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

AERN2.MP.Ball.Type

Contents

Auxiliary types
The Ball type
Ball construction/extraction functions

Description

Arbitrary precision dyadic balls

Synopsis

module AERN2.MP.Precision
module AERN2.MP.Accuracy
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
fromMPFloatEndpoints :: MPFloat -> MPFloat -> MPBall
mpBallEndpoints :: MPBall -> (MPBall, MPBall)
fromMPBallEndpoints :: MPBall -> MPBall -> MPBall

Auxiliary types

module AERN2.MP.Precision

module AERN2.MP.Accuracy

module AERN2.MP.Enclosure

The Ball type

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 #

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.

Ball construction/extraction functions

fromMPFloatEndpoints :: MPFloat -> MPFloat -> MPBall Source #

mpBallEndpoints :: MPBall -> (MPBall, MPBall) Source #

fromMPBallEndpoints :: MPBall -> MPBall -> MPBall Source #