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

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
type CanBeMPBallP t = ConvertibleWithPrecision t MPBall
mpBallP :: CanBeMPBallP t => Precision -> t -> MPBall
reducePrecionIfInaccurate :: MPBall -> MPBall
endpointsMP :: MPBall -> (MPFloat, MPFloat)
fromEndpointsMP :: MPFloat -> MPFloat -> MPBall

Auxiliary types

module AERN2.MP.Precision

module AERN2.MP.Accuracy

module AERN2.MP.Enclosure

The Ball type

data MPBall #

Constructors

MPBall
Fields ball_value :: MPFloat ball_error :: ErrorBound

Instances

Eq MPBall #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (==) :: MPBall -> MPBall -> Bool # (/=) :: MPBall -> MPBall -> Bool #
Floating MPBall #
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 #
Instance details Defined in AERN2.MP.Ball.PreludeOps Methods (/) :: MPBall -> MPBall -> MPBall # recip :: MPBall -> MPBall # fromRational :: Rational -> MPBall #
Num MPBall #
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 #
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 #
Instance details Defined in AERN2.MP.Ball.Type Methods showsPrec :: Int -> MPBall -> ShowS # show :: MPBall -> String # showList :: [MPBall] -> ShowS #
Generic MPBall #
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 #
Instance details Defined in AERN2.MP.Ball.Tests Methods arbitrary :: Gen MPBall # shrink :: MPBall -> [MPBall] #
CanSqrt MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type SqrtType MPBall :: Type # Methods sqrt :: MPBall -> SqrtType MPBall #
CanExp MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type ExpType MPBall :: Type # Methods exp :: MPBall -> ExpType MPBall #
CanLog MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type LogType MPBall :: Type # Methods log :: MPBall -> LogType MPBall #
CanSinCos MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type SinCosType MPBall :: Type # Methods cos :: MPBall -> SinCosType MPBall # sin :: MPBall -> SinCosType MPBall #
Field MPBall #
Instance details Defined in AERN2.MP.Ball
OrderedField MPBall #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyField MPBall #
Instance details Defined in AERN2.MP.Ball
Ring MPBall #
Instance details Defined in AERN2.MP.Ball
OrderedRing MPBall #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyRing MPBall #
Instance details Defined in AERN2.MP.Ball
HasIntegerBounds MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods integerBounds :: MPBall -> (Integer, Integer) #
CanAbs MPBall #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type AbsType MPBall :: Type # Methods abs :: MPBall -> AbsType MPBall #
CanTestNaN MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods isNaN :: MPBall -> Bool #
CanTestFinite MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods isInfinite :: MPBall -> Bool # isFinite :: MPBall -> Bool #
CanTestInteger MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods certainlyNotInteger :: MPBall -> Bool # certainlyInteger :: MPBall -> Bool # certainlyIntegerGetIt :: MPBall -> Maybe Integer #
CanTestZero MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyZero :: MPBall -> Bool # isCertainlyNonZero :: MPBall -> Bool #
CanTestPosNeg MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Methods isCertainlyPositive :: MPBall -> Bool # isCertainlyNonNegative :: MPBall -> Bool # isCertainlyNegative :: MPBall -> Bool # isCertainlyNonPositive :: MPBall -> Bool #
CanNeg MPBall #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type NegType MPBall :: Type # Methods negate :: MPBall -> NegType MPBall #
CanSetPrecision MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods setPrecision :: Precision -> MPBall -> MPBall #
HasPrecision MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods getPrecision :: MPBall -> Precision #
HasNorm MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods getNormLog :: MPBall -> NormLog #
HasApproximate MPBall #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type Approximate MPBall :: Type # Methods getApproximate :: Accuracy -> MPBall -> Approximate MPBall #
CanReduceSizeUsingAccuracyGuide MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods reduceSizeUsingAccuracyGuide :: Accuracy -> MPBall -> MPBall #
HasAccuracy MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods getAccuracy :: MPBall -> Accuracy #
IsBall MPBall #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type CentreType MPBall :: Type # Methods centre :: MPBall -> CentreType MPBall # centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound) # centreAsBall :: MPBall -> MPBall # radius :: MPBall -> ErrorBound # updateRadius :: (ErrorBound -> ErrorBound) -> MPBall -> MPBall # makeExactCentre :: MPBall -> MPBall #
CanNormalize MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods normalize :: MPBall -> MPBall #
Convertible MPBall ErrorBound #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvert :: MPBall -> ConvertResult ErrorBound #
