Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

AERN2.MP.Ball

Contents

Auxiliary types
The Ball type
Ball operations (see also instances)
Helpers for constructing ball functions
Orphan instances

Description

Arbitrary precision ball arithmetic

Synopsis

module AERN2.Norm
module AERN2.MP.Precision
module AERN2.MP.Accuracy
type CanBeErrorBound t = Convertible t ErrorBound
data ErrorBound
errorBound :: CanBeErrorBound t => t -> ErrorBound
module AERN2.MP.Enclosure
data MPBall = MPBall {
- ball_value :: MPFloat
- ball_error :: ErrorBound
}
type CanBeMPBall t = ConvertibleExactly t MPBall
mpBall :: CanBeMPBall t => t -> MPBall
cnMPBall :: CanBeMPBall a => CN a -> CN MPBall
type CanBeMPBallP t = ConvertibleWithPrecision t MPBall
mpBallP :: CanBeMPBallP t => Precision -> t -> MPBall
cnMPBallP :: CanBeMPBallP a => Precision -> CN a -> CN MPBall
reducePrecionIfInaccurate :: MPBall -> MPBall
giveUpIfVeryInaccurate :: CanGiveUpIfVeryInaccurate t => CN t -> CN t
piBallP :: Precision -> MPBall
intersectCNMPBall :: CN MPBall -> CN MPBall -> CN MPBall
hullMPBall :: MPBall -> MPBall -> MPBall
byEndpointsMP :: (MPFloat -> MPFloat -> MPFloat) -> MPBall -> MPBall -> MPBall
fromApproxWithLipschitz :: (MPFloat -> BoundsCEDU MPFloat) -> MPFloat -> MPBall -> MPBall

