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

AERN2.MP.UseMPFR.Ball.Type

Contents

Auxiliary types
The Ball type
Ball construction/extraction functions

Description

Arbitrary precision dyadic balls

Synopsis

Auxiliary types

module AERN2.MP.Precision

module AERN2.MP.Accuracy

module AERN2.MP.Enclosure

The Ball type

data MPBall #

Constructors

MPBall
Fields ball_value :: MPFloat ball_error :: ErrorBound

Instances

Show MPBall #
Methods showsPrec :: Int -> MPBall -> ShowS # show :: MPBall -> String # showList :: [MPBall] -> ShowS #
Generic MPBall #
Associated Types type Rep MPBall :: * -> * # Methods from :: MPBall -> Rep MPBall x # to :: Rep MPBall x -> MPBall #
CanAbs MPBall #
Associated Types type AbsType MPBall :: * # Methods abs :: MPBall -> AbsType MPBall #
CanTestNaN MPBall #
Methods isNaN :: MPBall -> Bool #
CanTestFinite MPBall #
Methods isInfinite :: MPBall -> Bool # isFinite :: MPBall -> Bool #
CanNeg MPBall #
Associated Types type NegType MPBall :: * # Methods negate :: MPBall -> NegType MPBall #
CanSetPrecision MPBall #
Methods setPrecision :: Precision -> MPBall -> MPBall #
HasPrecision MPBall #
Methods getPrecision :: MPBall -> Precision #
HasNorm MPBall #
Methods getNormLog :: MPBall -> NormLog #
HasApproximate MPBall #
Associated Types type Approximate MPBall :: * # Methods getApproximate :: Accuracy -> MPBall -> Approximate MPBall #
CanReduceSizeUsingAccuracyGuide MPBall #
Methods reduceSizeUsingAccuracyGuide :: Accuracy -> MPBall -> MPBall #
HasAccuracy MPBall #
Methods getAccuracy :: MPBall -> Accuracy #
IsBall MPBall #
Associated Types type CentreType MPBall :: * # Methods centre :: MPBall -> CentreType MPBall # centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound) # centreAsBall :: MPBall -> MPBall # radius :: MPBall -> ErrorBound # updateRadius :: (ErrorBound -> ErrorBound) -> MPBall -> MPBall # makeExactCentre :: MPBall -> MPBall #
CanNormalize MPBall #
Methods normalize :: MPBall -> MPBall #
SuitableForCE es => CanEnsureCE es MPBall #
Associated Types type EnsureCE es MPBall :: * # type EnsureNoCE es MPBall :: * # Methods ensureCE :: Maybe es -> MPBall -> EnsureCE es MPBall # deEnsureCE :: Maybe es -> EnsureCE es MPBall -> Either es MPBall # ensureNoCE :: Maybe es -> MPBall -> (Maybe (EnsureNoCE es MPBall), es) # noValueECE :: Maybe MPBall -> es -> EnsureCE es MPBall # prependErrorsECE :: Maybe MPBall -> es -> EnsureCE es MPBall -> EnsureCE es MPBall #
CanTestContains MPBall Int #
Methods contains :: MPBall -> Int -> Bool #
CanTestContains MPBall Integer #
Methods contains :: MPBall -> Integer -> Bool #
CanTestContains MPBall Rational #
Methods contains :: MPBall -> Rational -> Bool #
CanTestContains MPBall Dyadic #
Methods contains :: MPBall -> Dyadic -> Bool #
CanTestContains MPBall MPBall #
Methods contains :: MPBall -> MPBall -> Bool #
IsInterval MPBall MPFloat #
Methods fromEndpoints :: MPFloat -> MPFloat -> MPBall # endpoints :: MPBall -> (MPFloat, MPFloat) #
IsInterval MPBall MPBall #
Methods fromEndpoints :: MPBall -> MPBall -> MPBall # endpoints :: MPBall -> (MPBall, MPBall) #
type Rep MPBall #
type Rep MPBall = D1 * (MetaData "MPBall" "AERN2.MP.UseMPFR.Ball.Type" "aern2-mp-0.1.2.0-Kh5QoRzHVWq3J81aPr9Llb" False) (C1 * (MetaCons "MPBall" PrefixI True) ((::) (S1 * (MetaSel (Just Symbol "ball_value") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * MPFloat)) (S1 * (MetaSel (Just Symbol "ball_error") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * ErrorBound))))
type SqrtType MPBall #
type SqrtType MPBall = CN MPBall