CanDiv Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN Int MPBall :: Type # type DivType Int MPBall :: Type # Methods divideNoCN :: Int -> MPBall -> DivTypeNoCN Int MPBall # divide :: Int -> MPBall -> DivType Int MPBall #
CanDiv Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN Integer MPBall :: Type # type DivType Integer MPBall :: Type # Methods divideNoCN :: Integer -> MPBall -> DivTypeNoCN Integer MPBall # divide :: Integer -> MPBall -> DivType Integer MPBall #
CanDiv Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN Rational MPBall :: Type # type DivType Rational MPBall :: Type # Methods divideNoCN :: Rational -> MPBall -> DivTypeNoCN Rational MPBall # divide :: Rational -> MPBall -> DivType Rational MPBall #
CanDiv Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN Dyadic MPBall :: Type # type DivType Dyadic MPBall :: Type # Methods divideNoCN :: Dyadic -> MPBall -> DivTypeNoCN Dyadic MPBall # divide :: Dyadic -> MPBall -> DivType Dyadic MPBall #
CanDiv MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall Int :: Type # type DivType MPBall Int :: Type # Methods divideNoCN :: MPBall -> Int -> DivTypeNoCN MPBall Int # divide :: MPBall -> Int -> DivType MPBall Int #
CanDiv MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall Integer :: Type # type DivType MPBall Integer :: Type # Methods divideNoCN :: MPBall -> Integer -> DivTypeNoCN MPBall Integer # divide :: MPBall -> Integer -> DivType MPBall Integer #
CanDiv MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall Rational :: Type # type DivType MPBall Rational :: Type # Methods divideNoCN :: MPBall -> Rational -> DivTypeNoCN MPBall Rational # divide :: MPBall -> Rational -> DivType MPBall Rational #
CanDiv MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall Dyadic :: Type # type DivType MPBall Dyadic :: Type # Methods divideNoCN :: MPBall -> Dyadic -> DivTypeNoCN MPBall Dyadic # divide :: MPBall -> Dyadic -> DivType MPBall Dyadic #
CanDiv MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall MPBall :: Type # type DivType MPBall MPBall :: Type # Methods divideNoCN :: MPBall -> MPBall -> DivTypeNoCN MPBall MPBall # divide :: MPBall -> MPBall -> DivType MPBall MPBall #
CanMulAsymmetric Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Int MPBall :: Type # Methods mul :: Int -> MPBall -> MulType Int MPBall #
CanMulAsymmetric Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Integer MPBall :: Type # Methods mul :: Integer -> MPBall -> MulType Integer MPBall #
CanMulAsymmetric Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Rational MPBall :: Type # Methods mul :: Rational -> MPBall -> MulType Rational MPBall #
CanMulAsymmetric Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Dyadic MPBall :: Type # Methods mul :: Dyadic -> MPBall -> MulType Dyadic MPBall #
CanMulAsymmetric MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Int :: Type # Methods mul :: MPBall -> Int -> MulType MPBall Int #
CanMulAsymmetric MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Integer :: Type # Methods mul :: MPBall -> Integer -> MulType MPBall Integer #
CanMulAsymmetric MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Rational :: Type # Methods mul :: MPBall -> Rational -> MulType MPBall Rational #
CanMulAsymmetric MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Dyadic :: Type # Methods mul :: MPBall -> Dyadic -> MulType MPBall Dyadic #
CanMulAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall MPBall :: Type # Methods mul :: MPBall -> MPBall -> MulType MPBall MPBall #
CanPow MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowTypeNoCN MPBall Int :: Type # type PowType MPBall Int :: Type # Methods powNoCN :: MPBall -> Int -> PowTypeNoCN MPBall Int # pow :: MPBall -> Int -> PowType MPBall Int #
CanPow MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowTypeNoCN MPBall Integer :: Type # type PowType MPBall Integer :: Type # Methods powNoCN :: MPBall -> Integer -> PowTypeNoCN MPBall Integer # pow :: MPBall -> Integer -> PowType MPBall Integer #
CanPow MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowTypeNoCN MPBall Rational :: Type # type PowType MPBall Rational :: Type # Methods powNoCN :: MPBall -> Rational -> PowTypeNoCN MPBall Rational # pow :: MPBall -> Rational -> PowType MPBall Rational #
CanPow MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowTypeNoCN MPBall Dyadic :: Type # type PowType MPBall Dyadic :: Type # Methods powNoCN :: MPBall -> Dyadic -> PowTypeNoCN MPBall Dyadic # pow :: MPBall -> Dyadic -> PowType MPBall Dyadic #
CanPow MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowTypeNoCN MPBall MPBall :: Type # type PowType MPBall MPBall :: Type # Methods powNoCN :: MPBall -> MPBall -> PowTypeNoCN MPBall MPBall # pow :: MPBall -> MPBall -> PowType MPBall MPBall #
CanAddAsymmetric Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Int MPBall :: Type # Methods add :: Int -> MPBall -> AddType Int MPBall #