Auxiliary types

module AERN2.Norm

module AERN2.MP.Precision

module AERN2.MP.Accuracy

type CanBeErrorBound t = Convertible t ErrorBound Source #

data ErrorBound Source #

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

Instances

Instances details

Arbitrary ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods arbitrary :: Gen ErrorBound # shrink :: ErrorBound -> [ErrorBound] #
HasAccuracy ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods getAccuracy :: ErrorBound -> Accuracy Source # getFiniteAccuracy :: ErrorBound -> Accuracy Source #
Generic ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type Rep ErrorBound :: Type -> Type # Methods from :: ErrorBound -> Rep ErrorBound x # to :: Rep ErrorBound x -> ErrorBound #
Show ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods showsPrec :: Int -> ErrorBound -> ShowS # show :: ErrorBound -> String # showList :: [ErrorBound] -> ShowS #
NFData ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods rnf :: ErrorBound -> () #
Eq ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods (==) :: ErrorBound -> ErrorBound -> Bool # (/=) :: ErrorBound -> ErrorBound -> Bool #
Ord ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods compare :: ErrorBound -> ErrorBound -> Ordering # (<) :: ErrorBound -> ErrorBound -> Bool # (<=) :: ErrorBound -> ErrorBound -> Bool # (>) :: ErrorBound -> ErrorBound -> Bool # (>=) :: ErrorBound -> ErrorBound -> Bool # max :: ErrorBound -> ErrorBound -> ErrorBound # min :: ErrorBound -> ErrorBound -> ErrorBound #
Convertible MPBall ErrorBound Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvert :: MPBall -> ConvertResult ErrorBound #
Convertible MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvert :: MPFloat -> ConvertResult ErrorBound #
Convertible Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvert :: Rational -> ConvertResult ErrorBound #
Convertible Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvert :: Integer -> ConvertResult ErrorBound #
Convertible Int ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvert :: Int -> ConvertResult ErrorBound #
CanAddAsymmetric ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type AddType ErrorBound ErrorBound # Methods add :: ErrorBound -> ErrorBound -> AddType ErrorBound ErrorBound #
CanAddAsymmetric ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type AddType ErrorBound MPFloat # Methods add :: ErrorBound -> MPFloat -> AddType ErrorBound MPFloat #
CanAddAsymmetric MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type AddType MPFloat ErrorBound # Methods add :: MPFloat -> ErrorBound -> AddType MPFloat ErrorBound #
CanDiv ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type DivType ErrorBound Integer # Methods divide :: ErrorBound -> Integer -> DivType ErrorBound Integer #
HasEqAsymmetric ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType ErrorBound Rational # Methods equalTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational # notEqualTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational #
HasEqAsymmetric ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType ErrorBound Integer # Methods equalTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer # notEqualTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer #
HasEqAsymmetric ErrorBound Int Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType ErrorBound Int # Methods equalTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int # notEqualTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int #
HasEqAsymmetric Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType Rational ErrorBound # Methods equalTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound # notEqualTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound #
HasEqAsymmetric Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType Integer ErrorBound # Methods equalTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound # notEqualTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound #
HasEqAsymmetric Int ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type EqCompareType Int ErrorBound # Methods equalTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound # notEqualTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound #
ConvertibleExactly ErrorBound MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: ErrorBound -> ConvertResult MPBall #
ConvertibleExactly ErrorBound Dyadic Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult Dyadic #
ConvertibleExactly ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult ErrorBound #
ConvertibleExactly ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult MPFloat #
ConvertibleExactly ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult Rational #
CanMinMaxAsymmetric ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MinMaxType ErrorBound ErrorBound # Methods min :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound # max :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound #
CanMulAsymmetric ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType ErrorBound ErrorBound # Methods mul :: ErrorBound -> ErrorBound -> MulType ErrorBound ErrorBound #
CanMulAsymmetric ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType ErrorBound MPFloat # Methods mul :: ErrorBound -> MPFloat -> MulType ErrorBound MPFloat #
CanMulAsymmetric ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType ErrorBound Rational # Methods mul :: ErrorBound -> Rational -> MulType ErrorBound Rational #
CanMulAsymmetric ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType ErrorBound Integer # Methods mul :: ErrorBound -> Integer -> MulType ErrorBound Integer #
CanMulAsymmetric MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType MPFloat ErrorBound # Methods mul :: MPFloat -> ErrorBound -> MulType MPFloat ErrorBound #
CanMulAsymmetric Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType Rational ErrorBound # Methods mul :: Rational -> ErrorBound -> MulType Rational ErrorBound #
CanMulAsymmetric Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type MulType Integer ErrorBound # Methods mul :: Integer -> ErrorBound -> MulType Integer ErrorBound #
HasOrderAsymmetric ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType ErrorBound ErrorBound # Methods lessThan :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound # greaterThan :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound # leq :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound # geq :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound #
HasOrderAsymmetric ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType ErrorBound MPFloat # Methods lessThan :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat # greaterThan :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat # leq :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat # geq :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat #
HasOrderAsymmetric ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType ErrorBound Rational # Methods lessThan :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational # greaterThan :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational # leq :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational # geq :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational #
HasOrderAsymmetric ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType ErrorBound Integer # Methods lessThan :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer # greaterThan :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer # leq :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer # geq :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer #
HasOrderAsymmetric ErrorBound Int Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType ErrorBound Int # Methods lessThan :: ErrorBound -> Int -> OrderCompareType ErrorBound Int # greaterThan :: ErrorBound -> Int -> OrderCompareType ErrorBound Int # leq :: ErrorBound -> Int -> OrderCompareType ErrorBound Int # geq :: ErrorBound -> Int -> OrderCompareType ErrorBound Int #
HasOrderAsymmetric MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType MPFloat ErrorBound # Methods lessThan :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound # greaterThan :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound # leq :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound # geq :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound #
HasOrderAsymmetric Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType Rational ErrorBound # Methods lessThan :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound # greaterThan :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound # leq :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound # geq :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound #
HasOrderAsymmetric Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType Integer ErrorBound # Methods lessThan :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound # greaterThan :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound # leq :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound # geq :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound #
HasOrderAsymmetric Int ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound Associated Types type OrderCompareType Int ErrorBound # Methods lessThan :: Int -> ErrorBound -> OrderCompareType Int ErrorBound # greaterThan :: Int -> ErrorBound -> OrderCompareType Int ErrorBound # leq :: Int -> ErrorBound -> OrderCompareType Int ErrorBound # geq :: Int -> ErrorBound -> OrderCompareType Int ErrorBound #
type Rep ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type Rep ErrorBound = D1 ('MetaData "ErrorBound" "AERN2.MP.ErrorBound" "aern2-mp-0.2.15.1-6xeEefByTke3KEoNxGQRX3" 'True) (C1 ('MetaCons "ErrorBound" 'PrefixI 'True) (S1 ('MetaSel ('Just "er2mp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat)))
type AddType ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type AddType ErrorBound ErrorBound = ErrorBound
type AddType ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound type AddType ErrorBound MPFloat = ErrorBound
type AddType MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type AddType MPFloat ErrorBound = ErrorBound
type DivType ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound type DivType ErrorBound Integer = ErrorBound
type EqCompareType ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType ErrorBound Rational = Bool
type EqCompareType ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType ErrorBound Integer = Bool
type EqCompareType ErrorBound Int Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType ErrorBound Int = Bool
type EqCompareType Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType Rational ErrorBound = Bool
type EqCompareType Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType Integer ErrorBound = Bool
type EqCompareType Int ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type EqCompareType Int ErrorBound = Bool
type MinMaxType ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type MinMaxType ErrorBound ErrorBound = ErrorBound
type MulType ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType ErrorBound ErrorBound = ErrorBound
type MulType ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType ErrorBound MPFloat = ErrorBound
type MulType ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType ErrorBound Rational = ErrorBound
type MulType ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType ErrorBound Integer = ErrorBound
type MulType MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType MPFloat ErrorBound = ErrorBound
type MulType Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType Rational ErrorBound = ErrorBound
type MulType Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type MulType Integer ErrorBound = ErrorBound
type OrderCompareType ErrorBound ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType ErrorBound ErrorBound = Bool
type OrderCompareType ErrorBound MPFloat Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType ErrorBound MPFloat = Bool
type OrderCompareType ErrorBound Rational Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType ErrorBound Rational = Bool
type OrderCompareType ErrorBound Integer Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType ErrorBound Integer = Bool
type OrderCompareType ErrorBound Int Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType ErrorBound Int = Bool
type OrderCompareType MPFloat ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType MPFloat ErrorBound = Bool
type OrderCompareType Rational ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType Rational ErrorBound = Bool
type OrderCompareType Integer ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType Integer ErrorBound = Bool
type OrderCompareType Int ErrorBound Source #
Instance details Defined in AERN2.MP.ErrorBound type OrderCompareType Int ErrorBound = Bool