type ExpType MPBall #
type ExpType MPBall = MPBall
type LogType MPBall #
type LogType MPBall = CN MPBall
type SinCosType MPBall #
type SinCosType MPBall = MPBall
type AbsType MPBall #
type AbsType MPBall = MPBall
type NegType MPBall #
type NegType MPBall = MPBall
type Approximate MPBall #
type Approximate MPBall = (MPFloat, Bool)
type CentreType MPBall #
type CentreType MPBall = Dyadic
type DivType Int MPBall #
type DivType Int MPBall = CN MPBall
type DivType Integer MPBall #
type DivType Integer MPBall = CN MPBall
type DivType Rational MPBall #
type DivType Rational MPBall = EnsureCN (DivTypeNoCN Rational MPBall)
type DivType Dyadic MPBall #
type DivType Dyadic MPBall = CN MPBall
type DivType MPBall Int #
type DivType MPBall Int = CN MPBall
type DivType MPBall Integer #
type DivType MPBall Integer = CN MPBall
type DivType MPBall Rational #
type DivType MPBall Rational = EnsureCN (DivTypeNoCN MPBall Rational)
type DivType MPBall Dyadic #
type DivType MPBall Dyadic = CN MPBall
type DivType MPBall MPBall #
type DivType MPBall MPBall = CN MPBall
type DivTypeNoCN Int MPBall #
type DivTypeNoCN Int MPBall = MPBall
type DivTypeNoCN Integer MPBall #
type DivTypeNoCN Integer MPBall = MPBall
type DivTypeNoCN Rational MPBall #
type DivTypeNoCN Rational MPBall = MPBall
type DivTypeNoCN Dyadic MPBall #
type DivTypeNoCN Dyadic MPBall = MPBall
type DivTypeNoCN MPBall Int #
type DivTypeNoCN MPBall Int = MPBall
type DivTypeNoCN MPBall Integer #
type DivTypeNoCN MPBall Integer = MPBall
type DivTypeNoCN MPBall Rational #
type DivTypeNoCN MPBall Rational = MPBall
type DivTypeNoCN MPBall Dyadic #
type DivTypeNoCN MPBall Dyadic = MPBall
type DivTypeNoCN MPBall MPBall #
type DivTypeNoCN MPBall MPBall = MPBall
type MulType Int MPBall #
type MulType Int MPBall = MPBall
type MulType Integer MPBall #
type MulType Integer MPBall = MPBall
type MulType Rational MPBall #
type MulType Rational MPBall = MPBall
type MulType Dyadic MPBall #
type MulType Dyadic MPBall = MPBall
type MulType MPBall Int #
type MulType MPBall Int = MPBall
type MulType MPBall Integer #
type MulType MPBall Integer = MPBall
type MulType MPBall Rational #
type MulType MPBall Rational = MPBall
type MulType MPBall Dyadic #
type MulType MPBall Dyadic = MPBall
type MulType MPBall MPBall #
type MulType MPBall MPBall = MPBall
type PowType MPBall Int #
type PowType MPBall Int = EnsureCN (PowTypeNoCN MPBall Int)
type PowType MPBall Integer #
type PowType MPBall Integer = EnsureCN (PowTypeNoCN MPBall Integer)
type PowType MPBall Rational #
type PowType MPBall Rational = EnsureCN (PowTypeNoCN MPBall Rational)
type PowType MPBall Dyadic #
type PowType MPBall Dyadic = EnsureCN (PowTypeNoCN MPBall Dyadic)
type PowType MPBall MPBall #
type PowType MPBall MPBall = EnsureCN (PowTypeNoCN MPBall MPBall)
type PowTypeNoCN MPBall Int #
type PowTypeNoCN MPBall Int = MPBall
type PowTypeNoCN MPBall Integer #
type PowTypeNoCN MPBall Integer = MPBall
type PowTypeNoCN MPBall Rational #
type PowTypeNoCN MPBall Rational = MPBall
type PowTypeNoCN MPBall Dyadic #
type PowTypeNoCN MPBall Dyadic = MPBall
type PowTypeNoCN MPBall MPBall #
type PowTypeNoCN MPBall MPBall = MPBall
type AddType Int MPBall #
type AddType Int MPBall = MPBall
type AddType Integer MPBall #
type AddType Integer MPBall = MPBall
type AddType Rational MPBall #
type AddType Rational MPBall = MPBall
type AddType Dyadic MPBall #
type AddType Dyadic MPBall = MPBall
type AddType MPBall Int #
type AddType MPBall Int = MPBall
type AddType MPBall Integer #
type AddType MPBall Integer = MPBall
