AERN2.MP.Ball

Arbitrary precision ball arithmetic

Auxiliary types

module AERN2.Norm

module AERN2.MP.Precision

module AERN2.MP.Accuracy

data ErrorBound

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

Instances

Arbitrary ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

arbitrary :: Gen ErrorBound

shrink :: ErrorBound -> [ErrorBound]

HasAccuracy ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

getAccuracy :: ErrorBound -> Accuracy

getFiniteAccuracy :: ErrorBound -> Accuracy

Generic ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type Rep ErrorBound :: Type -> Type

Methods

from :: ErrorBound -> Rep ErrorBound x

to :: Rep ErrorBound x -> ErrorBound

Show ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

showsPrec :: Int -> ErrorBound -> ShowS

show :: ErrorBound -> String

showList :: [ErrorBound] -> ShowS

NFData ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

rnf :: ErrorBound -> ()

Eq ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

(==) :: ErrorBound -> ErrorBound -> Bool

(/=) :: ErrorBound -> ErrorBound -> Bool

Ord ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

compare :: ErrorBound -> ErrorBound -> Ordering

(<) :: ErrorBound -> ErrorBound -> Bool

(<=) :: ErrorBound -> ErrorBound -> Bool

(>) :: ErrorBound -> ErrorBound -> Bool

(>=) :: ErrorBound -> ErrorBound -> Bool

max :: ErrorBound -> ErrorBound -> ErrorBound

min :: ErrorBound -> ErrorBound -> ErrorBound

Convertible MPBall ErrorBound

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvert :: MPBall -> ConvertResult ErrorBound

Convertible MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: MPFloat -> ConvertResult ErrorBound

Convertible Rational ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Rational -> ConvertResult ErrorBound

Convertible Integer ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Integer -> ConvertResult ErrorBound

Convertible Int ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Int -> ConvertResult ErrorBound

CanAddAsymmetric ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType ErrorBound ErrorBound

Methods

add :: ErrorBound -> ErrorBound -> AddType ErrorBound ErrorBound

CanAddAsymmetric ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType ErrorBound MPFloat

Methods

add :: ErrorBound -> MPFloat -> AddType ErrorBound MPFloat

CanAddAsymmetric MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType MPFloat ErrorBound

Methods

add :: MPFloat -> ErrorBound -> AddType MPFloat ErrorBound

CanDiv ErrorBound Integer

Defined in AERN2.MP.ErrorBound

Associated Types

type DivType ErrorBound Integer

Methods

divide :: ErrorBound -> Integer -> DivType ErrorBound Integer

HasEqAsymmetric ErrorBound Rational

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType ErrorBound Rational

Methods

equalTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational

notEqualTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational

HasEqAsymmetric ErrorBound Integer

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType ErrorBound Integer

Methods

equalTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer

notEqualTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer

HasEqAsymmetric ErrorBound Int

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType ErrorBound Int

Methods

equalTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int

notEqualTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int

HasEqAsymmetric Rational ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType Rational ErrorBound

Methods

equalTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound

notEqualTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound

HasEqAsymmetric Integer ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType Integer ErrorBound

Methods

equalTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound

notEqualTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound

HasEqAsymmetric Int ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType Int ErrorBound

Methods

equalTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound

notEqualTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound

ConvertibleExactly ErrorBound MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPBall

ConvertibleExactly ErrorBound Dyadic

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult Dyadic

ConvertibleExactly ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult ErrorBound

ConvertibleExactly ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPFloat

ConvertibleExactly ErrorBound Rational

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult Rational

CanMinMaxAsymmetric ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type MinMaxType ErrorBound ErrorBound

Methods

min :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound

max :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound

CanMulAsymmetric ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound ErrorBound

Methods

mul :: ErrorBound -> ErrorBound -> MulType ErrorBound ErrorBound

CanMulAsymmetric ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound MPFloat

Methods

mul :: ErrorBound -> MPFloat -> MulType ErrorBound MPFloat

CanMulAsymmetric ErrorBound Rational

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound Rational

Methods

mul :: ErrorBound -> Rational -> MulType ErrorBound Rational

CanMulAsymmetric ErrorBound Integer

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound Integer

Methods

mul :: ErrorBound -> Integer -> MulType ErrorBound Integer

CanMulAsymmetric MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType MPFloat ErrorBound

Methods

mul :: MPFloat -> ErrorBound -> MulType MPFloat ErrorBound

CanMulAsymmetric Rational ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType Rational ErrorBound

Methods

mul :: Rational -> ErrorBound -> MulType Rational ErrorBound

CanMulAsymmetric Integer ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType Integer ErrorBound

Methods

mul :: Integer -> ErrorBound -> MulType Integer ErrorBound

HasOrderAsymmetric ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType ErrorBound ErrorBound

Methods

lessThan :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound

greaterThan :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound

leq :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound

geq :: ErrorBound -> ErrorBound -> OrderCompareType ErrorBound ErrorBound

HasOrderAsymmetric ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType ErrorBound MPFloat

Methods

lessThan :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat

greaterThan :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat

leq :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat

geq :: ErrorBound -> MPFloat -> OrderCompareType ErrorBound MPFloat

HasOrderAsymmetric ErrorBound Rational

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType ErrorBound Rational

Methods

lessThan :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational

greaterThan :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational

leq :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational

geq :: ErrorBound -> Rational -> OrderCompareType ErrorBound Rational

HasOrderAsymmetric ErrorBound Integer

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType ErrorBound Integer

Methods

lessThan :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer

greaterThan :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer

leq :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer

geq :: ErrorBound -> Integer -> OrderCompareType ErrorBound Integer

HasOrderAsymmetric ErrorBound Int

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType ErrorBound Int

Methods

lessThan :: ErrorBound -> Int -> OrderCompareType ErrorBound Int

greaterThan :: ErrorBound -> Int -> OrderCompareType ErrorBound Int

leq :: ErrorBound -> Int -> OrderCompareType ErrorBound Int

geq :: ErrorBound -> Int -> OrderCompareType ErrorBound Int

HasOrderAsymmetric MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType MPFloat ErrorBound