errorBound :: CanBeErrorBound t => t -> ErrorBound Source #

module AERN2.MP.Enclosure

The Ball type

data MPBall Source #

Constructors

MPBall
Fields ball_value :: MPFloat ball_error :: ErrorBound

Instances

Instances details

Arbitrary MPBall Source #
Instance details Defined in AERN2.MP.Ball.Tests Methods arbitrary :: Gen MPBall # shrink :: MPBall -> [MPBall] #
HasAccuracy MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getAccuracy :: MPBall -> Accuracy Source # getFiniteAccuracy :: MPBall -> Accuracy Source #
HasApproximate MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type Approximate MPBall Source # Methods getApproximate :: Accuracy -> MPBall -> Approximate MPBall Source #
ShowWithAccuracy MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods showWithAccuracy :: Accuracy -> MPBall -> String Source #
IsBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type CentreType MPBall Source # Methods centre :: MPBall -> CentreType MPBall Source # centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound) Source # centreAsBall :: MPBall -> MPBall Source # radius :: MPBall -> ErrorBound Source # updateRadius :: (ErrorBound -> ErrorBound) -> MPBall -> MPBall Source # makeExactCentre :: MPBall -> MPBall Source #
IsInterval MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type IntervalEndpoint MPBall Source # Methods endpoints :: MPBall -> (IntervalEndpoint MPBall, IntervalEndpoint MPBall) Source # fromEndpoints :: IntervalEndpoint MPBall -> IntervalEndpoint MPBall -> MPBall Source #
CanSetPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods setPrecision :: Precision -> MPBall -> MPBall Source #
HasPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getPrecision :: MPBall -> Precision Source #
HasNorm MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getNormLog :: MPBall -> NormLog Source #
CanNormalize MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods normalize :: MPBall -> MPBall Source #
Floating MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods pi :: MPBall # exp :: MPBall -> MPBall # log :: MPBall -> MPBall # sqrt :: MPBall -> MPBall # (**) :: MPBall -> MPBall -> MPBall # logBase :: MPBall -> MPBall -> MPBall # sin :: MPBall -> MPBall # cos :: MPBall -> MPBall # tan :: MPBall -> MPBall # asin :: MPBall -> MPBall # acos :: MPBall -> MPBall # atan :: MPBall -> MPBall # sinh :: MPBall -> MPBall # cosh :: MPBall -> MPBall # tanh :: MPBall -> MPBall # asinh :: MPBall -> MPBall # acosh :: MPBall -> MPBall # atanh :: MPBall -> MPBall # log1p :: MPBall -> MPBall # expm1 :: MPBall -> MPBall # log1pexp :: MPBall -> MPBall # log1mexp :: MPBall -> MPBall #
Generic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type Rep MPBall :: Type -> Type # Methods from :: MPBall -> Rep MPBall x # to :: Rep MPBall x -> MPBall #
Num MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (+) :: MPBall -> MPBall -> MPBall # (-) :: MPBall -> MPBall -> MPBall # (*) :: MPBall -> MPBall -> MPBall # negate :: MPBall -> MPBall # abs :: MPBall -> MPBall # signum :: MPBall -> MPBall # fromInteger :: Integer -> MPBall #
Fractional MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (/) :: MPBall -> MPBall -> MPBall # recip :: MPBall -> MPBall # fromRational :: Rational -> MPBall #
Show MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods showsPrec :: Int -> MPBall -> ShowS # show :: MPBall -> String # showList :: [MPBall] -> ShowS #
NFData MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods rnf :: MPBall -> () #
Eq MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (==) :: MPBall -> MPBall -> Bool # (/=) :: MPBall -> MPBall -> Bool #
Ord MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods compare :: MPBall -> MPBall -> Ordering # (<) :: MPBall -> MPBall -> Bool # (<=) :: MPBall -> MPBall -> Bool # (>) :: MPBall -> MPBall -> Bool # (>=) :: MPBall -> MPBall -> Bool # max :: MPBall -> MPBall -> MPBall # min :: MPBall -> MPBall -> MPBall #
CanNeg MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type NegType MPBall # Methods negate :: MPBall -> NegType MPBall #
CanExp MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type ExpType MPBall # Methods exp :: MPBall -> ExpType MPBall #
CanLog MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type LogType MPBall # Methods log :: MPBall -> LogType MPBall #
CanSinCos MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type SinCosType MPBall # Methods cos :: MPBall -> SinCosType MPBall # sin :: MPBall -> SinCosType MPBall #
CanSqrt MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type SqrtType MPBall # Methods sqrt :: MPBall -> SqrtType MPBall #
CanTestFinite MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods isInfinite :: MPBall -> Bool # isFinite :: MPBall -> Bool #
CanTestInteger MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods certainlyNotInteger :: MPBall -> Bool # certainlyInteger :: MPBall -> Bool # certainlyIntegerGetIt :: MPBall -> Maybe Integer #
CanTestNaN MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods isNaN :: MPBall -> Bool #
CanTestValid MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods isValid :: MPBall -> Bool #
CanTestZero MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyZero :: MPBall -> Bool # isCertainlyNonZero :: MPBall -> Bool #
CanAbs MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type AbsType MPBall # Methods abs :: MPBall -> AbsType MPBall #
CanTestPosNeg MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyPositive :: MPBall -> Bool # isCertainlyNonNegative :: MPBall -> Bool # isCertainlyNegative :: MPBall -> Bool # isCertainlyNonPositive :: MPBall -> Bool #
CanTestIsIntegerType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods isIntegerType :: MPBall -> Bool #
CanGiveUpIfVeryInaccurate MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods giveUpIfVeryInaccurate :: CN MPBall -> CN MPBall #
OrderedCertainlyRing MPBall Source #
Instance details Defined in AERN2.MP.Ball
OrderedRing MPBall Source #
Instance details Defined in AERN2.MP.Ball
Ring MPBall Source #
Instance details Defined in AERN2.MP.Ball
HasIntegerBounds MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods integerBounds :: MPBall -> (Integer, Integer) #
CanIntersectAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall MPBall Source # Methods intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall Source #
CanBeErrorBound t => CanPlusMinus MPBall t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType MPBall t Source # Methods plusMinus :: MPBall -> t -> PlusMinusType MPBall t Source #
CanTestContains MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> MPBall -> Bool Source #
CanTestContains MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Dyadic -> Bool Source #
CanTestContains MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Rational -> Bool Source #
CanTestContains MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Integer -> Bool Source #
CanTestContains MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Int -> Bool Source #
CanUnionAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall MPBall Source # Methods union :: MPBall -> MPBall -> UnionType MPBall MPBall Source #
ConvertibleWithPrecision Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall Source #
ConvertibleWithPrecision Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Rational -> ConvertResult MPBall Source #
ConvertibleWithPrecision Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Integer -> ConvertResult MPBall Source #
ConvertibleWithPrecision Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Int -> ConvertResult MPBall Source #
Convertible MPBall ErrorBound Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvert :: MPBall -> ConvertResult ErrorBound #
CanAddAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall MPBall # Methods add :: MPBall -> MPBall -> AddType MPBall MPBall #
CanAddAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Dyadic # Methods add :: MPBall -> Dyadic -> AddType MPBall Dyadic #
CanAddAsymmetric MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Rational # Methods add :: MPBall -> Rational -> AddType MPBall Rational #
CanAddAsymmetric MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Integer # Methods add :: MPBall -> Integer -> AddType MPBall Integer #
CanAddAsymmetric MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Int # Methods add :: MPBall -> Int -> AddType MPBall Int #
CanAddAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Dyadic MPBall # Methods add :: Dyadic -> MPBall -> AddType Dyadic MPBall #
CanAddAsymmetric Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Rational MPBall # Methods add :: Rational -> MPBall -> AddType Rational MPBall #