CanAddAsymmetric Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Integer MPBall :: Type # Methods add :: Integer -> MPBall -> AddType Integer MPBall #
CanAddAsymmetric Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Rational MPBall :: Type # Methods add :: Rational -> MPBall -> AddType Rational MPBall #
CanAddAsymmetric Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Dyadic MPBall :: Type # Methods add :: Dyadic -> MPBall -> AddType Dyadic MPBall #
CanAddAsymmetric MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Int :: Type # Methods add :: MPBall -> Int -> AddType MPBall Int #
CanAddAsymmetric MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Integer :: Type # Methods add :: MPBall -> Integer -> AddType MPBall Integer #
CanAddAsymmetric MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Rational :: Type # Methods add :: MPBall -> Rational -> AddType MPBall Rational #
CanAddAsymmetric MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Dyadic :: Type # Methods add :: MPBall -> Dyadic -> AddType MPBall Dyadic #
CanAddAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall MPBall :: Type # Methods add :: MPBall -> MPBall -> AddType MPBall MPBall #
CanSub Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Int MPBall :: Type # Methods sub :: Int -> MPBall -> SubType Int MPBall #
CanSub Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Integer MPBall :: Type # Methods sub :: Integer -> MPBall -> SubType Integer MPBall #
CanSub Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Rational MPBall :: Type # Methods sub :: Rational -> MPBall -> SubType Rational MPBall #
CanSub Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Dyadic MPBall :: Type # Methods sub :: Dyadic -> MPBall -> SubType Dyadic MPBall #
CanSub MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Int :: Type # Methods sub :: MPBall -> Int -> SubType MPBall Int #
CanSub MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Integer :: Type # Methods sub :: MPBall -> Integer -> SubType MPBall Integer #
CanSub MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Rational :: Type # Methods sub :: MPBall -> Rational -> SubType MPBall Rational #
CanSub MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Dyadic :: Type # Methods sub :: MPBall -> Dyadic -> SubType MPBall Dyadic #
CanSub MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall MPBall :: Type # Methods sub :: MPBall -> MPBall -> SubType MPBall MPBall #
CanMinMaxAsymmetric Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Int MPBall :: Type # Methods min :: Int -> MPBall -> MinMaxType Int MPBall # max :: Int -> MPBall -> MinMaxType Int MPBall #
CanMinMaxAsymmetric Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Integer MPBall :: Type # Methods min :: Integer -> MPBall -> MinMaxType Integer MPBall # max :: Integer -> MPBall -> MinMaxType Integer MPBall #
CanMinMaxAsymmetric Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Rational MPBall :: Type # Methods min :: Rational -> MPBall -> MinMaxType Rational MPBall # max :: Rational -> MPBall -> MinMaxType Rational MPBall #
CanMinMaxAsymmetric Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Dyadic MPBall :: Type # Methods min :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall # max :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall #
CanMinMaxAsymmetric MPBall Int #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Int :: Type # Methods min :: MPBall -> Int -> MinMaxType MPBall Int # max :: MPBall -> Int -> MinMaxType MPBall Int #
CanMinMaxAsymmetric MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Integer :: Type # Methods min :: MPBall -> Integer -> MinMaxType MPBall Integer # max :: MPBall -> Integer -> MinMaxType MPBall Integer #
CanMinMaxAsymmetric MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Rational :: Type # Methods min :: MPBall -> Rational -> MinMaxType MPBall Rational # max :: MPBall -> Rational -> MinMaxType MPBall Rational #
CanMinMaxAsymmetric MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Dyadic :: Type # Methods min :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic # max :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic #
CanMinMaxAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall MPBall :: Type # Methods min :: MPBall -> MPBall -> MinMaxType MPBall MPBall # max :: MPBall -> MPBall -> MinMaxType MPBall MPBall #
HasEqAsymmetric Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Int MPBall :: Type # Methods equalTo :: Int -> MPBall -> EqCompareType Int MPBall # notEqualTo :: Int -> MPBall -> EqCompareType Int MPBall #
HasEqAsymmetric Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Integer MPBall :: Type # Methods equalTo :: Integer -> MPBall -> EqCompareType Integer MPBall # notEqualTo :: Integer -> MPBall -> EqCompareType Integer MPBall #
HasEqAsymmetric Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Rational MPBall :: Type # Methods equalTo :: Rational -> MPBall -> EqCompareType Rational MPBall # notEqualTo :: Rational -> MPBall -> EqCompareType Rational MPBall #