Methods

lessThan :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound

greaterThan :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound

leq :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound

geq :: MPFloat -> ErrorBound -> OrderCompareType MPFloat ErrorBound

HasOrderAsymmetric Rational ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType Rational ErrorBound

Methods

lessThan :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound

greaterThan :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound

leq :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound

geq :: Rational -> ErrorBound -> OrderCompareType Rational ErrorBound

HasOrderAsymmetric Integer ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType Integer ErrorBound

Methods

lessThan :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound

greaterThan :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound

leq :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound

geq :: Integer -> ErrorBound -> OrderCompareType Integer ErrorBound

HasOrderAsymmetric Int ErrorBound

Defined in AERN2.MP.ErrorBound

Associated Types

type OrderCompareType Int ErrorBound

Methods

lessThan :: Int -> ErrorBound -> OrderCompareType Int ErrorBound

greaterThan :: Int -> ErrorBound -> OrderCompareType Int ErrorBound

leq :: Int -> ErrorBound -> OrderCompareType Int ErrorBound

geq :: Int -> ErrorBound -> OrderCompareType Int ErrorBound

type Rep ErrorBound

Defined in AERN2.MP.ErrorBound

type Rep ErrorBound = D1 ('MetaData "ErrorBound" "AERN2.MP.ErrorBound" "aern2-mp-0.2.16.1-IJDSJSVfOW8Hl8Ias4Iudc" 'True) (C1 ('MetaCons "ErrorBound" 'PrefixI 'True) (S1 ('MetaSel ('Just "er2mp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat)))

type AddType ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

type AddType ErrorBound ErrorBound = ErrorBound

type AddType ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

type AddType ErrorBound MPFloat = ErrorBound

type AddType MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

type AddType MPFloat ErrorBound = ErrorBound

type DivType ErrorBound Integer

Defined in AERN2.MP.ErrorBound

type DivType ErrorBound Integer = ErrorBound

type EqCompareType ErrorBound Rational

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Rational = Bool

type EqCompareType ErrorBound Integer

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Integer = Bool

type EqCompareType ErrorBound Int

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Int = Bool

type EqCompareType Rational ErrorBound

Defined in AERN2.MP.ErrorBound

type EqCompareType Rational ErrorBound = Bool

type EqCompareType Integer ErrorBound

Defined in AERN2.MP.ErrorBound

type EqCompareType Integer ErrorBound = Bool

type EqCompareType Int ErrorBound

Defined in AERN2.MP.ErrorBound

type EqCompareType Int ErrorBound = Bool

type MinMaxType ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

type MinMaxType ErrorBound ErrorBound = ErrorBound

type MulType ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound ErrorBound = ErrorBound

type MulType ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound MPFloat = ErrorBound

type MulType ErrorBound Rational

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound Rational = ErrorBound

type MulType ErrorBound Integer

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound Integer = ErrorBound

type MulType MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

type MulType MPFloat ErrorBound = ErrorBound

type MulType Rational ErrorBound

Defined in AERN2.MP.ErrorBound

type MulType Rational ErrorBound = ErrorBound

type MulType Integer ErrorBound

Defined in AERN2.MP.ErrorBound

type MulType Integer ErrorBound = ErrorBound

type OrderCompareType ErrorBound ErrorBound

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound ErrorBound = Bool

type OrderCompareType ErrorBound MPFloat

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound MPFloat = Bool

type OrderCompareType ErrorBound Rational

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Rational = Bool

type OrderCompareType ErrorBound Integer

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Integer = Bool

type OrderCompareType ErrorBound Int

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Int = Bool

type OrderCompareType MPFloat ErrorBound

Defined in AERN2.MP.ErrorBound

type OrderCompareType MPFloat ErrorBound = Bool

type OrderCompareType Rational ErrorBound

Defined in AERN2.MP.ErrorBound

type OrderCompareType Rational ErrorBound = Bool

type OrderCompareType Integer ErrorBound

Defined in AERN2.MP.ErrorBound

type OrderCompareType Integer ErrorBound = Bool

type OrderCompareType Int ErrorBound

Defined in AERN2.MP.ErrorBound

type OrderCompareType Int ErrorBound = Bool

type CanBeErrorBound t = Convertible t ErrorBound

errorBound :: CanBeErrorBound t => t -> ErrorBound

module AERN2.MP.Enclosure

The Ball type

data MPBall

Constructors

MPBall

Fields

• ball_value :: MPFloat
• ball_error :: ErrorBound

Instances

Arbitrary MPBall

Defined in AERN2.MP.Ball.Tests

Methods

arbitrary :: Gen MPBall

shrink :: MPBall -> [MPBall]

HasAccuracy MPBall

Defined in AERN2.MP.Ball.Type

Methods

getAccuracy :: MPBall -> Accuracy

getFiniteAccuracy :: MPBall -> Accuracy

HasApproximate MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type Approximate MPBall

Methods

getApproximate :: Accuracy -> MPBall -> Approximate MPBall

ShowWithAccuracy MPBall

Defined in AERN2.MP.Ball.Type

Methods

showWithAccuracy :: Accuracy -> MPBall -> String

IsBall MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type CentreType MPBall

Methods

centre :: MPBall -> CentreType MPBall

centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound)

centreAsBall :: MPBall -> MPBall

radius :: MPBall -> ErrorBound

updateRadius :: (ErrorBound -> ErrorBound) -> MPBall -> MPBall

makeExactCentre :: MPBall -> MPBall

IsInterval MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type IntervalEndpoint MPBall