CanAddAsymmetric Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Integer MPBall # Methods add :: Integer -> MPBall -> AddType Integer MPBall #
CanAddAsymmetric Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Int MPBall # Methods add :: Int -> MPBall -> AddType Int MPBall #
CanSub MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall MPBall # Methods sub :: MPBall -> MPBall -> SubType MPBall MPBall #
CanSub MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Dyadic # Methods sub :: MPBall -> Dyadic -> SubType MPBall Dyadic #
CanSub MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Rational # Methods sub :: MPBall -> Rational -> SubType MPBall Rational #
CanSub MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Integer # Methods sub :: MPBall -> Integer -> SubType MPBall Integer #
CanSub MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Int # Methods sub :: MPBall -> Int -> SubType MPBall Int #
CanSub Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Dyadic MPBall # Methods sub :: Dyadic -> MPBall -> SubType Dyadic MPBall #
CanSub Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Rational MPBall # Methods sub :: Rational -> MPBall -> SubType Rational MPBall #
CanSub Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Integer MPBall # Methods sub :: Integer -> MPBall -> SubType Integer MPBall #
CanSub Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Int MPBall # Methods sub :: Int -> MPBall -> SubType Int MPBall #
CanDiv MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall MPBall # Methods divide :: MPBall -> MPBall -> DivType MPBall MPBall #
CanDiv MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall Dyadic # Methods divide :: MPBall -> Dyadic -> DivType MPBall Dyadic #
CanDiv MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall Rational # Methods divide :: MPBall -> Rational -> DivType MPBall Rational #
CanDiv MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall Integer # Methods divide :: MPBall -> Integer -> DivType MPBall Integer #
CanDiv MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall Int # Methods divide :: MPBall -> Int -> DivType MPBall Int #
CanDiv Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Dyadic MPBall # Methods divide :: Dyadic -> MPBall -> DivType Dyadic MPBall #
CanDiv Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Rational MPBall # Methods divide :: Rational -> MPBall -> DivType Rational MPBall #
CanDiv Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Integer MPBall # Methods divide :: Integer -> MPBall -> DivType Integer MPBall #
CanDiv Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Int MPBall # Methods divide :: Int -> MPBall -> DivType Int MPBall #
HasEqAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall MPBall # Methods equalTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall # notEqualTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall #
HasEqAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Dyadic # Methods equalTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic # notEqualTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic #
HasEqAsymmetric MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Rational # Methods equalTo :: MPBall -> Rational -> EqCompareType MPBall Rational # notEqualTo :: MPBall -> Rational -> EqCompareType MPBall Rational #
HasEqAsymmetric MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Integer # Methods equalTo :: MPBall -> Integer -> EqCompareType MPBall Integer # notEqualTo :: MPBall -> Integer -> EqCompareType MPBall Integer #
HasEqAsymmetric MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Int # Methods equalTo :: MPBall -> Int -> EqCompareType MPBall Int # notEqualTo :: MPBall -> Int -> EqCompareType MPBall Int #
HasEqAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Dyadic MPBall # Methods equalTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall # notEqualTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall #
HasEqAsymmetric Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Rational MPBall # Methods equalTo :: Rational -> MPBall -> EqCompareType Rational MPBall # notEqualTo :: Rational -> MPBall -> EqCompareType Rational MPBall #
HasEqAsymmetric Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Integer MPBall # Methods equalTo :: Integer -> MPBall -> EqCompareType Integer MPBall # notEqualTo :: Integer -> MPBall -> EqCompareType Integer MPBall #
HasEqAsymmetric Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Int MPBall # Methods equalTo :: Int -> MPBall -> EqCompareType Int MPBall # notEqualTo :: Int -> MPBall -> EqCompareType Int MPBall #
ConvertibleExactly MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: MPBall -> ConvertResult MPBall #
ConvertibleExactly Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Dyadic -> ConvertResult MPBall #
ConvertibleExactly ErrorBound MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: ErrorBound -> ConvertResult MPBall #
ConvertibleExactly Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Integer -> ConvertResult MPBall #
ConvertibleExactly Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Int -> ConvertResult MPBall #
CanMinMaxAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall MPBall # Methods min :: MPBall -> MPBall -> MinMaxType MPBall MPBall # max :: MPBall -> MPBall -> MinMaxType MPBall MPBall #
CanMinMaxAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Dyadic # Methods min :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic # max :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic #
CanMinMaxAsymmetric MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Rational # Methods min :: MPBall -> Rational -> MinMaxType MPBall Rational # max :: MPBall -> Rational -> MinMaxType MPBall Rational #
CanMinMaxAsymmetric MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Integer # Methods min :: MPBall -> Integer -> MinMaxType MPBall Integer # max :: MPBall -> Integer -> MinMaxType MPBall Integer #
CanMinMaxAsymmetric MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Int # Methods min :: MPBall -> Int -> MinMaxType MPBall Int # max :: MPBall -> Int -> MinMaxType MPBall Int #
CanMinMaxAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Dyadic MPBall # Methods min :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall # max :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall #
CanMinMaxAsymmetric Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Rational MPBall # Methods min :: Rational -> MPBall -> MinMaxType Rational MPBall # max :: Rational -> MPBall -> MinMaxType Rational MPBall #
CanMinMaxAsymmetric Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Integer MPBall # Methods min :: Integer -> MPBall -> MinMaxType Integer MPBall # max :: Integer -> MPBall -> MinMaxType Integer MPBall #
CanMinMaxAsymmetric Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Int MPBall # Methods min :: Int -> MPBall -> MinMaxType Int MPBall # max :: Int -> MPBall -> MinMaxType Int MPBall #
CanMulAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall MPBall # Methods mul :: MPBall -> MPBall -> MulType MPBall MPBall #
CanMulAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Dyadic # Methods mul :: MPBall -> Dyadic -> MulType MPBall Dyadic #
CanMulAsymmetric MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Rational # Methods mul :: MPBall -> Rational -> MulType MPBall Rational #
CanMulAsymmetric MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Integer # Methods mul :: MPBall -> Integer -> MulType MPBall Integer #
CanMulAsymmetric MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Int # Methods mul :: MPBall -> Int -> MulType MPBall Int #
CanMulAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Dyadic MPBall # Methods mul :: Dyadic -> MPBall -> MulType Dyadic MPBall #
CanMulAsymmetric Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Rational MPBall # Methods mul :: Rational -> MPBall -> MulType Rational MPBall #
CanMulAsymmetric Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Integer MPBall # Methods mul :: Integer -> MPBall -> MulType Integer MPBall #
CanMulAsymmetric Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Int MPBall # Methods mul :: Int -> MPBall -> MulType Int MPBall #
HasOrderAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall MPBall # Methods lessThan :: MPBall -> MPBall -> OrderCompareType MPBall MPBall # greaterThan :: MPBall -> MPBall -> OrderCompareType MPBall MPBall # leq :: MPBall -> MPBall -> OrderCompareType MPBall MPBall # geq :: MPBall -> MPBall -> OrderCompareType MPBall MPBall #
HasOrderAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Dyadic # Methods lessThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # greaterThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # leq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # geq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic #
HasOrderAsymmetric MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Rational # Methods lessThan :: MPBall -> Rational -> OrderCompareType MPBall Rational # greaterThan :: MPBall -> Rational -> OrderCompareType MPBall Rational # leq :: MPBall -> Rational -> OrderCompareType MPBall Rational # geq :: MPBall -> Rational -> OrderCompareType MPBall Rational #
HasOrderAsymmetric MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Integer # Methods lessThan :: MPBall -> Integer -> OrderCompareType MPBall Integer # greaterThan :: MPBall -> Integer -> OrderCompareType MPBall Integer # leq :: MPBall -> Integer -> OrderCompareType MPBall Integer # geq :: MPBall -> Integer -> OrderCompareType MPBall Integer #
HasOrderAsymmetric MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Int # Methods lessThan :: MPBall -> Int -> OrderCompareType MPBall Int # greaterThan :: MPBall -> Int -> OrderCompareType MPBall Int # leq :: MPBall -> Int -> OrderCompareType MPBall Int # geq :: MPBall -> Int -> OrderCompareType MPBall Int #
HasOrderAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Dyadic MPBall # Methods lessThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # greaterThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # leq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # geq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall #
HasOrderAsymmetric Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Rational MPBall # Methods lessThan :: Rational -> MPBall -> OrderCompareType Rational MPBall # greaterThan :: Rational -> MPBall -> OrderCompareType Rational MPBall # leq :: Rational -> MPBall -> OrderCompareType Rational MPBall # geq :: Rational -> MPBall -> OrderCompareType Rational MPBall #
HasOrderAsymmetric Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Integer MPBall # Methods lessThan :: Integer -> MPBall -> OrderCompareType Integer MPBall # greaterThan :: Integer -> MPBall -> OrderCompareType Integer MPBall # leq :: Integer -> MPBall -> OrderCompareType Integer MPBall # geq :: Integer -> MPBall -> OrderCompareType Integer MPBall #
HasOrderAsymmetric Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Int MPBall # Methods lessThan :: Int -> MPBall -> OrderCompareType Int MPBall # greaterThan :: Int -> MPBall -> OrderCompareType Int MPBall # leq :: Int -> MPBall -> OrderCompareType Int MPBall # geq :: Int -> MPBall -> OrderCompareType Int MPBall #
CanPow MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall MPBall # type PPowType MPBall MPBall # Methods pow :: MPBall -> MPBall -> PowType MPBall MPBall # ppow :: MPBall -> MPBall -> PPowType MPBall MPBall #
CanPow MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall Dyadic # type PPowType MPBall Dyadic # Methods pow :: MPBall -> Dyadic -> PowType MPBall Dyadic # ppow :: MPBall -> Dyadic -> PPowType MPBall Dyadic #
CanPow MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall Rational # type PPowType MPBall Rational # Methods pow :: MPBall -> Rational -> PowType MPBall Rational # ppow :: MPBall -> Rational -> PPowType MPBall Rational #
CanPow MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall Integer # type PPowType MPBall Integer # Methods pow :: MPBall -> Integer -> PowType MPBall Integer # ppow :: MPBall -> Integer -> PPowType MPBall Integer #
CanPow MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall Int # type PPowType MPBall Int # Methods pow :: MPBall -> Int -> PowType MPBall Int # ppow :: MPBall -> Int -> PPowType MPBall Int #
CanPow Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Rational MPBall # type PPowType Rational MPBall # Methods pow :: Rational -> MPBall -> PowType Rational MPBall # ppow :: Rational -> MPBall -> PPowType Rational MPBall #
CanPow Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Integer MPBall # type PPowType Integer MPBall # Methods pow :: Integer -> MPBall -> PowType Integer MPBall # ppow :: Integer -> MPBall -> PPowType Integer MPBall #
CanPow Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Int MPBall # type PPowType Int MPBall # Methods pow :: Int -> MPBall -> PowType Int MPBall # ppow :: Int -> MPBall -> PPowType Int MPBall #
CanDivIMod MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivIType MPBall MPBall # type ModType MPBall MPBall # Methods divIMod :: MPBall -> MPBall -> (DivIType MPBall MPBall, ModType MPBall MPBall) # mod :: MPBall -> MPBall -> ModType MPBall MPBall # divI :: MPBall -> MPBall -> DivIType MPBall MPBall #
(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), KnownNat p) => HasLimits ix (CN (WithCurrentPrec p (CN MPBall))) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.Limit Associated Types type LimitType ix (CN (WithCurrentPrec p (CN MPBall))) Source # Methods limit :: (ix -> CN (WithCurrentPrec p (CN MPBall))) -> LimitType ix (CN (WithCurrentPrec p (CN MPBall))) Source #
CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall (CN b) # Methods add :: MPBall -> CN b -> AddType MPBall (CN b) #
CanSub MPBall b => CanSub MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall (CN b) # Methods sub :: MPBall -> CN b -> SubType MPBall (CN b) #
(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall (CN b) # Methods divide :: MPBall -> CN b -> DivType MPBall (CN b) #
CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall (CN b) # Methods mul :: MPBall -> CN b -> MulType MPBall (CN b) #
CanPow MPBall b => CanPow MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall (CN b) # type PPowType MPBall (CN b) # Methods pow :: MPBall -> CN b -> PowType MPBall (CN b) # ppow :: MPBall -> CN b -> PPowType MPBall (CN b) #
HasLimits Rational (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit Associated Types type LimitType Rational (CN MPBall -> CN MPBall) Source # Methods limit :: (Rational -> CN MPBall -> CN MPBall) -> LimitType Rational (CN MPBall -> CN MPBall) Source #
HasLimits Integer (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit Associated Types type LimitType Integer (CN MPBall -> CN MPBall) Source # Methods limit :: (Integer -> CN MPBall -> CN MPBall) -> LimitType Integer (CN MPBall -> CN MPBall) Source #
HasLimits Int (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit Associated Types type LimitType Int (CN MPBall -> CN MPBall) Source # Methods limit :: (Int -> CN MPBall -> CN MPBall) -> LimitType Int (CN MPBall -> CN MPBall) Source #
(CanIntersectAsymmetric MPBall b, CanBeErrors es) => CanIntersectAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall (CollectErrors es b) Source # Methods intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b) Source #
(CanUnionAsymmetric MPBall b, CanBeErrors es) => CanUnionAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall (CollectErrors es b) Source # Methods union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b) Source #
(HasEqAsymmetric MPBall b, IsBool (EqCompareType MPBall b), CanTestCertainly (EqCompareType MPBall b), CanBeErrors es) => HasEqAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall (CollectErrors es b) # Methods equalTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) # notEqualTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) #
(CanMinMaxAsymmetric MPBall b, CanBeErrors es) => CanMinMaxAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall (CollectErrors es b) # Methods min :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) # max :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) #
(HasOrderAsymmetric MPBall b, IsBool (OrderCompareType MPBall b), CanTestCertainly (OrderCompareType MPBall b), CanBeErrors es) => HasOrderAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall (CollectErrors es b) # Methods lessThan :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b) # greaterThan :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b) # leq :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b) # geq :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b) #
(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), KnownNat p) => HasLimits ix (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.Limit Associated Types type LimitType ix (WithCurrentPrec p (CN MPBall)) Source # Methods limit :: (ix -> WithCurrentPrec p (CN MPBall)) -> LimitType ix (WithCurrentPrec p (CN MPBall)) Source #
OrderedCertainlyRing (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
OrderedRing (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
Ring (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
