Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP

Contents

Interval (centre-radius) arithmetic
Supporting concepts

Description

Multiple-precision ball arithmetic

Synopsis

data MPBall = MPBall {
- ball_value :: MPFloat
- ball_error :: ErrorBound
}
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
giveUpIfVeryInaccurate :: CanGiveUpIfVeryInaccurate t => CN t -> CN t
module AERN2.Kleenean
module AERN2.Norm
module AERN2.MP.Precision
module AERN2.MP.Accuracy
module AERN2.MP.ErrorBound
module AERN2.MP.Enclosure

Interval (centre-radius) arithmetic

data MPBall Source #

Constructors

MPBall
Fields ball_value :: MPFloat ball_error :: ErrorBound

Instances

Instances details

Eq MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (==) :: MPBall -> MPBall -> Bool # (/=) :: MPBall -> MPBall -> Bool #
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 #
Fractional MPBall Source #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (/) :: MPBall -> MPBall -> MPBall # recip :: MPBall -> MPBall # fromRational :: Rational -> 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 #
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 #
Show MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods showsPrec :: Int -> MPBall -> ShowS # show :: MPBall -> String # showList :: [MPBall] -> ShowS #
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 #
Arbitrary MPBall Source #
Instance details Defined in AERN2.MP.Ball.Tests Methods arbitrary :: Gen MPBall # shrink :: MPBall -> [MPBall] #
NFData MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods rnf :: MPBall -> () #
CanSqrt MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type SqrtType MPBall # Methods sqrt :: MPBall -> SqrtType 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 #
Field MPBall Source #
Instance details Defined in AERN2.MP.Ball
OrderedField MPBall Source #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyField 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) #
Ring MPBall Source #
Instance details Defined in AERN2.MP.Ball
OrderedRing MPBall Source #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyRing MPBall Source #
Instance details Defined in AERN2.MP.Ball
CanAbs MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type AbsType MPBall # Methods abs :: MPBall -> AbsType MPBall #
CanTestNaN MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods isNaN :: MPBall -> Bool #
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 #
CanTestZero MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyZero :: MPBall -> Bool # isCertainlyNonZero :: MPBall -> Bool #
CanTestPosNeg MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyPositive :: MPBall -> Bool # isCertainlyNonNegative :: MPBall -> Bool # isCertainlyNegative :: MPBall -> Bool # isCertainlyNonPositive :: MPBall -> Bool #
CanNeg MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type NegType MPBall # Methods negate :: MPBall -> NegType MPBall #
CanGiveUpIfVeryInaccurate MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods giveUpIfVeryInaccurate :: CN MPBall -> CN MPBall #
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 #
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 #
HasAccuracy MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getAccuracy :: MPBall -> Accuracy Source # getFiniteAccuracy :: MPBall -> Accuracy 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 #
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 #
CanNormalize MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods normalize :: MPBall -> MPBall Source #
CanPow Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Int MPBall # Methods pow :: Int -> MPBall -> PowType Int MPBall #
CanPow Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Integer MPBall # Methods pow :: Integer -> MPBall -> PowType Integer MPBall #
CanPow Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType Rational MPBall # Methods pow :: Rational -> MPBall -> PowType Rational MPBall #
CanPow MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall Int # Methods pow :: MPBall -> Int -> PowType MPBall Int #
CanPow MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall Integer # Methods pow :: MPBall -> Integer -> PowType MPBall Integer #
CanPow MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall Rational # Methods pow :: MPBall -> Rational -> PowType MPBall Rational #
CanPow MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall Dyadic # Methods pow :: MPBall -> Dyadic -> PowType MPBall Dyadic #
CanPow MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall MPBall # Methods pow :: MPBall -> MPBall -> PowType MPBall 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 #
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 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 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 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 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 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 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 MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall MPBall # Methods divide :: MPBall -> MPBall -> DivType MPBall 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 #
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 #
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 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 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 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 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 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 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 MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall MPBall # Methods mul :: MPBall -> MPBall -> MulType MPBall 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 #
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 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 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 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 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 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 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 MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall MPBall # Methods add :: MPBall -> MPBall -> AddType MPBall 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 #
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 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 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 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 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 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 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 MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall MPBall # Methods sub :: MPBall -> MPBall -> SubType MPBall 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 #
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 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 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 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 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 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 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 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 #
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 #
