Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

AERN2.MP.Accuracy

Description

A type for roughly measuring the accuracy of an enclosure.

Synopsis

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 #
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 #
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 #
ConvertibleExactly Int Accuracy #
Methods safeConvertExactly :: Int -> ConvertResult Accuracy #
ConvertibleExactly Integer Accuracy #
Methods safeConvertExactly :: Integer -> ConvertResult Accuracy #
ConvertibleExactly Precision Accuracy #
Methods safeConvertExactly :: Precision -> ConvertResult Accuracy #
ConvertibleExactly NormLog Accuracy #
Methods safeConvertExactly :: NormLog -> 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 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 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 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 #