CanBeErrorBound t => CanPlusMinus (CN MPBall) t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType (CN MPBall) t Source # Methods plusMinus :: CN MPBall -> t -> PlusMinusType (CN MPBall) t Source #
CanAddAsymmetric a MPBall => CanAddAsymmetric (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType (CN a) MPBall # Methods add :: CN a -> MPBall -> AddType (CN a) MPBall #
CanSub a MPBall => CanSub (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType (CN a) MPBall # Methods sub :: CN a -> MPBall -> SubType (CN a) MPBall #
CanDiv a MPBall => CanDiv (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType (CN a) MPBall # Methods divide :: CN a -> MPBall -> DivType (CN a) MPBall #
CanMulAsymmetric a MPBall => CanMulAsymmetric (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType (CN a) MPBall # Methods mul :: CN a -> MPBall -> MulType (CN a) MPBall #
CanPow a MPBall => CanPow (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType (CN a) MPBall # type PPowType (CN a) MPBall # Methods pow :: CN a -> MPBall -> PowType (CN a) MPBall # ppow :: CN a -> MPBall -> PPowType (CN a) MPBall #
(CanIntersectAsymmetric a MPBall, CanBeErrors es) => CanIntersectAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType (CollectErrors es a) MPBall Source # Methods intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall Source #
(CanUnionAsymmetric a MPBall, CanBeErrors es) => CanUnionAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType (CollectErrors es a) MPBall Source # Methods union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall Source #
ConvertibleWithPrecision (Rational, Rational) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult MPBall Source #
(HasEqAsymmetric a MPBall, IsBool (EqCompareType a MPBall), CanTestCertainly (EqCompareType a MPBall), CanBeErrors es) => HasEqAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType (CollectErrors es a) MPBall # Methods equalTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall # notEqualTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall #
(ConvertibleExactly c Dyadic, ConvertibleExactly e Dyadic, Show c, Show e, Typeable c, Typeable e) => ConvertibleExactly (c, e) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: (c, e) -> ConvertResult MPBall #
(CanMinMaxAsymmetric a MPBall, CanBeErrors es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType (CollectErrors es a) MPBall # Methods min :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall # max :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall #
(HasOrderAsymmetric a MPBall, IsBool (OrderCompareType a MPBall), CanTestCertainly (OrderCompareType a MPBall), CanBeErrors es) => HasOrderAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType (CollectErrors es a) MPBall # Methods lessThan :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall # greaterThan :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall # leq :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall # geq :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall #
KnownNat p => Floating (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.PreludeInstances Methods pi :: WithCurrentPrec p (CN MPBall) # exp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # log :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # sqrt :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # (**) :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # logBase :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # sin :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # cos :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # tan :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # asin :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # acos :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # atan :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # sinh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # cosh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # tanh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # asinh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # acosh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # atanh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # log1p :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # expm1 :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # log1pexp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) # log1mexp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) #
KnownNat p => Field (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec
KnownNat p => OrderedField (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec
KnownNat p => OrderedRing (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec
KnownNat p => Ring (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec
type Approximate MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type Approximate MPBall = (MPFloat, Bool)
type CentreType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type CentreType MPBall = Dyadic
type IntervalEndpoint MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type IntervalEndpoint MPBall = MPFloat
type Rep MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type Rep MPBall = D1 ('MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.2.15.1-6xeEefByTke3KEoNxGQRX3" 'False) (C1 ('MetaCons "MPBall" 'PrefixI 'True) (S1 ('MetaSel ('Just "ball_value") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat) :*: S1 ('MetaSel ('Just "ball_error") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ErrorBound)))
type NegType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type NegType MPBall = MPBall
type ExpType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type ExpType MPBall = MPBall
type LogType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type LogType MPBall = MPBall
type SinCosType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type SinCosType MPBall = MPBall
type SqrtType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type SqrtType MPBall = MPBall
type AbsType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type AbsType MPBall = MPBall
type IntersectionType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall MPBall = CN MPBall
type PlusMinusType MPBall t Source #
Instance details Defined in AERN2.MP.Ball.Conversions type PlusMinusType MPBall t = MPBall
type UnionType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall MPBall = CN MPBall
type AddType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall MPBall = MPBall
type AddType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Dyadic = MPBall
type AddType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Rational = MPBall
type AddType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Integer = MPBall
type AddType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Int = MPBall
type AddType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Dyadic MPBall = MPBall
type AddType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Rational MPBall = MPBall
type AddType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Integer MPBall = MPBall
type AddType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Int MPBall = MPBall
type SubType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall MPBall = AddType MPBall (NegType MPBall)
type SubType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type SubType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Rational = AddType MPBall (NegType Rational)
type SubType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Integer = AddType MPBall (NegType Integer)
type SubType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Int = AddType MPBall (NegType Int)
type SubType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Rational MPBall = AddType Rational (NegType MPBall)
type SubType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Integer MPBall = AddType Integer (NegType MPBall)
type SubType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Int MPBall = AddType Int (NegType MPBall)
type DivType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall MPBall = MPBall
type DivType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Dyadic = MPBall
type DivType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Rational = MPBall
type DivType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Integer = MPBall
type DivType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Int = MPBall
type DivType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic MPBall = MPBall
type DivType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Rational MPBall = MPBall
type DivType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Integer MPBall = MPBall