type AddType MPBall Rational #
type AddType MPBall Rational = MPBall
type AddType MPBall Dyadic #
type AddType MPBall Dyadic = MPBall
type AddType MPBall MPBall #
type AddType MPBall MPBall = MPBall
type SubType Int MPBall #
type SubType Int MPBall = AddType Int (NegType MPBall)
type SubType Integer MPBall #
type SubType Integer MPBall = AddType Integer (NegType MPBall)
type SubType Rational MPBall #
type SubType Rational MPBall = AddType Rational (NegType MPBall)
type SubType Dyadic MPBall #
type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Int #
type SubType MPBall Int = AddType MPBall (NegType Int)
type SubType MPBall Integer #
type SubType MPBall Integer = AddType MPBall (NegType Integer)
type SubType MPBall Rational #
type SubType MPBall Rational = AddType MPBall (NegType Rational)
type SubType MPBall Dyadic #
type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type SubType MPBall MPBall #
type SubType MPBall MPBall = AddType MPBall (NegType MPBall)
type MinMaxType Int MPBall #
type MinMaxType Int MPBall = MPBall
type MinMaxType Integer MPBall #
type MinMaxType Integer MPBall = MPBall
type MinMaxType Rational MPBall #
type MinMaxType Rational MPBall = MPBall
type MinMaxType Dyadic MPBall #
type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Int #
type MinMaxType MPBall Int = MPBall
type MinMaxType MPBall Integer #
type MinMaxType MPBall Integer = MPBall
type MinMaxType MPBall Rational #
type MinMaxType MPBall Rational = MPBall
type MinMaxType MPBall Dyadic #
type MinMaxType MPBall Dyadic = MPBall
type MinMaxType MPBall MPBall #
type MinMaxType MPBall MPBall = MPBall
type EqCompareType Int MPBall #
type EqCompareType Int MPBall = Maybe Bool
type EqCompareType Integer MPBall #
type EqCompareType Integer MPBall = Maybe Bool
type EqCompareType Rational MPBall #
type EqCompareType Rational MPBall = Maybe Bool
type EqCompareType Dyadic MPBall #
type EqCompareType Dyadic MPBall = Maybe Bool
type EqCompareType MPBall Int #
type EqCompareType MPBall Int = Maybe Bool
type EqCompareType MPBall Integer #
type EqCompareType MPBall Integer = Maybe Bool
type EqCompareType MPBall Rational #
type EqCompareType MPBall Rational = Maybe Bool
type EqCompareType MPBall Dyadic #
type EqCompareType MPBall Dyadic = Maybe Bool
type EqCompareType MPBall MPBall #
type EqCompareType MPBall MPBall = Maybe Bool
type OrderCompareType Int MPBall #
type OrderCompareType Int MPBall = Maybe Bool
type OrderCompareType Integer MPBall #
type OrderCompareType Integer MPBall = Maybe Bool
type OrderCompareType Rational MPBall #
type OrderCompareType Rational MPBall = Maybe Bool
type OrderCompareType Dyadic MPBall #
type OrderCompareType Dyadic MPBall = Maybe Bool
type OrderCompareType MPBall Int #
type OrderCompareType MPBall Int = Maybe Bool
type OrderCompareType MPBall Integer #
type OrderCompareType MPBall Integer = Maybe Bool
type OrderCompareType MPBall Rational #
type OrderCompareType MPBall Rational = Maybe Bool
type OrderCompareType MPBall Dyadic #
type OrderCompareType MPBall Dyadic = Maybe Bool
type OrderCompareType MPBall MPBall #
type OrderCompareType MPBall MPBall = Maybe Bool
type EnsureNoCE es MPBall #
type EnsureNoCE es MPBall = MPBall
type EnsureCE es MPBall #
type EnsureCE es MPBall = CollectErrors es MPBall
type UnionType MPBall MPBall #
type UnionType MPBall MPBall = EnsureCN MPBall
type IntersectionType MPBall MPBall #
type IntersectionType MPBall MPBall = EnsureCN MPBall
type DivType MPBall (CollectErrors es b) #
type DivType MPBall (CollectErrors es b) = EnsureCE es (DivType MPBall b)