HasEqAsymmetric Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Dyadic MPBall :: Type # Methods equalTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall # notEqualTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall #
HasEqAsymmetric MPBall Int #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Int :: Type # Methods equalTo :: MPBall -> Int -> EqCompareType MPBall Int # notEqualTo :: MPBall -> Int -> EqCompareType MPBall Int #
HasEqAsymmetric MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Integer :: Type # Methods equalTo :: MPBall -> Integer -> EqCompareType MPBall Integer # notEqualTo :: MPBall -> Integer -> EqCompareType MPBall Integer #
HasEqAsymmetric MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Rational :: Type # Methods equalTo :: MPBall -> Rational -> EqCompareType MPBall Rational # notEqualTo :: MPBall -> Rational -> EqCompareType MPBall Rational #
HasEqAsymmetric MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Dyadic :: Type # Methods equalTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic # notEqualTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic #
HasEqAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall MPBall :: Type # Methods equalTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall # notEqualTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall #
HasOrderAsymmetric Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Int MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Integer MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Rational MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Dyadic MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Int :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Integer :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Rational :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Dyadic :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Int -> ConvertResult MPBall #
ConvertibleExactly Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Integer -> ConvertResult MPBall #
ConvertibleExactly Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Dyadic -> ConvertResult MPBall #
ConvertibleExactly ErrorBound MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: ErrorBound -> ConvertResult MPBall #
ConvertibleExactly MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: MPBall -> ConvertResult MPBall #
SuitableForCE es => CanEnsureCE es MPBall #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type EnsureCE es MPBall :: Type # type EnsureNoCE es MPBall :: Type # Methods ensureCE :: Maybe es -> MPBall -> EnsureCE es MPBall # deEnsureCE :: Maybe es -> EnsureCE es MPBall -> Either es MPBall # ensureNoCE :: Maybe es -> MPBall -> (Maybe (EnsureNoCE es MPBall), es) # noValueECE :: Maybe MPBall -> es -> EnsureCE es MPBall # prependErrorsECE :: Maybe MPBall -> es -> EnsureCE es MPBall -> EnsureCE es MPBall #
ConvertibleWithPrecision Int MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Int -> ConvertResult MPBall #
ConvertibleWithPrecision Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Integer -> ConvertResult MPBall #
ConvertibleWithPrecision Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Rational -> ConvertResult MPBall #
ConvertibleWithPrecision Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall #
CanUnionAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall MPBall :: Type # Methods union :: MPBall -> MPBall -> UnionType MPBall MPBall #
CanIntersectAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall MPBall :: Type # Methods intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall #
CanTestContains MPBall Int #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Int -> Bool #
CanTestContains MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Integer -> Bool #
CanTestContains MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Rational -> Bool #
CanTestContains MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Dyadic -> Bool #
CanTestContains MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> MPBall -> Bool #
IsInterval MPBall MPFloat #
Instance details Defined in AERN2.MP.Ball.Type Methods fromEndpoints :: MPFloat -> MPFloat -> MPBall # endpoints :: MPBall -> (MPFloat, MPFloat) #
IsInterval MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Type Methods fromEndpoints :: MPBall -> MPBall -> MPBall # endpoints :: MPBall -> (MPBall, MPBall) #
(CanDiv MPBall b, CanEnsureCE es b, CanEnsureCE es (DivType MPBall b), CanEnsureCE es (DivTypeNoCN MPBall b), SuitableForCE es) => CanDiv MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN MPBall (CollectErrors es b) :: Type # type DivType MPBall (CollectErrors es b) :: Type # Methods divideNoCN :: MPBall -> CollectErrors es b -> DivTypeNoCN MPBall (CollectErrors es b) # divide :: MPBall -> CollectErrors es b -> DivType MPBall (CollectErrors es b) #
(CanMulAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (MulType MPBall b), SuitableForCE es) => CanMulAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall (CollectErrors es b) :: Type # Methods mul :: MPBall -> CollectErrors es b -> MulType MPBall (CollectErrors es b) #
(CanPow MPBall b, CanEnsureCE es b, CanEnsureCE es (PowType MPBall b), CanEnsureCE es (PowTypeNoCN MPBall b), SuitableForCE es) => CanPow MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowTypeNoCN MPBall (CollectErrors es b) :: Type # type PowType MPBall (CollectErrors es b) :: Type # Methods powNoCN :: MPBall -> CollectErrors es b -> PowTypeNoCN MPBall (CollectErrors es b) # pow :: MPBall -> CollectErrors es b -> PowType MPBall (CollectErrors es b) #
(CanAddAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (AddType MPBall b), SuitableForCE es) => CanAddAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall (CollectErrors es b) :: Type # Methods add :: MPBall -> CollectErrors es b -> AddType MPBall (CollectErrors es b) #
(CanSub MPBall b, CanEnsureCE es b, CanEnsureCE es (SubType MPBall b), SuitableForCE es) => CanSub MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall (CollectErrors es b) :: Type # Methods sub :: MPBall -> CollectErrors es b -> SubType MPBall (CollectErrors es b) #
(CanMinMaxAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (MinMaxType MPBall b), SuitableForCE es) => CanMinMaxAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall (CollectErrors es b) :: Type # Methods min :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) # max :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) #
(HasEqAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (EqCompareType MPBall b), IsBool (EnsureCE es (EqCompareType MPBall b)), SuitableForCE es) => HasEqAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall (CollectErrors es b) :: Type # Methods equalTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) # notEqualTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) #
(HasOrderAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType MPBall b), IsBool (EnsureCE es (OrderCompareType MPBall b)), SuitableForCE es) => HasOrderAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall (CollectErrors es b) :: Type # 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) #
(CanUnionAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (UnionType MPBall b), SuitableForCE es) => CanUnionAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall (CollectErrors es b) :: Type # Methods union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b) #
(CanIntersectAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (IntersectionType MPBall b), SuitableForCE es) => CanIntersectAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall (CollectErrors es b) :: Type # Methods intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b) #
Field (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
OrderedField (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyField (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
Ring (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
OrderedRing (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
OrderedCertainlyRing (CN MPBall) #
Instance details Defined in AERN2.MP.Ball
(CanDiv a MPBall, CanEnsureCE es a, CanEnsureCE es (DivType a MPBall), CanEnsureCE es (DivTypeNoCN a MPBall), SuitableForCE es) => CanDiv (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivTypeNoCN (CollectErrors es a) MPBall :: Type # type DivType (CollectErrors es a) MPBall :: Type # Methods divideNoCN :: CollectErrors es a -> MPBall -> DivTypeNoCN (CollectErrors es a) MPBall # divide :: CollectErrors es a -> MPBall -> DivType (CollectErrors es a) MPBall #
(CanMulAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (MulType a MPBall), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType (CollectErrors es a) MPBall :: Type # Methods mul :: CollectErrors es a -> MPBall -> MulType (CollectErrors es a) MPBall #
(CanPow a MPBall, CanEnsureCE es a, CanEnsureCE es (PowType a MPBall), CanEnsureCE es (PowTypeNoCN a MPBall), SuitableForCE es) => CanPow (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type PowTypeNoCN (CollectErrors es a) MPBall :: Type # type PowType (CollectErrors es a) MPBall :: Type # Methods powNoCN :: CollectErrors es a -> MPBall -> PowTypeNoCN (CollectErrors es a) MPBall # pow :: CollectErrors es a -> MPBall -> PowType (CollectErrors es a) MPBall #
(CanAddAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (AddType a MPBall), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType (CollectErrors es a) MPBall :: Type # Methods add :: CollectErrors es a -> MPBall -> AddType (CollectErrors es a) MPBall #
(CanSub a MPBall, CanEnsureCE es a, CanEnsureCE es (SubType a MPBall), SuitableForCE es) => CanSub (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType (CollectErrors es a) MPBall :: Type # Methods sub :: CollectErrors es a -> MPBall -> SubType (CollectErrors es a) MPBall #
(CanMinMaxAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (MinMaxType a MPBall), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType (CollectErrors es a) MPBall :: Type # Methods min :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall # max :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall #
(HasEqAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (EqCompareType a MPBall), IsBool (EnsureCE es (EqCompareType a MPBall)), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType (CollectErrors es a) MPBall :: Type # Methods equalTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall # notEqualTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall #
(HasOrderAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a MPBall), IsBool (EnsureCE es (OrderCompareType a MPBall)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType (CollectErrors es a) MPBall :: Type # 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 #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: (c, e) -> ConvertResult MPBall #
ConvertibleWithPrecision (Rational, Rational) MPBall #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult MPBall #
(CanUnionAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (UnionType a MPBall), SuitableForCE es) => CanUnionAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType (CollectErrors es a) MPBall :: Type # Methods union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall #
(CanIntersectAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (IntersectionType a MPBall), SuitableForCE es) => CanIntersectAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType (CollectErrors es a) MPBall :: Type # Methods intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall #
type Rep MPBall #
Instance details Defined in AERN2.MP.Ball.Type type Rep MPBall = D1 (MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.1.3.1-7Uync4oftadAfXbmapMRHk" 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 #
Instance details Defined in AERN2.MP.Ball.Elementary type SqrtType MPBall = CN MPBall
type ExpType MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary type ExpType MPBall = MPBall
type LogType MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary type LogType MPBall = CN MPBall
type SinCosType MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary type SinCosType MPBall = MPBall
type AbsType MPBall #
Instance details Defined in AERN2.MP.Ball.Type type AbsType MPBall = MPBall
type NegType MPBall #
Instance details Defined in AERN2.MP.Ball.Type type NegType MPBall = MPBall
type Approximate MPBall #
Instance details Defined in AERN2.MP.Ball.Type type Approximate MPBall = (MPFloat, Bool)
type CentreType MPBall #
Instance details Defined in AERN2.MP.Ball.Type type CentreType MPBall = Dyadic
type DivType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType Int MPBall = CN MPBall
type DivType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType Integer MPBall = CN MPBall
type DivType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType Rational MPBall = EnsureCN (DivTypeNoCN Rational MPBall)
type DivType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic MPBall = CN MPBall
type DivType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Int = CN MPBall
type DivType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Integer = CN MPBall
type DivType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Rational = EnsureCN (DivTypeNoCN MPBall Rational)
type DivType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Dyadic = CN MPBall
type DivType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall MPBall = CN MPBall
type DivTypeNoCN Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN Int MPBall = MPBall
type DivTypeNoCN Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN Integer MPBall = MPBall
type DivTypeNoCN Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN Rational MPBall = MPBall
type DivTypeNoCN Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN Dyadic MPBall = MPBall
type DivTypeNoCN MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall Int = MPBall
type DivTypeNoCN MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall Integer = MPBall
type DivTypeNoCN MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall Rational = MPBall
type DivTypeNoCN MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall Dyadic = MPBall
type DivTypeNoCN MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall MPBall = MPBall
type MulType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType Int MPBall = MPBall
type MulType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType Integer MPBall = MPBall
type MulType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType Rational MPBall = MPBall
type MulType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType Dyadic MPBall = MPBall
type MulType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Int = MPBall
