AERN2.MP.Accuracy

A type for roughly measuring the accuracy of an enclosure.

Documentation

data Accuracy

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

Constructors

NoInformation

Exact

Instances

Bounded Accuracy

Methods

minBound :: Accuracy

maxBound :: Accuracy

Enum 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]

Eq Accuracy

Methods

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

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

Ord 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

Show Accuracy

Methods

showsPrec :: Int -> Accuracy -> ShowS

show :: Accuracy -> String

showList :: [Accuracy] -> ShowS

Arbitrary Accuracy

Methods

arbitrary :: Gen Accuracy

shrink :: Accuracy -> [Accuracy]

CanNeg Accuracy

Associated Types

type NegType Accuracy :: *

Methods

negate :: Accuracy -> NegType Accuracy

CanMulAsymmetric Integer Accuracy

Associated Types

type MulType Integer Accuracy :: *

Methods

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

CanMulAsymmetric Accuracy Integer

Associated Types

type MulType Accuracy Integer :: *

Methods

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

CanAddAsymmetric Integer Accuracy

Associated Types

type AddType Integer Accuracy :: *

Methods

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

CanAddAsymmetric Accuracy Integer

Associated Types

type AddType Accuracy Integer :: *

Methods

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

CanAddAsymmetric Accuracy Accuracy

Associated Types

type AddType Accuracy Accuracy :: *

Methods

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

CanSub Accuracy Integer

Associated Types

type SubType Accuracy Integer :: *

Methods

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

CanSub Accuracy Accuracy

Associated Types

type SubType Accuracy Accuracy :: *

Methods

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

CanMinMaxAsymmetric Int Accuracy

Associated Types

type MinMaxType Int Accuracy :: *

Methods

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

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

CanMinMaxAsymmetric Integer Accuracy

Associated Types

type MinMaxType Integer Accuracy :: *

Methods

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

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

CanMinMaxAsymmetric Accuracy Int

Associated Types

type MinMaxType Accuracy Int :: *

Methods

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

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

CanMinMaxAsymmetric Accuracy Integer

Associated Types

type MinMaxType Accuracy Integer :: *

Methods

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

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

CanMinMaxAsymmetric Accuracy Accuracy

Associated Types

type MinMaxType Accuracy Accuracy :: *

Methods

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

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

HasOrderAsymmetric Int Accuracy

Associated Types

type OrderCompareType Int Accuracy :: *

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

HasOrderAsymmetric Integer Accuracy

Associated Types

type OrderCompareType Integer Accuracy :: *

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 Accuracy Int

Associated Types

type OrderCompareType Accuracy Int :: *

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 Accuracy Integer

Associated Types

type OrderCompareType Accuracy Integer :: *

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 Accuracy

Associated Types

type OrderCompareType Accuracy Accuracy :: *

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

HasEqAsymmetric Int Accuracy

Associated Types

type EqCompareType Int Accuracy :: *

Methods

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

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

HasEqAsymmetric Integer Accuracy

Associated Types

type EqCompareType Integer Accuracy :: *

Methods

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

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

HasEqAsymmetric Accuracy Int

Associated Types

type EqCompareType Accuracy Int :: *

Methods

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

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

HasEqAsymmetric Accuracy Integer

Associated Types

type EqCompareType Accuracy Integer :: *

Methods

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

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

HasEqAsymmetric Accuracy Accuracy

Associated Types

type EqCompareType Accuracy Accuracy :: *

Methods

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

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

ConvertibleExactly Int Accuracy

Methods

safeConvertExactly :: Int -> ConvertResult Accuracy

ConvertibleExactly Integer Accuracy

Methods

safeConvertExactly :: Integer -> ConvertResult Accuracy

ConvertibleExactly NormLog Accuracy

Methods

safeConvertExactly :: NormLog -> ConvertResult Accuracy

ConvertibleExactly Precision Accuracy

Methods

safeConvertExactly :: Precision -> ConvertResult Accuracy

(Arrow to, CanUnionAsymmetric e1 e2) => CanUnionAsymmetric (to Accuracy e1) (to Accuracy e2)

Associated Types

type UnionType (to Accuracy e1) (to Accuracy e2) :: *

Methods

union :: to Accuracy e1 -> to Accuracy e2 -> UnionType (to Accuracy e1) (to Accuracy e2)

type NegType Accuracy

type NegType Accuracy = Accuracy

type MulType Integer Accuracy

type MulType Integer Accuracy = Accuracy

type MulType Accuracy Integer

type MulType Accuracy Integer = Accuracy

type AddType Integer Accuracy

type AddType Integer Accuracy = Accuracy

type AddType Accuracy Integer

type AddType Accuracy Integer = Accuracy

type AddType Accuracy Accuracy

type AddType Accuracy Accuracy = Accuracy

type SubType Accuracy Integer

type SubType Accuracy Integer = Accuracy

type SubType Accuracy Accuracy

type SubType Accuracy Accuracy = AddType Accuracy (NegType Accuracy)