Methods

endpoints :: MPBall -> (IntervalEndpoint MPBall, IntervalEndpoint MPBall)

fromEndpoints :: IntervalEndpoint MPBall -> IntervalEndpoint MPBall -> MPBall

CanSetPrecision MPBall

Defined in AERN2.MP.Ball.Type

Methods

setPrecision :: Precision -> MPBall -> MPBall

HasPrecision MPBall

Defined in AERN2.MP.Ball.Type

Methods

getPrecision :: MPBall -> Precision

HasNorm MPBall

Defined in AERN2.MP.Ball.Type

Methods

getNormLog :: MPBall -> NormLog

CanNormalize MPBall

Defined in AERN2.MP.Ball.Type

Methods

normalize :: MPBall -> MPBall

Floating MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

pi :: MPBall

exp :: MPBall -> MPBall

log :: MPBall -> MPBall

sqrt :: MPBall -> MPBall

(**) :: MPBall -> MPBall -> MPBall

logBase :: MPBall -> MPBall -> MPBall

sin :: MPBall -> MPBall

cos :: MPBall -> MPBall

tan :: MPBall -> MPBall

asin :: MPBall -> MPBall

acos :: MPBall -> MPBall

atan :: MPBall -> MPBall

sinh :: MPBall -> MPBall

cosh :: MPBall -> MPBall

tanh :: MPBall -> MPBall

asinh :: MPBall -> MPBall

acosh :: MPBall -> MPBall

atanh :: MPBall -> MPBall

log1p :: MPBall -> MPBall

expm1 :: MPBall -> MPBall

log1pexp :: MPBall -> MPBall

log1mexp :: MPBall -> MPBall

Generic MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type Rep MPBall :: Type -> Type

Methods

from :: MPBall -> Rep MPBall x

to :: Rep MPBall x -> MPBall

Num MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

(+) :: MPBall -> MPBall -> MPBall

(-) :: MPBall -> MPBall -> MPBall

(*) :: MPBall -> MPBall -> MPBall

negate :: MPBall -> MPBall

abs :: MPBall -> MPBall

signum :: MPBall -> MPBall

fromInteger :: Integer -> MPBall

Fractional MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

(/) :: MPBall -> MPBall -> MPBall

recip :: MPBall -> MPBall

fromRational :: Rational -> MPBall

Show MPBall

Defined in AERN2.MP.Ball.Type

Methods

showsPrec :: Int -> MPBall -> ShowS

show :: MPBall -> String

showList :: [MPBall] -> ShowS

NFData MPBall

Defined in AERN2.MP.Ball.Type

Methods

rnf :: MPBall -> ()

Eq MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

(==) :: MPBall -> MPBall -> Bool

(/=) :: MPBall -> MPBall -> Bool

Ord MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

compare :: MPBall -> MPBall -> Ordering

(<) :: MPBall -> MPBall -> Bool

(<=) :: MPBall -> MPBall -> Bool

(>) :: MPBall -> MPBall -> Bool

(>=) :: MPBall -> MPBall -> Bool

max :: MPBall -> MPBall -> MPBall

min :: MPBall -> MPBall -> MPBall

CanNeg MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type NegType MPBall

Methods

negate :: MPBall -> NegType MPBall

CanExp MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type ExpType MPBall

Methods

exp :: MPBall -> ExpType MPBall

CanLog MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type LogType MPBall

Methods

log :: MPBall -> LogType MPBall

CanSinCos MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type SinCosType MPBall

Methods

cos :: MPBall -> SinCosType MPBall

sin :: MPBall -> SinCosType MPBall

CanSqrt MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type SqrtType MPBall

Methods

sqrt :: MPBall -> SqrtType MPBall

CanTestFinite MPBall

Defined in AERN2.MP.Ball.Type

Methods

isInfinite :: MPBall -> Bool

isFinite :: MPBall -> Bool

CanTestInteger MPBall

Defined in AERN2.MP.Ball.Comparisons

Methods

certainlyNotInteger :: MPBall -> Bool

certainlyInteger :: MPBall -> Bool

certainlyIntegerGetIt :: MPBall -> Maybe Integer

CanTestNaN MPBall

Defined in AERN2.MP.Ball.Type

Methods

isNaN :: MPBall -> Bool

CanTestValid MPBall

Defined in AERN2.MP.Ball.Type

Methods

isValid :: MPBall -> Bool

CanTestZero MPBall

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyZero :: MPBall -> Bool

isCertainlyNonZero :: MPBall -> Bool

CanAbs MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type AbsType MPBall

Methods

abs :: MPBall -> AbsType MPBall

CanTestPosNeg MPBall

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyPositive :: MPBall -> Bool

isCertainlyNonNegative :: MPBall -> Bool

isCertainlyNegative :: MPBall -> Bool

isCertainlyNonPositive :: MPBall -> Bool

CanTestIsIntegerType MPBall

Defined in AERN2.MP.Ball.Type

Methods

isIntegerType :: MPBall -> Bool

CanGiveUpIfVeryInaccurate MPBall

Defined in AERN2.MP.Ball.Type

Methods

giveUpIfVeryInaccurate :: CN MPBall -> CN MPBall

OrderedCertainlyRing MPBall

Defined in AERN2.MP.Ball

OrderedRing MPBall

Defined in AERN2.MP.Ball

Ring MPBall

Defined in AERN2.MP.Ball

HasIntegerBounds MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

integerBounds :: MPBall -> (Integer, Integer)

CanIntersectAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType MPBall MPBall

Methods

intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall

CanBeErrorBound t => CanPlusMinus MPBall t

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType MPBall t

Methods

plusMinus :: MPBall -> t -> PlusMinusType MPBall t

CanTestContains MPBall MPBall

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> MPBall -> Bool

CanTestContains MPBall Dyadic

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Dyadic -> Bool

CanTestContains MPBall Rational

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Rational -> Bool

CanTestContains MPBall Integer

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Integer -> Bool

CanTestContains MPBall Int

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Int -> Bool

CanUnionAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType MPBall MPBall

Methods

union :: MPBall -> MPBall -> UnionType MPBall MPBall

ConvertibleWithPrecision Dyadic MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall

ConvertibleWithPrecision Rational MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Rational -> ConvertResult MPBall

ConvertibleWithPrecision Integer MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Integer -> ConvertResult MPBall

ConvertibleWithPrecision Int MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Int -> ConvertResult MPBall

Convertible MPBall ErrorBound

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvert :: MPBall -> ConvertResult ErrorBound

CanAddAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall MPBall

Methods

add :: MPBall -> MPBall -> AddType MPBall MPBall

CanAddAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Dyadic

Methods

add :: MPBall -> Dyadic -> AddType MPBall Dyadic

CanAddAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Rational

Methods

add :: MPBall -> Rational -> AddType MPBall Rational

CanAddAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Integer

Methods

add :: MPBall -> Integer -> AddType MPBall Integer

CanAddAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Int

Methods

add :: MPBall -> Int -> AddType MPBall Int

CanAddAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Dyadic MPBall

Methods

add :: Dyadic -> MPBall -> AddType Dyadic MPBall

CanAddAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Rational MPBall

Methods

add :: Rational -> MPBall -> AddType Rational MPBall

CanAddAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Integer MPBall

Methods

add :: Integer -> MPBall -> AddType Integer MPBall

CanAddAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Int MPBall

Methods

add :: Int -> MPBall -> AddType Int MPBall

CanSub MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall MPBall

Methods

sub :: MPBall -> MPBall -> SubType MPBall MPBall

CanSub MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Dyadic

Methods

sub :: MPBall -> Dyadic -> SubType MPBall Dyadic

CanSub MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Rational

Methods

sub :: MPBall -> Rational -> SubType MPBall Rational

CanSub MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Integer

Methods

sub :: MPBall -> Integer -> SubType MPBall Integer

CanSub MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Int

Methods

sub :: MPBall -> Int -> SubType MPBall Int

CanSub Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Dyadic MPBall

Methods

sub :: Dyadic -> MPBall -> SubType Dyadic MPBall

CanSub Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Rational MPBall

Methods

sub :: Rational -> MPBall -> SubType Rational MPBall

CanSub Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Integer MPBall

Methods

sub :: Integer -> MPBall -> SubType Integer MPBall

CanSub Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Int MPBall

Methods

sub :: Int -> MPBall -> SubType Int MPBall

CanDiv MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall MPBall

Methods

divide :: MPBall -> MPBall -> DivType MPBall MPBall

CanDiv MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Dyadic

Methods

divide :: MPBall -> Dyadic -> DivType MPBall Dyadic

CanDiv MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Rational

Methods

divide :: MPBall -> Rational -> DivType MPBall Rational

CanDiv MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Integer

Methods

divide :: MPBall -> Integer -> DivType MPBall Integer

CanDiv MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Int

Methods

divide :: MPBall -> Int -> DivType MPBall Int

CanDiv Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Dyadic MPBall

Methods

divide :: Dyadic -> MPBall -> DivType Dyadic MPBall

CanDiv Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Rational MPBall

Methods

divide :: Rational -> MPBall -> DivType Rational MPBall

CanDiv Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Integer MPBall

Methods

divide :: Integer -> MPBall -> DivType Integer MPBall

CanDiv Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Int MPBall

Methods

divide :: Int -> MPBall -> DivType Int MPBall

HasEqAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall MPBall

Methods

equalTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall

notEqualTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall

HasEqAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Dyadic

Methods

equalTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic

notEqualTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic

HasEqAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Rational

Methods

equalTo :: MPBall -> Rational -> EqCompareType MPBall Rational

notEqualTo :: MPBall -> Rational -> EqCompareType MPBall Rational

HasEqAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Integer

Methods

equalTo :: MPBall -> Integer -> EqCompareType MPBall Integer

notEqualTo :: MPBall -> Integer -> EqCompareType MPBall Integer

HasEqAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Int

Methods

equalTo :: MPBall -> Int -> EqCompareType MPBall Int

notEqualTo :: MPBall -> Int -> EqCompareType MPBall Int

HasEqAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Dyadic MPBall

Methods

equalTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall

notEqualTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall

HasEqAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Rational MPBall

Methods

equalTo :: Rational -> MPBall -> EqCompareType Rational MPBall

notEqualTo :: Rational -> MPBall -> EqCompareType Rational MPBall

HasEqAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Integer MPBall

Methods

equalTo :: Integer -> MPBall -> EqCompareType Integer MPBall

notEqualTo :: Integer -> MPBall -> EqCompareType Integer MPBall

HasEqAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Int MPBall

Methods

equalTo :: Int -> MPBall -> EqCompareType Int MPBall

notEqualTo :: Int -> MPBall -> EqCompareType Int MPBall

ConvertibleExactly MPBall MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: MPBall -> ConvertResult MPBall

ConvertibleExactly Dyadic MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Dyadic -> ConvertResult MPBall

ConvertibleExactly ErrorBound MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPBall

ConvertibleExactly Integer MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Integer -> ConvertResult MPBall

ConvertibleExactly Int MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Int -> ConvertResult MPBall

CanMinMaxAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall MPBall

Methods

min :: MPBall -> MPBall -> MinMaxType MPBall MPBall

max :: MPBall -> MPBall -> MinMaxType MPBall MPBall

CanMinMaxAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Dyadic

Methods

min :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic

max :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic

CanMinMaxAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Rational

Methods

min :: MPBall -> Rational -> MinMaxType MPBall Rational

max :: MPBall -> Rational -> MinMaxType MPBall Rational

CanMinMaxAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Integer

Methods

min :: MPBall -> Integer -> MinMaxType MPBall Integer

max :: MPBall -> Integer -> MinMaxType MPBall Integer

CanMinMaxAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Int

Methods

min :: MPBall -> Int -> MinMaxType MPBall Int

max :: MPBall -> Int -> MinMaxType MPBall Int

CanMinMaxAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Dyadic MPBall

Methods

min :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall

max :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall

CanMinMaxAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Rational MPBall

Methods

min :: Rational -> MPBall -> MinMaxType Rational MPBall

max :: Rational -> MPBall -> MinMaxType Rational MPBall

CanMinMaxAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Integer MPBall

Methods

min :: Integer -> MPBall -> MinMaxType Integer MPBall

max :: Integer -> MPBall -> MinMaxType Integer MPBall

CanMinMaxAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Int MPBall

Methods

min :: Int -> MPBall -> MinMaxType Int MPBall

max :: Int -> MPBall -> MinMaxType Int MPBall

CanMulAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall MPBall

Methods

mul :: MPBall -> MPBall -> MulType MPBall MPBall

CanMulAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Dyadic

Methods

mul :: MPBall -> Dyadic -> MulType MPBall Dyadic

CanMulAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Rational

Methods

mul :: MPBall -> Rational -> MulType MPBall Rational

CanMulAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Integer

Methods

mul :: MPBall -> Integer -> MulType MPBall Integer

CanMulAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Int

Methods

mul :: MPBall -> Int -> MulType MPBall Int

CanMulAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Dyadic MPBall

Methods

mul :: Dyadic -> MPBall -> MulType Dyadic MPBall

CanMulAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Rational MPBall

Methods

mul :: Rational -> MPBall -> MulType Rational MPBall

CanMulAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Integer MPBall

Methods

mul :: Integer -> MPBall -> MulType Integer MPBall

CanMulAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Int MPBall

Methods

mul :: Int -> MPBall -> MulType Int MPBall

HasOrderAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall MPBall

Methods

lessThan :: MPBall -> MPBall -> OrderCompareType MPBall MPBall

greaterThan :: MPBall -> MPBall -> OrderCompareType MPBall MPBall

leq :: MPBall -> MPBall -> OrderCompareType MPBall MPBall

geq :: MPBall -> MPBall -> OrderCompareType MPBall MPBall

HasOrderAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Dyadic

Methods

lessThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic

greaterThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic

leq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic

geq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic

HasOrderAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Rational

Methods

lessThan :: MPBall -> Rational -> OrderCompareType MPBall Rational

greaterThan :: MPBall -> Rational -> OrderCompareType MPBall Rational

leq :: MPBall -> Rational -> OrderCompareType MPBall Rational

geq :: MPBall -> Rational -> OrderCompareType MPBall Rational

HasOrderAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Integer

Methods

lessThan :: MPBall -> Integer -> OrderCompareType MPBall Integer

greaterThan :: MPBall -> Integer -> OrderCompareType MPBall Integer

leq :: MPBall -> Integer -> OrderCompareType MPBall Integer

geq :: MPBall -> Integer -> OrderCompareType MPBall Integer

HasOrderAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Int

Methods

lessThan :: MPBall -> Int -> OrderCompareType MPBall Int

greaterThan :: MPBall -> Int -> OrderCompareType MPBall Int

leq :: MPBall -> Int -> OrderCompareType MPBall Int

geq :: MPBall -> Int -> OrderCompareType MPBall Int

HasOrderAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Dyadic MPBall

Methods

lessThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall

greaterThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall

leq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall

geq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall

HasOrderAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Rational MPBall

Methods

lessThan :: Rational -> MPBall -> OrderCompareType Rational MPBall

greaterThan :: Rational -> MPBall -> OrderCompareType Rational MPBall

leq :: Rational -> MPBall -> OrderCompareType Rational MPBall

geq :: Rational -> MPBall -> OrderCompareType Rational MPBall

HasOrderAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Integer MPBall

Methods

lessThan :: Integer -> MPBall -> OrderCompareType Integer MPBall

greaterThan :: Integer -> MPBall -> OrderCompareType Integer MPBall

leq :: Integer -> MPBall -> OrderCompareType Integer MPBall

geq :: Integer -> MPBall -> OrderCompareType Integer MPBall

HasOrderAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Int MPBall

Methods

lessThan :: Int -> MPBall -> OrderCompareType Int MPBall

greaterThan :: Int -> MPBall -> OrderCompareType Int MPBall

leq :: Int -> MPBall -> OrderCompareType Int MPBall

geq :: Int -> MPBall -> OrderCompareType Int MPBall

CanPow MPBall MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall MPBall

type PPowType MPBall MPBall

Methods

pow :: MPBall -> MPBall -> PowType MPBall MPBall

ppow :: MPBall -> MPBall -> PPowType MPBall MPBall

CanPow MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall Dyadic

type PPowType MPBall Dyadic

Methods

pow :: MPBall -> Dyadic -> PowType MPBall Dyadic

ppow :: MPBall -> Dyadic -> PPowType MPBall Dyadic

CanPow MPBall Rational

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall Rational

type PPowType MPBall Rational

Methods

pow :: MPBall -> Rational -> PowType MPBall Rational

ppow :: MPBall -> Rational -> PPowType MPBall Rational

CanPow MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall Integer

type PPowType MPBall Integer

Methods

pow :: MPBall -> Integer -> PowType MPBall Integer

ppow :: MPBall -> Integer -> PPowType MPBall Integer

CanPow MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall Int

type PPowType MPBall Int

Methods

pow :: MPBall -> Int -> PowType MPBall Int

ppow :: MPBall -> Int -> PPowType MPBall Int

CanPow Rational MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Rational MPBall

type PPowType Rational MPBall

Methods

pow :: Rational -> MPBall -> PowType Rational MPBall

ppow :: Rational -> MPBall -> PPowType Rational MPBall

CanPow Integer MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Integer MPBall

type PPowType Integer MPBall

Methods

pow :: Integer -> MPBall -> PowType Integer MPBall

ppow :: Integer -> MPBall -> PPowType Integer MPBall

CanPow Int MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Int MPBall

type PPowType Int MPBall

Methods

pow :: Int -> MPBall -> PowType Int MPBall

ppow :: Int -> MPBall -> PPowType Int MPBall

CanDivIMod MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivIType MPBall MPBall

type ModType MPBall MPBall

Methods

divIMod :: MPBall -> MPBall -> (DivIType MPBall MPBall, ModType MPBall MPBall)

mod :: MPBall -> MPBall -> ModType MPBall MPBall

divI :: MPBall -> MPBall -> DivIType MPBall MPBall

(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), KnownNat p) => HasLimits ix (CN (WithCurrentPrec p (CN MPBall)))

Defined in AERN2.MP.WithCurrentPrec.Limit

Associated Types

type LimitType ix (CN (WithCurrentPrec p (CN MPBall)))

Methods

limit :: (ix -> CN (WithCurrentPrec p (CN MPBall))) -> LimitType ix (CN (WithCurrentPrec p (CN MPBall)))

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CN b)

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)