type MulType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Integer = MPBall
type MulType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Rational = MPBall
type MulType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Dyadic = MPBall
type MulType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall MPBall = MPBall
type PowType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Int = EnsureCN (PowTypeNoCN MPBall Int)
type PowType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Integer = EnsureCN (PowTypeNoCN MPBall Integer)
type PowType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Rational = EnsureCN (PowTypeNoCN MPBall Rational)
type PowType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Dyadic = EnsureCN (PowTypeNoCN MPBall Dyadic)
type PowType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall MPBall = EnsureCN (PowTypeNoCN MPBall MPBall)
type PowTypeNoCN MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type PowTypeNoCN MPBall Int = MPBall
type PowTypeNoCN MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type PowTypeNoCN MPBall Integer = MPBall
type PowTypeNoCN MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Elementary type PowTypeNoCN MPBall Rational = MPBall
type PowTypeNoCN MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Elementary type PowTypeNoCN MPBall Dyadic = MPBall
type PowTypeNoCN MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Elementary type PowTypeNoCN MPBall MPBall = MPBall
type AddType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType Int MPBall = MPBall
type AddType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType Integer MPBall = MPBall
type AddType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType Rational MPBall = MPBall
type AddType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType Dyadic MPBall = MPBall
type AddType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Int = MPBall
type AddType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Integer = MPBall
type AddType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Rational = MPBall
type AddType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Dyadic = MPBall
type AddType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall MPBall = MPBall
type SubType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType Int MPBall = AddType Int (NegType MPBall)
type SubType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType Integer MPBall = AddType Integer (NegType MPBall)
type SubType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType Rational MPBall = AddType Rational (NegType MPBall)
type SubType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Int = AddType MPBall (NegType Int)
type SubType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Integer = AddType MPBall (NegType Integer)
type SubType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Rational = AddType MPBall (NegType Rational)
type SubType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type SubType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall MPBall = AddType MPBall (NegType MPBall)
type MinMaxType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Int MPBall = MPBall
type MinMaxType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Integer MPBall = MPBall
type MinMaxType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Rational MPBall = MPBall
type MinMaxType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Int = MPBall
type MinMaxType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Integer = MPBall
type MinMaxType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Rational = MPBall
type MinMaxType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Dyadic = MPBall
type MinMaxType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall MPBall = MPBall
type EqCompareType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Int MPBall = Maybe Bool
type EqCompareType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Integer MPBall = Maybe Bool
type EqCompareType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Rational MPBall = Maybe Bool
type EqCompareType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Dyadic MPBall = Maybe Bool
type EqCompareType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Int = Maybe Bool
type EqCompareType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Integer = Maybe Bool
type EqCompareType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Rational = Maybe Bool
type EqCompareType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Dyadic = Maybe Bool
type EqCompareType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall MPBall = Maybe Bool
type OrderCompareType Int MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Int MPBall = Maybe Bool
type OrderCompareType Integer MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Integer MPBall = Maybe Bool
type OrderCompareType Rational MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Rational MPBall = Maybe Bool
