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type OrderCompareType Accuracy Accuracy
Instance details Defined in AERN2.MP.Accuracy type OrderCompareType Accuracy Accuracy = Bool

Methods

lessThan :: Accuracy -> Accuracy -> OrderCompareType Accuracy Accuracy #

greaterThan :: Accuracy -> Accuracy -> OrderCompareType Accuracy Accuracy #

leq :: Accuracy -> Accuracy -> OrderCompareType Accuracy Accuracy #

geq :: Accuracy -> Accuracy -> OrderCompareType Accuracy Accuracy #

HasOrderAsymmetric Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type OrderCompareType Accuracy Integer
Instance details Defined in AERN2.MP.Accuracy type OrderCompareType Accuracy Integer = Bool

Methods

lessThan :: Accuracy -> Integer -> OrderCompareType Accuracy Integer #

greaterThan :: Accuracy -> Integer -> OrderCompareType Accuracy Integer #

leq :: Accuracy -> Integer -> OrderCompareType Accuracy Integer #

geq :: Accuracy -> Integer -> OrderCompareType Accuracy Integer #

HasOrderAsymmetric Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type OrderCompareType Accuracy Int
Instance details Defined in AERN2.MP.Accuracy type OrderCompareType Accuracy Int = Bool

Methods

lessThan :: Accuracy -> Int -> OrderCompareType Accuracy Int #

greaterThan :: Accuracy -> Int -> OrderCompareType Accuracy Int #

leq :: Accuracy -> Int -> OrderCompareType Accuracy Int #

geq :: Accuracy -> Int -> OrderCompareType Accuracy Int #

HasOrderAsymmetric Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type OrderCompareType Integer Accuracy
Instance details Defined in AERN2.MP.Accuracy type OrderCompareType Integer Accuracy = Bool

Methods

lessThan :: Integer -> Accuracy -> OrderCompareType Integer Accuracy #

greaterThan :: Integer -> Accuracy -> OrderCompareType Integer Accuracy #

leq :: Integer -> Accuracy -> OrderCompareType Integer Accuracy #

geq :: Integer -> Accuracy -> OrderCompareType Integer Accuracy #

HasOrderAsymmetric Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Associated Types

type OrderCompareType Int Accuracy
Instance details Defined in AERN2.MP.Accuracy type OrderCompareType Int Accuracy = Bool

Methods

lessThan :: Int -> Accuracy -> OrderCompareType Int Accuracy #

greaterThan :: Int -> Accuracy -> OrderCompareType Int Accuracy #

leq :: Int -> Accuracy -> OrderCompareType Int Accuracy #

geq :: Int -> Accuracy -> OrderCompareType Int Accuracy #

type NegType Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type NegType Accuracy = Accuracy

type AddType Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type AddType Accuracy Accuracy = Accuracy

type AddType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type AddType Accuracy Integer = Accuracy

type AddType Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type AddType Integer Accuracy = Accuracy

type SubType Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type SubType Accuracy Accuracy = AddType Accuracy (NegType Accuracy)

type SubType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type SubType Accuracy Integer = Accuracy

type EqCompareType Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type EqCompareType Accuracy Accuracy = Bool

type EqCompareType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type EqCompareType Accuracy Integer = Bool

type EqCompareType Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

type EqCompareType Accuracy Int = Bool

type EqCompareType Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type EqCompareType Integer Accuracy = Bool

type EqCompareType Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type EqCompareType Int Accuracy = Bool

type MinMaxType Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type MinMaxType Accuracy Accuracy = Accuracy

type MinMaxType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type MinMaxType Accuracy Integer = Accuracy

type MinMaxType Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

type MinMaxType Accuracy Int = Accuracy

type MinMaxType Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type MinMaxType Integer Accuracy = Accuracy

type MinMaxType Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type MinMaxType Int Accuracy = Accuracy

type MulType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type MulType Accuracy Integer = Accuracy

type MulType Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type MulType Integer Accuracy = Accuracy

type OrderCompareType Accuracy Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type OrderCompareType Accuracy Accuracy = Bool

type OrderCompareType Accuracy Integer Source #

Instance details

Defined in AERN2.MP.Accuracy

type OrderCompareType Accuracy Integer = Bool

type OrderCompareType Accuracy Int Source #

Instance details

Defined in AERN2.MP.Accuracy

type OrderCompareType Accuracy Int = Bool

type OrderCompareType Integer Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type OrderCompareType Integer Accuracy = Bool

type OrderCompareType Int Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

type OrderCompareType Int Accuracy = Bool

bits :: ConvertibleExactly t Accuracy => t -> Accuracy Source #

fromAccuracy :: Accuracy -> Integer Source #

class HasAccuracy a where Source #

Minimal complete definition

getAccuracy

Methods

getAccuracy :: a -> Accuracy Source #

getFiniteAccuracy :: a -> Accuracy Source #

Return accuracy, except when the element is Exact, return its nominal Precision dressed as Accuracy. This function is useful when we have a convergent sequence where all elements happen to be actually equal to the limit and we need the property that the sequence elements keep improving.

default getFiniteAccuracy :: HasPrecision a => a -> Accuracy Source #

Instances

Instances details

HasAccuracy Kleenean Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Kleenean -> Accuracy Source # getFiniteAccuracy :: Kleenean -> Accuracy Source #
HasAccuracy MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getAccuracy :: MPBall -> Accuracy Source # getFiniteAccuracy :: MPBall -> Accuracy Source #
HasAccuracy Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getAccuracy :: Dyadic -> Accuracy Source # getFiniteAccuracy :: Dyadic -> Accuracy Source #
HasAccuracy ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods getAccuracy :: ErrorBound -> Accuracy Source # getFiniteAccuracy :: ErrorBound -> Accuracy Source #
HasAccuracy Rational Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Rational -> Accuracy Source # getFiniteAccuracy :: Rational -> Accuracy Source #
HasAccuracy Integer Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Integer -> Accuracy Source # getFiniteAccuracy :: Integer -> Accuracy Source #
HasAccuracy Bool Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Bool -> Accuracy Source # getFiniteAccuracy :: Bool -> Accuracy Source #
HasAccuracy Int Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Int -> Accuracy Source # getFiniteAccuracy :: Int -> Accuracy Source #
HasAccuracy t => HasAccuracy (Complex t) Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Complex t -> Accuracy Source # getFiniteAccuracy :: Complex t -> Accuracy Source #
HasAccuracy t => HasAccuracy (Maybe t) Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: Maybe t -> Accuracy Source # getFiniteAccuracy :: Maybe t -> Accuracy Source #
HasAccuracy t => HasAccuracy [t] Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: [t] -> Accuracy Source # getFiniteAccuracy :: [t] -> Accuracy Source #
(HasAccuracy a, CanBeErrors es) => HasAccuracy (CollectErrors es a) Source #
Instance details Defined in AERN2.MP.Accuracy Methods getAccuracy :: CollectErrors es a -> Accuracy Source # getFiniteAccuracy :: CollectErrors es a -> Accuracy Source #