type DivType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Int MPBall = MPBall
type EqCompareType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall MPBall = Kleenean
type EqCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Dyadic = Kleenean
type EqCompareType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Rational = Kleenean
type EqCompareType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Integer = Kleenean
type EqCompareType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Int = Kleenean
type EqCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Dyadic MPBall = Kleenean
type EqCompareType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Rational MPBall = Kleenean
type EqCompareType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Integer MPBall = Kleenean
type EqCompareType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Int MPBall = Kleenean
type MinMaxType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall MPBall = MPBall
type MinMaxType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Dyadic = MPBall
type MinMaxType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Rational = MPBall
type MinMaxType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Integer = MPBall
type MinMaxType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Int = MPBall
type MinMaxType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Dyadic MPBall = MPBall
type MinMaxType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Rational MPBall = MPBall
type MinMaxType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Integer MPBall = MPBall
type MinMaxType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Int MPBall = MPBall
type MulType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall MPBall = MPBall
type MulType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Dyadic = MPBall
type MulType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Rational = MPBall
type MulType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Integer = MPBall
type MulType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Int = MPBall
type MulType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Dyadic MPBall = MPBall
type MulType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Rational MPBall = MPBall
type MulType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Integer MPBall = MPBall
type MulType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Int MPBall = MPBall
type OrderCompareType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall MPBall = Kleenean
type OrderCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Dyadic = Kleenean
type OrderCompareType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Rational = Kleenean
type OrderCompareType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Integer = Kleenean
type OrderCompareType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Int = Kleenean
type OrderCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Dyadic MPBall = Kleenean
type OrderCompareType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Rational MPBall = Kleenean
type OrderCompareType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Integer MPBall = Kleenean
type OrderCompareType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Int MPBall = Kleenean
type PPowType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType MPBall MPBall = PowType MPBall MPBall
type PPowType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType MPBall Dyadic = PowType MPBall Dyadic
type PPowType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType MPBall Rational = PowType MPBall Rational
type PPowType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall Integer = PowType MPBall Integer
type PPowType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall Int = PowType MPBall Int
type PPowType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType Rational MPBall = PowType Rational MPBall
type PPowType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType Integer MPBall = PowType Integer MPBall
type PPowType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PPowType Int MPBall = PowType Int MPBall
type PowType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall MPBall = MPBall
type PowType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Dyadic = MPBall
type PowType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Rational = MPBall
type PowType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Integer = MPBall
type PowType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Int = MPBall
type PowType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Rational MPBall = MPBall
type PowType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Integer MPBall = MPBall
type PowType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Int MPBall = MPBall
type DivIType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivIType MPBall MPBall = Integer
type ModType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type ModType MPBall MPBall = MPBall
type LimitType ix (CN (WithCurrentPrec p (CN MPBall))) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.Limit type LimitType ix (CN (WithCurrentPrec p (CN MPBall))) = WithCurrentPrec p (CN MPBall)
type AddType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall (CN b) = CN (AddType MPBall b)
type SubType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall (CN b) = CN (SubType MPBall b)
type DivType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall (CN b) = CN (DivType MPBall b)
type MulType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall (CN b) = CN (MulType MPBall b)
type PPowType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall (CN b) = PowType MPBall (CN b)
type PowType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall (CN b) = CN (PowType MPBall b)
type LimitType Rational (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit type LimitType Rational (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type LimitType Integer (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit type LimitType Integer (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type LimitType Int (CN MPBall -> CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball.Limit type LimitType Int (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type IntersectionType MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall (CollectErrors es b) = CollectErrors es (IntersectionType MPBall b)
type UnionType MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall (CollectErrors es b) = CollectErrors es (UnionType MPBall b)
type EqCompareType MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall (CollectErrors es b) = CollectErrors es (EqCompareType MPBall b)
type MinMaxType MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall (CollectErrors es b) = CollectErrors es (MinMaxType MPBall b)
type OrderCompareType MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall (CollectErrors es b) = CollectErrors es (OrderCompareType MPBall b)
type LimitType ix (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.Limit type LimitType ix (WithCurrentPrec p (CN MPBall)) = WithCurrentPrec p (CN MPBall)
type PlusMinusType (CN MPBall) t Source #
Instance details Defined in AERN2.MP.Ball.Conversions type PlusMinusType (CN MPBall) t = CN MPBall
type AddType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType (CN a) MPBall = CN (AddType a MPBall)
type SubType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType (CN a) MPBall = CN (SubType a MPBall)
type DivType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType (CN a) MPBall = CN (DivType a MPBall)
type MulType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType (CN a) MPBall = CN (MulType a MPBall)
type PPowType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type PPowType (CN a) MPBall = PowType (CN a) MPBall
type PowType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType (CN a) MPBall = CN (PowType a MPBall)
type IntersectionType (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType (CollectErrors es a) MPBall = CollectErrors es (IntersectionType a MPBall)
type UnionType (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType (CollectErrors es a) MPBall = CollectErrors es (UnionType a MPBall)
type EqCompareType (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType (CollectErrors es a) MPBall = CollectErrors es (EqCompareType a MPBall)
type MinMaxType (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType (CollectErrors es a) MPBall = CollectErrors es (MinMaxType a MPBall)
type OrderCompareType (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType (CollectErrors es a) MPBall = CollectErrors es (OrderCompareType a MPBall)