type DivTypeNoCN MPBall (CollectErrors es b) #
type DivTypeNoCN MPBall (CollectErrors es b) = EnsureCE es (DivTypeNoCN MPBall b)
type MulType MPBall (CollectErrors es b) #
type MulType MPBall (CollectErrors es b) = EnsureCE es (MulType MPBall b)
type PowType MPBall (CollectErrors es b) #
type PowType MPBall (CollectErrors es b) = EnsureCE es (PowType MPBall b)
type PowTypeNoCN MPBall (CollectErrors es b) #
type PowTypeNoCN MPBall (CollectErrors es b) = EnsureCE es (PowTypeNoCN MPBall b)
type AddType MPBall (CollectErrors es b) #
type AddType MPBall (CollectErrors es b) = EnsureCE es (AddType MPBall b)
type SubType MPBall (CollectErrors es b) #
type SubType MPBall (CollectErrors es b) = EnsureCE es (SubType MPBall b)
type MinMaxType MPBall (CollectErrors es b) #
type MinMaxType MPBall (CollectErrors es b) = EnsureCE es (MinMaxType MPBall b)
type EqCompareType MPBall (CollectErrors es b) #
type EqCompareType MPBall (CollectErrors es b) = EnsureCE es (EqCompareType MPBall b)
type OrderCompareType MPBall (CollectErrors es b) #
type OrderCompareType MPBall (CollectErrors es b) = EnsureCE es (OrderCompareType MPBall b)
type UnionType MPBall (CollectErrors es b) #
type UnionType MPBall (CollectErrors es b) = EnsureCE es (UnionType MPBall b)
type IntersectionType MPBall (CollectErrors es b) #
type IntersectionType MPBall (CollectErrors es b) = EnsureCE es (IntersectionType MPBall b)
type DivType (CollectErrors es a) MPBall #
type DivType (CollectErrors es a) MPBall = EnsureCE es (DivType a MPBall)
type DivTypeNoCN (CollectErrors es a) MPBall #
type DivTypeNoCN (CollectErrors es a) MPBall = EnsureCE es (DivTypeNoCN a MPBall)
type MulType (CollectErrors es a) MPBall #
type MulType (CollectErrors es a) MPBall = EnsureCE es (MulType a MPBall)
type PowType (CollectErrors es a) MPBall #
type PowType (CollectErrors es a) MPBall = EnsureCE es (PowType a MPBall)
type PowTypeNoCN (CollectErrors es a) MPBall #
type PowTypeNoCN (CollectErrors es a) MPBall = EnsureCE es (PowTypeNoCN a MPBall)
type AddType (CollectErrors es a) MPBall #
type AddType (CollectErrors es a) MPBall = EnsureCE es (AddType a MPBall)
type SubType (CollectErrors es a) MPBall #
type SubType (CollectErrors es a) MPBall = EnsureCE es (SubType a MPBall)
type MinMaxType (CollectErrors es a) MPBall #
type MinMaxType (CollectErrors es a) MPBall = EnsureCE es (MinMaxType a MPBall)
type EqCompareType (CollectErrors es a) MPBall #
type EqCompareType (CollectErrors es a) MPBall = EnsureCE es (EqCompareType a MPBall)
type OrderCompareType (CollectErrors es a) MPBall #
type OrderCompareType (CollectErrors es a) MPBall = EnsureCE es (OrderCompareType a MPBall)
type UnionType (CollectErrors es a) MPBall #
type UnionType (CollectErrors es a) MPBall = EnsureCE es (UnionType a MPBall)
type IntersectionType (CollectErrors es a) MPBall #
type IntersectionType (CollectErrors es a) MPBall = EnsureCE es (IntersectionType a MPBall)

type CanBeMPBall t = ConvertibleExactly t MPBall #

mpBall :: CanBeMPBall t => t -> MPBall #

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall #

mpBallP :: CanBeMPBallP t => Precision -> t -> MPBall #

reducePrecionIfInaccurate :: MPBall -> MPBall #

Reduce the precision of the ball centre if the accuracy of the ball is poor.

More precisely, reduce the precision of the centre so that the ulp is approximately (radius / 1024), unless the ulp is already lower than this.

Ball construction/extraction functions

endpointsMP :: MPBall -> (MPFloat, MPFloat) #

fromEndpointsMP :: MPFloat -> MPFloat -> MPBall #