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall (CN b)

Methods

sub :: MPBall -> CN b -> SubType MPBall (CN b)

(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CN b)

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)

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall (CN b)

Methods

mul :: MPBall -> CN b -> MulType MPBall (CN b)

CanPow MPBall b => CanPow MPBall (CN b)

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall (CN b)

type PPowType MPBall (CN b)

Methods

pow :: MPBall -> CN b -> PowType MPBall (CN b)

ppow :: MPBall -> CN b -> PPowType MPBall (CN b)

HasLimits Rational (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Rational (CN MPBall -> CN MPBall)

Methods

limit :: (Rational -> CN MPBall -> CN MPBall) -> LimitType Rational (CN MPBall -> CN MPBall)

HasLimits Integer (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Integer (CN MPBall -> CN MPBall)

Methods

limit :: (Integer -> CN MPBall -> CN MPBall) -> LimitType Integer (CN MPBall -> CN MPBall)

HasLimits Int (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Int (CN MPBall -> CN MPBall)

Methods

limit :: (Int -> CN MPBall -> CN MPBall) -> LimitType Int (CN MPBall -> CN MPBall)

(CanIntersectAsymmetric MPBall b, CanBeErrors es) => CanIntersectAsymmetric MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType MPBall (CollectErrors es b)

Methods

intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b)

(CanUnionAsymmetric MPBall b, CanBeErrors es) => CanUnionAsymmetric MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType MPBall (CollectErrors es b)

Methods

union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b)

(HasEqAsymmetric MPBall b, IsBool (EqCompareType MPBall b), CanTestCertainly (EqCompareType MPBall b), CanBeErrors es) => HasEqAsymmetric MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall (CollectErrors es b)

Methods

equalTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b)

notEqualTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b)

(CanMinMaxAsymmetric MPBall b, CanBeErrors es) => CanMinMaxAsymmetric MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall (CollectErrors es b)

Methods

min :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b)

max :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b)

(HasOrderAsymmetric MPBall b, IsBool (OrderCompareType MPBall b), CanTestCertainly (OrderCompareType MPBall b), CanBeErrors es) => HasOrderAsymmetric MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall (CollectErrors es b)

Methods

lessThan :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b)

greaterThan :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b)

leq :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b)

geq :: MPBall -> CollectErrors es b -> OrderCompareType MPBall (CollectErrors es b)

(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), KnownNat p) => HasLimits ix (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec.Limit

Associated Types

type LimitType ix (WithCurrentPrec p (CN MPBall))

Methods

limit :: (ix -> WithCurrentPrec p (CN MPBall)) -> LimitType ix (WithCurrentPrec p (CN MPBall))

OrderedCertainlyRing (CN MPBall)

Defined in AERN2.MP.Ball

OrderedRing (CN MPBall)

Defined in AERN2.MP.Ball

Ring (CN MPBall)

Defined in AERN2.MP.Ball

CanBeErrorBound t => CanPlusMinus (CN MPBall) t

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType (CN MPBall) t

Methods

plusMinus :: CN MPBall -> t -> PlusMinusType (CN MPBall) t

CanAddAsymmetric a MPBall => CanAddAsymmetric (CN a) MPBall

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

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType (CN a) MPBall

Methods

sub :: CN a -> MPBall -> SubType (CN a) MPBall

CanDiv a MPBall => CanDiv (CN a) MPBall

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

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType (CN a) MPBall

Methods

mul :: CN a -> MPBall -> MulType (CN a) MPBall

CanPow a MPBall => CanPow (CN a) MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType (CN a) MPBall

type PPowType (CN a) MPBall

Methods

pow :: CN a -> MPBall -> PowType (CN a) MPBall

ppow :: CN a -> MPBall -> PPowType (CN a) MPBall

(CanIntersectAsymmetric a MPBall, CanBeErrors es) => CanIntersectAsymmetric (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType (CollectErrors es a) MPBall

Methods

intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall

(CanUnionAsymmetric a MPBall, CanBeErrors es) => CanUnionAsymmetric (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType (CollectErrors es a) MPBall

Methods

union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall

ConvertibleWithPrecision (CentreRadius Rational Rational) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> CentreRadius Rational Rational -> ConvertResult MPBall

(HasEqAsymmetric a MPBall, IsBool (EqCompareType a MPBall), CanTestCertainly (EqCompareType a MPBall), CanBeErrors es) => HasEqAsymmetric (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType (CollectErrors es a) MPBall

Methods

equalTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall

notEqualTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall

(ConvertibleExactly c Dyadic, ConvertibleExactly e Dyadic, Show c, Show e, Typeable c, Typeable e) => ConvertibleExactly (CentreRadius c e) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: CentreRadius c e -> ConvertResult MPBall

ConvertibleExactly (WithSample MPBall Rational) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: WithSample MPBall Rational -> ConvertResult MPBall

ConvertibleExactly (WithSample MPBall Integer) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: WithSample MPBall Integer -> ConvertResult MPBall

(CanMinMaxAsymmetric a MPBall, CanBeErrors es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType (CollectErrors es a) MPBall

Methods

min :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall

max :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall

(HasOrderAsymmetric a MPBall, IsBool (OrderCompareType a MPBall), CanTestCertainly (OrderCompareType a MPBall), CanBeErrors es) => HasOrderAsymmetric (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType (CollectErrors es a) MPBall

Methods

lessThan :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall

greaterThan :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall

leq :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall

geq :: CollectErrors es a -> MPBall -> OrderCompareType (CollectErrors es a) MPBall

KnownNat p => Floating (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec.PreludeInstances

Methods

pi :: WithCurrentPrec p (CN MPBall)

exp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

log :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

sqrt :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

(**) :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

logBase :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

sin :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

cos :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

tan :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

asin :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

acos :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

atan :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

sinh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

cosh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

tanh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

asinh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

acosh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

atanh :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

log1p :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

expm1 :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

log1pexp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

log1mexp :: WithCurrentPrec p (CN MPBall) -> WithCurrentPrec p (CN MPBall)

KnownNat p => Field (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec

KnownNat p => OrderedField (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec

KnownNat p => OrderedRing (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec

KnownNat p => Ring (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec

type Approximate MPBall

Defined in AERN2.MP.Ball.Type

type Approximate MPBall = (MPFloat, Bool)

type CentreType MPBall

Defined in AERN2.MP.Ball.Type

type CentreType MPBall = Dyadic

type IntervalEndpoint MPBall

Defined in AERN2.MP.Ball.Type

type IntervalEndpoint MPBall = MPFloat

type Rep MPBall

Defined in AERN2.MP.Ball.Type

type Rep MPBall = D1 ('MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.2.16.1-IJDSJSVfOW8Hl8Ias4Iudc" 'False) (C1 ('MetaCons "MPBall" 'PrefixI 'True) (S1 ('MetaSel ('Just "ball_value") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat) :*: S1 ('MetaSel ('Just "ball_error") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ErrorBound)))

type NegType MPBall

Defined in AERN2.MP.Ball.Type

type NegType MPBall = MPBall

type ExpType MPBall

Defined in AERN2.MP.Ball.Elementary

type ExpType MPBall = MPBall

type LogType MPBall

Defined in AERN2.MP.Ball.Elementary

type LogType MPBall = MPBall

type SinCosType MPBall

Defined in AERN2.MP.Ball.Elementary

type SinCosType MPBall = MPBall

type SqrtType MPBall

Defined in AERN2.MP.Ball.Elementary

type SqrtType MPBall = MPBall

type AbsType MPBall

Defined in AERN2.MP.Ball.Type

type AbsType MPBall = MPBall

type IntersectionType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType MPBall MPBall = CN MPBall

type PlusMinusType MPBall t

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType MPBall t = MPBall

type UnionType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type UnionType MPBall MPBall = CN MPBall

type AddType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type AddType MPBall MPBall = MPBall

type AddType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type AddType MPBall Dyadic = MPBall

type AddType MPBall Rational

Defined in AERN2.MP.Ball.Field

type AddType MPBall Rational = MPBall

type AddType MPBall Integer

Defined in AERN2.MP.Ball.Field

type AddType MPBall Integer = MPBall

type AddType MPBall Int

Defined in AERN2.MP.Ball.Field

type AddType MPBall Int = MPBall

type AddType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type AddType Dyadic MPBall = MPBall

type AddType Rational MPBall

Defined in AERN2.MP.Ball.Field

type AddType Rational MPBall = MPBall

type AddType Integer MPBall

Defined in AERN2.MP.Ball.Field

type AddType Integer MPBall = MPBall

type AddType Int MPBall

Defined in AERN2.MP.Ball.Field

type AddType Int MPBall = MPBall

type SubType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type SubType MPBall MPBall = AddType MPBall (NegType MPBall)

type SubType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)

type SubType MPBall Rational

Defined in AERN2.MP.Ball.Field

type SubType MPBall Rational = AddType MPBall (NegType Rational)

type SubType MPBall Integer

Defined in AERN2.MP.Ball.Field

type SubType MPBall Integer = AddType MPBall (NegType Integer)

type SubType MPBall Int

Defined in AERN2.MP.Ball.Field

type SubType MPBall Int = AddType MPBall (NegType Int)

type SubType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)

type SubType Rational MPBall

Defined in AERN2.MP.Ball.Field

type SubType Rational MPBall = AddType Rational (NegType MPBall)

type SubType Integer MPBall

Defined in AERN2.MP.Ball.Field

type SubType Integer MPBall = AddType Integer (NegType MPBall)

type SubType Int MPBall

Defined in AERN2.MP.Ball.Field

type SubType Int MPBall = AddType Int (NegType MPBall)

type DivType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type DivType MPBall MPBall = MPBall

type DivType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type DivType MPBall Dyadic = MPBall

type DivType MPBall Rational

Defined in AERN2.MP.Ball.Field

type DivType MPBall Rational = MPBall

type DivType MPBall Integer

Defined in AERN2.MP.Ball.Field

type DivType MPBall Integer = MPBall

type DivType MPBall Int

Defined in AERN2.MP.Ball.Field

type DivType MPBall Int = MPBall

type DivType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type DivType Dyadic MPBall = MPBall

type DivType Rational MPBall

Defined in AERN2.MP.Ball.Field

type DivType Rational MPBall = MPBall

type DivType Integer MPBall

Defined in AERN2.MP.Ball.Field

type DivType Integer MPBall = MPBall

type DivType Int MPBall

Defined in AERN2.MP.Ball.Field

type DivType Int MPBall = MPBall

type EqCompareType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall MPBall = Kleenean

type EqCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Dyadic = Kleenean

type EqCompareType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Rational = Kleenean

type EqCompareType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Integer = Kleenean

type EqCompareType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Int = Kleenean

type EqCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Dyadic MPBall = Kleenean

type EqCompareType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Rational MPBall = Kleenean

type EqCompareType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Integer MPBall = Kleenean

type EqCompareType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Int MPBall = Kleenean

type MinMaxType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall MPBall = MPBall

type MinMaxType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Dyadic = MPBall

type MinMaxType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Rational = MPBall

type MinMaxType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Integer = MPBall

type MinMaxType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Int = MPBall

type MinMaxType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Dyadic MPBall = MPBall

type MinMaxType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Rational MPBall = MPBall

type MinMaxType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Integer MPBall = MPBall

type MinMaxType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Int MPBall = MPBall

type MulType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type MulType MPBall MPBall = MPBall

type MulType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type MulType MPBall Dyadic = MPBall

type MulType MPBall Rational

Defined in AERN2.MP.Ball.Field

type MulType MPBall Rational = MPBall

type MulType MPBall Integer

Defined in AERN2.MP.Ball.Field

type MulType MPBall Integer = MPBall

type MulType MPBall Int

Defined in AERN2.MP.Ball.Field

type MulType MPBall Int = MPBall

type MulType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type MulType Dyadic MPBall = MPBall