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 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 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 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 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 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 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 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 #
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 #
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 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 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 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 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 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 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 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 #
ConvertibleExactly Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Int -> ConvertResult MPBall #
ConvertibleExactly Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Integer -> 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 MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: MPBall -> ConvertResult MPBall #
Convertible MPBall ErrorBound Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvert :: MPBall -> ConvertResult ErrorBound #
ConvertibleWithPrecision Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Int -> ConvertResult MPBall Source #
ConvertibleWithPrecision Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Integer -> ConvertResult MPBall Source #
ConvertibleWithPrecision Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Rational -> ConvertResult MPBall Source #
ConvertibleWithPrecision Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall 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 #
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 #
CanTestContains MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Int -> Bool Source #
CanTestContains MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Integer -> Bool Source #
CanTestContains MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Rational -> Bool Source #
CanTestContains MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Dyadic -> Bool Source #
CanTestContains MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> MPBall -> Bool 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 #
CanPow MPBall b => CanPow MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType MPBall (CN b) # Methods pow :: MPBall -> CN b -> PowType 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) #
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) #
(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) #
(HasEqAsymmetric MPBall b, IsBool (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) #
(HasOrderAsymmetric MPBall b, IsBool (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 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 #
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 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 #
(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 #
(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 #
(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), HasCurrentPrecision p) => HasLimits ix (WithCurrentPrec (CN MPBall) p) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec Associated Types type LimitType ix (WithCurrentPrec (CN MPBall) p) Source # Methods limit :: (ix -> WithCurrentPrec (CN MPBall) p) -> LimitType ix (WithCurrentPrec (CN MPBall) p) Source #
Field (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
OrderedField (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyField (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
Ring (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
OrderedRing (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyRing (CN MPBall) Source #
Instance details Defined in AERN2.MP.Ball
CanPow a MPBall => CanPow (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowType (CN a) MPBall # Methods pow :: CN a -> MPBall -> PowType (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 #
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 #
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 #
(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 #
(HasEqAsymmetric a MPBall, IsBool (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 #
(HasOrderAsymmetric a MPBall, IsBool (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 #
(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 #
ConvertibleWithPrecision (Rational, Rational) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult 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 #
(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 #
HasCurrentPrecision p => Floating (WithCurrentPrec (CN MPBall) p) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec Methods pi :: WithCurrentPrec (CN MPBall) p # exp :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # log :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # sqrt :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # (**) :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # logBase :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # sin :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # cos :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # tan :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # asin :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # acos :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # atan :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # sinh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # cosh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # tanh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # asinh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # acosh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # atanh :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # log1p :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # expm1 :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # log1pexp :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p # log1mexp :: WithCurrentPrec (CN MPBall) p -> WithCurrentPrec (CN MPBall) p #
type Rep MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type Rep MPBall = D1 ('MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.2.2.0-DTtN6apnExTAMCmcKkOJZI" '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 SqrtType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type SqrtType 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 AbsType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type AbsType MPBall = MPBall
type NegType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type NegType MPBall = MPBall
type Approximate MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type Approximate MPBall = (MPFloat, Bool)
type IntervalEndpoint MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type IntervalEndpoint MPBall = MPFloat
type CentreType MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type type CentreType MPBall = Dyadic
type PowType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Int MPBall = MPBall
type PowType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Integer MPBall = MPBall
type PowType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType Rational MPBall = MPBall
type PowType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Int = MPBall
type PowType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Integer = MPBall
type PowType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Rational = MPBall
type PowType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Dyadic = MPBall
type PowType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall MPBall = MPBall