type MinMaxType Int Accuracy

type MinMaxType Int Accuracy = Accuracy

type MinMaxType Integer Accuracy

type MinMaxType Integer Accuracy = Accuracy

type MinMaxType Accuracy Int

type MinMaxType Accuracy Int = Accuracy

type MinMaxType Accuracy Integer

type MinMaxType Accuracy Integer = Accuracy

type MinMaxType Accuracy Accuracy

type MinMaxType Accuracy Accuracy = Accuracy

type OrderCompareType Int Accuracy

type OrderCompareType Int Accuracy = Bool

type OrderCompareType Integer Accuracy

type OrderCompareType Integer Accuracy = Bool

type OrderCompareType Accuracy Int

type OrderCompareType Accuracy Int = Bool

type OrderCompareType Accuracy Integer

type OrderCompareType Accuracy Integer = Bool

type OrderCompareType Accuracy Accuracy

type OrderCompareType Accuracy Accuracy = Bool

type EqCompareType Int Accuracy

type EqCompareType Int Accuracy = Bool

type EqCompareType Integer Accuracy

type EqCompareType Integer Accuracy = Bool

type EqCompareType Accuracy Int

type EqCompareType Accuracy Int = Bool

type EqCompareType Accuracy Integer

type EqCompareType Accuracy Integer = Bool

type EqCompareType Accuracy Accuracy

type EqCompareType Accuracy Accuracy = Bool

type UnionType (to Accuracy e1) (to Accuracy e2)

type UnionType (to Accuracy e1) (to Accuracy e2) = to Accuracy (UnionType e1 e2)

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

fromAccuracy :: Accuracy -> Integer

class HasAccuracy a where

Minimal complete definition

getAccuracy

Methods

getAccuracy :: a -> Accuracy

Instances

HasAccuracy Bool

Methods

getAccuracy :: Bool -> Accuracy

HasAccuracy Int

Methods

getAccuracy :: Int -> Accuracy

HasAccuracy Integer

Methods

getAccuracy :: Integer -> Accuracy

HasAccuracy Rational

Methods

getAccuracy :: Rational -> Accuracy

HasAccuracy Dyadic

Methods

getAccuracy :: Dyadic -> Accuracy

HasAccuracy ErrorBound

Methods

getAccuracy :: ErrorBound -> Accuracy

HasAccuracy MPBall

Methods

getAccuracy :: MPBall -> Accuracy

HasAccuracy t => HasAccuracy [t]

Methods

getAccuracy :: [t] -> Accuracy

HasAccuracy t => HasAccuracy (Maybe t)

Methods

getAccuracy :: Maybe t -> Accuracy

HasAccuracy t => HasAccuracy (Complex t)

Methods

getAccuracy :: Complex t -> Accuracy

(HasAccuracy a, SuitableForCE es) => HasAccuracy (CollectErrors es a)

Methods

getAccuracy :: CollectErrors es a -> Accuracy

class HasAccuracyGuide a where

Minimal complete definition

getAccuracyGuide

Methods

getAccuracyGuide :: a -> Accuracy

class HasAccuracyGuide a => CanSetAccuracyGuide a where

Minimal complete definition

setAccuracyGuide

Methods

setAccuracyGuide :: Accuracy -> a -> a

adjustAccuracyGuide :: CanSetAccuracyGuide a => (Accuracy -> Accuracy) -> a -> a

getFiniteAccuracy :: (HasAccuracy t, HasPrecision t) => t -> Accuracy

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.

ac2prec :: Accuracy -> Precision

class CanReduceSizeUsingAccuracyGuide t where

Minimal complete definition

reduceSizeUsingAccuracyGuide

Methods

reduceSizeUsingAccuracyGuide :: Accuracy -> t -> t

Instances

CanReduceSizeUsingAccuracyGuide MPBall

Methods

reduceSizeUsingAccuracyGuide :: Accuracy -> MPBall -> MPBall

specCanReduceSizeUsingAccuracyGuide :: (CanReduceSizeUsingAccuracyGuide t, HasEqCertainly t t, Arbitrary t, Show t) => T t -> Spec

iterateUntilAccurate :: HasAccuracy t => Accuracy -> (Precision -> Maybe t) -> [(Precision, Maybe t)]

convergentList2CauchySeq :: HasAccuracy t => [t] -> Accuracy -> t

seqByPrecision2CauchySeq :: HasAccuracy t => (Precision -> t) -> Accuracy -> t

setPrecisionAtLeastAccuracy :: CanSetPrecision t => Accuracy -> t -> t

Change the precision so that it is at least as high as the supplied accuracy (assuming the accuracy is finite).

class HasApproximate t where

An unsafe approximation of an enclosure or exact value, useful mainly for showing something brief and readable to humans.

Minimal complete definition

getApproximate

Associated Types

type Approximate t

Methods

getApproximate :: Accuracy -> t -> Approximate t

Instances

HasApproximate MPBall

Associated Types

type Approximate MPBall :: *

Methods

getApproximate :: Accuracy -> MPBall -> Approximate MPBall