type MulType Rational MPBall

Defined in AERN2.MP.Ball.Field

type MulType Rational MPBall = MPBall

type MulType Integer MPBall

Defined in AERN2.MP.Ball.Field

type MulType Integer MPBall = MPBall

type MulType Int MPBall

Defined in AERN2.MP.Ball.Field

type MulType Int MPBall = MPBall

type OrderCompareType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall MPBall = Kleenean

type OrderCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Dyadic = Kleenean

type OrderCompareType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Rational = Kleenean

type OrderCompareType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Integer = Kleenean

type OrderCompareType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Int = Kleenean

type OrderCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Dyadic MPBall = Kleenean

type OrderCompareType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Rational MPBall = Kleenean

type OrderCompareType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Integer MPBall = Kleenean

type OrderCompareType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Int MPBall = Kleenean

type PPowType MPBall MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall MPBall = PowType MPBall MPBall

type PPowType MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall Dyadic = PowType MPBall Dyadic

type PPowType MPBall Rational

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall Rational = PowType MPBall Rational

type PPowType MPBall Integer

Defined in AERN2.MP.Ball.Field

type PPowType MPBall Integer = PowType MPBall Integer

type PPowType MPBall Int

Defined in AERN2.MP.Ball.Field

type PPowType MPBall Int = PowType MPBall Int

type PPowType Rational MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Rational MPBall = PowType Rational MPBall

type PPowType Integer MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Integer MPBall = PowType Integer MPBall

type PPowType Int MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Int MPBall = PowType Int MPBall

type PowType MPBall MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall MPBall = MPBall

type PowType MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Dyadic = MPBall

type PowType MPBall Rational

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Rational = MPBall

type PowType MPBall Integer

Defined in AERN2.MP.Ball.Field

type PowType MPBall Integer = MPBall

type PowType MPBall Int

Defined in AERN2.MP.Ball.Field

type PowType MPBall Int = MPBall

type PowType Rational MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Rational MPBall = MPBall

type PowType Integer MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Integer MPBall = MPBall

type PowType Int MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Int MPBall = MPBall

type DivIType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type DivIType MPBall MPBall = Integer

type ModType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type ModType MPBall MPBall = MPBall

type LimitType ix (CN (WithCurrentPrec p (CN MPBall)))

Defined in AERN2.MP.WithCurrentPrec.Limit

type LimitType ix (CN (WithCurrentPrec p (CN MPBall))) = WithCurrentPrec p (CN MPBall)

type AddType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type AddType MPBall (CN b) = CN (AddType MPBall b)

type SubType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type SubType MPBall (CN b) = CN (SubType MPBall b)

type DivType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type DivType MPBall (CN b) = CN (DivType MPBall b)

type MulType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type MulType MPBall (CN b) = CN (MulType MPBall b)

type PPowType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type PPowType MPBall (CN b) = PowType MPBall (CN b)

type PowType MPBall (CN b)

Defined in AERN2.MP.Ball.Field

type PowType MPBall (CN b) = CN (PowType MPBall b)

type LimitType Rational (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

type LimitType Rational (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall

type LimitType Integer (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

type LimitType Integer (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall

type LimitType Int (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

type LimitType Int (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall

type IntersectionType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType MPBall (CollectErrors es b) = CollectErrors es (IntersectionType MPBall b)

type UnionType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type UnionType MPBall (CollectErrors es b) = CollectErrors es (UnionType MPBall b)

type EqCompareType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall (CollectErrors es b) = CollectErrors es (EqCompareType MPBall b)

type MinMaxType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall (CollectErrors es b) = CollectErrors es (MinMaxType MPBall b)

type OrderCompareType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall (CollectErrors es b) = CollectErrors es (OrderCompareType MPBall b)

type LimitType ix (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec.Limit

type LimitType ix (WithCurrentPrec p (CN MPBall)) = WithCurrentPrec p (CN MPBall)

type PlusMinusType (CN MPBall) t

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType (CN MPBall) t = CN MPBall

type AddType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type AddType (CN a) MPBall = CN (AddType a MPBall)

type SubType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type SubType (CN a) MPBall = CN (SubType a MPBall)

type DivType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type DivType (CN a) MPBall = CN (DivType a MPBall)

type MulType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type MulType (CN a) MPBall = CN (MulType a MPBall)

type PPowType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type PPowType (CN a) MPBall = PowType (CN a) MPBall

type PowType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

type PowType (CN a) MPBall = CN (PowType a MPBall)

type IntersectionType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType (CollectErrors es a) MPBall = CollectErrors es (IntersectionType a MPBall)

type UnionType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

type UnionType (CollectErrors es a) MPBall = CollectErrors es (UnionType a MPBall)

type EqCompareType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType (CollectErrors es a) MPBall = CollectErrors es (EqCompareType a MPBall)

type MinMaxType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType (CollectErrors es a) MPBall = CollectErrors es (MinMaxType a MPBall)

type OrderCompareType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType (CollectErrors es a) MPBall = CollectErrors es (OrderCompareType a MPBall)

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

data CentreRadius c e

Constructors

CentreRadius c e

Instances

ConvertibleWithPrecision (CentreRadius Rational Rational) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> CentreRadius Rational Rational -> ConvertResult MPBall

(ConvertibleExactly c Dyadic, ConvertibleExactly e Dyadic, Show c, Show e, Typeable c, Typeable e) => ConvertibleExactly (CentreRadius c e) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: CentreRadius c e -> ConvertResult 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.

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

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

Ball operations (see also instances)

piBallP :: Precision -> MPBall

intersectCNMPBall :: CN MPBall -> CN MPBall -> CN MPBall

hullMPBall :: MPBall -> MPBall -> MPBall

Helpers for constructing ball functions

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

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

fromApproxWithLipschitz

Arguments

:: (MPFloat -> BoundsCEDU MPFloat)

fCEDU: a version of f on MPFloat returning rigorous bounds

-> MPFloat

lip a Lipschitz constant for f, lip > 0

-> MPBall -> MPBall

f on MPBall rounding *outwards*

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

Orphan instances

OrderedCertainlyRing MPBall

OrderedRing MPBall

Ring MPBall

OrderedCertainlyRing (CN MPBall)

OrderedRing (CN MPBall)

Ring (CN MPBall)