type DivType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Int MPBall = MPBall
type DivType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Integer MPBall = MPBall
type DivType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Rational MPBall = MPBall
type DivType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic MPBall = MPBall
type DivType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Int = MPBall
type DivType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Integer = MPBall
type DivType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Rational = MPBall
type DivType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Dyadic = MPBall
type DivType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall MPBall = MPBall
type ModType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type ModType MPBall MPBall = MPBall
type DivIType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivIType MPBall MPBall = Integer
type MulType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Int MPBall = MPBall
type MulType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Integer MPBall = MPBall
type MulType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Rational MPBall = MPBall
type MulType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Dyadic MPBall = MPBall
type MulType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Int = MPBall
type MulType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Integer = MPBall
type MulType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Rational = MPBall
type MulType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Dyadic = MPBall
type MulType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall MPBall = MPBall
type AddType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Int MPBall = MPBall
type AddType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Integer MPBall = MPBall
type AddType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Rational MPBall = MPBall
type AddType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Dyadic MPBall = MPBall
type AddType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Int = MPBall
type AddType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Integer = MPBall
type AddType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Rational = MPBall
type AddType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Dyadic = MPBall
type AddType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall MPBall = MPBall
type SubType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Int MPBall = AddType Int (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 Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Rational MPBall = AddType Rational (NegType MPBall)
type SubType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Int = AddType MPBall (NegType Int)
type SubType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Integer = AddType MPBall (NegType Integer)
type SubType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Rational = AddType MPBall (NegType Rational)
type SubType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type SubType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall MPBall = AddType MPBall (NegType MPBall)
type MinMaxType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Int MPBall = MPBall
type MinMaxType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Integer MPBall = MPBall
type MinMaxType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Rational MPBall = MPBall
type MinMaxType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Int = MPBall
type MinMaxType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Integer = MPBall
type MinMaxType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Rational = MPBall
type MinMaxType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Dyadic = MPBall
type MinMaxType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall MPBall = MPBall
type EqCompareType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Int MPBall = Kleenean
type EqCompareType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Integer MPBall = Kleenean
type EqCompareType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Rational MPBall = Kleenean
type EqCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Dyadic MPBall = Kleenean
type EqCompareType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Int = Kleenean
type EqCompareType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Integer = Kleenean
type EqCompareType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Rational = Kleenean
type EqCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Dyadic = Kleenean
type EqCompareType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall MPBall = Kleenean
type OrderCompareType Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Int MPBall = Kleenean
type OrderCompareType Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Integer MPBall = Kleenean
type OrderCompareType Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Rational MPBall = Kleenean
type OrderCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Dyadic MPBall = Kleenean
type OrderCompareType MPBall Int Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Int = Kleenean
type OrderCompareType MPBall Integer Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Integer = Kleenean
type OrderCompareType MPBall Rational Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Rational = Kleenean
type OrderCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Dyadic = Kleenean
type OrderCompareType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall MPBall = Kleenean
type UnionType MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall MPBall = CN 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 PowType MPBall (CN b) Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall (CN b) = CN (PowType 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 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 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 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 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 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 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 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 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 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 LimitType ix (WithCurrentPrec (CN MPBall) p) Source #
Instance details Defined in AERN2.MP.WithCurrentPrec type LimitType ix (WithCurrentPrec (CN MPBall) p) = WithCurrentPrec (CN MPBall) p
type PowType (CN a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type PowType (CN a) MPBall = CN (PowType 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 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 PlusMinusType (CN MPBall) t Source #
Instance details Defined in AERN2.MP.Ball.Conversions type PlusMinusType (CN MPBall) t = CN 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 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 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 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 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 CanBeMPBall t = ConvertibleExactly t MPBall Source #

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

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall Source #

mpBallP :: CanBeMPBallP t => Precision -> t -> 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.

Supporting concepts

module AERN2.Kleenean

module AERN2.Norm

module AERN2.MP.Precision

module AERN2.MP.Accuracy

module AERN2.MP.ErrorBound

module AERN2.MP.Enclosure