type OrderCompareType Dyadic MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Dyadic MPBall = Maybe Bool
type OrderCompareType MPBall Int #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Int = Maybe Bool
type OrderCompareType MPBall Integer #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Integer = Maybe Bool
type OrderCompareType MPBall Rational #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Rational = Maybe Bool
type OrderCompareType MPBall Dyadic #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Dyadic = Maybe Bool
type OrderCompareType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall MPBall = Maybe Bool
type EnsureNoCE es MPBall #
Instance details Defined in AERN2.MP.Ball.Type type EnsureNoCE es MPBall = MPBall
type EnsureCE es MPBall #
Instance details Defined in AERN2.MP.Ball.Type type EnsureCE es MPBall = CollectErrors es MPBall
type UnionType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall MPBall = EnsureCN MPBall
type IntersectionType MPBall MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall MPBall = EnsureCN MPBall
type DivType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall (CollectErrors es b) = EnsureCE es (DivType MPBall b)
type DivTypeNoCN MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN MPBall (CollectErrors es b) = EnsureCE es (DivTypeNoCN MPBall b)
type MulType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall (CollectErrors es b) = EnsureCE es (MulType MPBall b)
type PowType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall (CollectErrors es b) = EnsureCE es (PowType MPBall b)
type PowTypeNoCN MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type PowTypeNoCN MPBall (CollectErrors es b) = EnsureCE es (PowTypeNoCN MPBall b)
type AddType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall (CollectErrors es b) = EnsureCE es (AddType MPBall b)
type SubType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall (CollectErrors es b) = EnsureCE es (SubType MPBall b)
type MinMaxType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall (CollectErrors es b) = EnsureCE es (MinMaxType MPBall b)
type EqCompareType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall (CollectErrors es b) = EnsureCE es (EqCompareType MPBall b)
type OrderCompareType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall (CollectErrors es b) = EnsureCE es (OrderCompareType MPBall b)
type UnionType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall (CollectErrors es b) = EnsureCE es (UnionType MPBall b)
type IntersectionType MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall (CollectErrors es b) = EnsureCE es (IntersectionType MPBall b)
type DivType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivType (CollectErrors es a) MPBall = EnsureCE es (DivType a MPBall)
type DivTypeNoCN (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type DivTypeNoCN (CollectErrors es a) MPBall = EnsureCE es (DivTypeNoCN a MPBall)
type MulType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type MulType (CollectErrors es a) MPBall = EnsureCE es (MulType a MPBall)
type PowType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type PowType (CollectErrors es a) MPBall = EnsureCE es (PowType a MPBall)
type PowTypeNoCN (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type PowTypeNoCN (CollectErrors es a) MPBall = EnsureCE es (PowTypeNoCN a MPBall)
type AddType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type AddType (CollectErrors es a) MPBall = EnsureCE es (AddType a MPBall)
type SubType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Field type SubType (CollectErrors es a) MPBall = EnsureCE es (SubType a MPBall)
type MinMaxType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType (CollectErrors es a) MPBall = EnsureCE es (MinMaxType a MPBall)
type EqCompareType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType (CollectErrors es a) MPBall = EnsureCE es (EqCompareType a MPBall)
type OrderCompareType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType (CollectErrors es a) MPBall = EnsureCE es (OrderCompareType a MPBall)
type UnionType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType (CollectErrors es a) MPBall = EnsureCE es (UnionType a MPBall)
type IntersectionType (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType (CollectErrors es a) MPBall = EnsureCE es (IntersectionType a MPBall)

type CanBeMPBall t = ConvertibleExactly t MPBall #

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

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall #

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

reducePrecionIfInaccurate :: MPBall -> MPBall #

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

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

Ball construction/extraction functions

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

fromEndpointsMP :: MPFloat -> MPFloat -> MPBall #