type CanBeMPBall t = ConvertibleExactly t MPBall Source #

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

cnMPBall :: CanBeMPBall a => CN a -> CN MPBall Source #

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall Source #

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

cnMPBallP :: CanBeMPBallP a => Precision -> CN a -> CN MPBall Source #

reducePrecionIfInaccurate :: MPBall -> MPBall Source #

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.

giveUpIfVeryInaccurate :: CanGiveUpIfVeryInaccurate t => CN t -> CN t #

If the value contains so little information that it is seen as useless, drop the value and add an error indicating what happened.

Ball operations (see also instances)

piBallP :: Precision -> MPBall Source #

intersectCNMPBall :: CN MPBall -> CN MPBall -> CN MPBall Source #

hullMPBall :: MPBall -> MPBall -> MPBall Source #

Helpers for constructing ball functions

byEndpointsMP :: (MPFloat -> MPFloat -> MPFloat) -> MPBall -> MPBall -> MPBall Source #

Compute an MPBall function from *exact* MPFloat operations on interval endpoints. This works only for *non-decreasing* operations, eg addition, min, max.

fromApproxWithLipschitz Source #

Arguments

:: (MPFloat -> BoundsCEDU MPFloat)	`fCEDU`: a version of `f` on MPFloat returning rigorous bounds
-> MPFloat	`lip` a Lipschitz constant for `f`, `lip > 0`
-> MPBall -> MPBall	`f` on MPBall rounding outwards

Computes a real function f from correctly rounded MPFR-approximations and a number lip which is a Lipschitz constant for f, i.e. |f(x) - f(y)| <= lip * |x - y| for all x,y.

Orphan instances

OrderedCertainlyRing MPBall Source #
Instance details
OrderedRing MPBall Source #
Instance details
Ring MPBall Source #
Instance details
OrderedCertainlyRing (CN MPBall) Source #
Instance details
OrderedRing (CN MPBall) Source #
Instance details
Ring (CN MPBall) Source #
Instance details