AERN2.MP.Ball.Type

Arbitrary precision dyadic balls

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

Defined in AERN2.MP.Ball.PreludeOps

Methods

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

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

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

Fractional MPBall

Defined in AERN2.MP.Ball.PreludeOps

Methods

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

recip :: MPBall -> MPBall

fromRational :: Rational -> 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

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

Show MPBall

Defined in AERN2.MP.Ball.Type

Methods

showsPrec :: Int -> MPBall -> ShowS

show :: MPBall -> String

showList :: [MPBall] -> ShowS

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

Arbitrary MPBall

Defined in AERN2.MP.Ball.Tests

Methods

arbitrary :: Gen MPBall

shrink :: MPBall -> [MPBall]

NFData MPBall

Defined in AERN2.MP.Ball.Type

Methods

rnf :: MPBall -> ()

CanSqrt MPBall

Defined in AERN2.MP.Ball.Elementary

Associated Types

type SqrtType MPBall

Methods

sqrt :: MPBall -> SqrtType 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

CanTestIsIntegerType MPBall

Defined in AERN2.MP.Ball.Type

Methods

isIntegerType :: MPBall -> Bool

Ring MPBall

Defined in AERN2.MP.Ball

OrderedRing MPBall

Defined in AERN2.MP.Ball

OrderedCertainlyRing MPBall

Defined in AERN2.MP.Ball

HasIntegerBounds MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

integerBounds :: MPBall -> (Integer, Integer)

CanAbs MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type AbsType MPBall

Methods

abs :: MPBall -> AbsType MPBall

CanGiveUpIfVeryInaccurate MPBall

Defined in AERN2.MP.Ball.Type

Methods

giveUpIfVeryInaccurate :: CN MPBall -> CN MPBall

CanTestNaN MPBall

Defined in AERN2.MP.Ball.Type

Methods

isNaN :: MPBall -> Bool

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

CanTestZero MPBall

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyZero :: MPBall -> Bool

isCertainlyNonZero :: MPBall -> Bool

CanTestPosNeg MPBall

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyPositive :: MPBall -> Bool

isCertainlyNonNegative :: MPBall -> Bool

isCertainlyNegative :: MPBall -> Bool

isCertainlyNonPositive :: MPBall -> Bool

CanNeg MPBall

Defined in AERN2.MP.Ball.Type

Associated Types

type NegType MPBall

Methods

negate :: MPBall -> NegType 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

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

HasAccuracy MPBall

Defined in AERN2.MP.Ball.Type

Methods

getAccuracy :: MPBall -> Accuracy

getFiniteAccuracy :: MPBall -> Accuracy

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

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

CanNormalize MPBall

Defined in AERN2.MP.Ball.Type

Methods

normalize :: MPBall -> MPBall

CanDiv Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Int MPBall

Methods

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

CanDiv Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Integer MPBall

Methods

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

CanDiv Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Rational MPBall

Methods

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

CanDiv Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Dyadic MPBall

Methods

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

CanDiv MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Int

Methods

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

CanDiv MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Integer

Methods

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

CanDiv MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Rational

Methods

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

CanDiv MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Dyadic

Methods

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

CanDiv MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall MPBall

Methods

divide :: MPBall -> MPBall -> DivType MPBall 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

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 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 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 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 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 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 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

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

CanMulAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Int MPBall

Methods

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

CanMulAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Integer MPBall

Methods

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

CanMulAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Rational MPBall

Methods

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

CanMulAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Dyadic MPBall

Methods

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

CanMulAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Int

Methods

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

CanMulAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Integer

Methods

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

CanMulAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Rational

Methods

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

CanMulAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Dyadic

Methods

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

CanMulAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall MPBall

Methods

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

CanAddAsymmetric Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Int MPBall

Methods

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

CanAddAsymmetric Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Integer MPBall

Methods

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

CanAddAsymmetric Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Rational MPBall

Methods

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

CanAddAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Dyadic MPBall

Methods

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

CanAddAsymmetric MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Int

Methods

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

CanAddAsymmetric MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Integer

Methods

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

CanAddAsymmetric MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Rational

Methods

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

CanAddAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Dyadic

Methods

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

CanAddAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall MPBall

Methods

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

CanSub Int MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Int MPBall

Methods

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

CanSub Integer MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Integer MPBall

Methods

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

CanSub Rational MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Rational MPBall

Methods

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

CanSub Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Dyadic MPBall

Methods

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

CanSub MPBall Int

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Int

Methods

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

CanSub MPBall Integer

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Integer

Methods

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

CanSub MPBall Rational

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Rational

Methods

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

CanSub MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Dyadic

Methods

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

CanSub MPBall MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall MPBall

Methods

sub :: MPBall -> MPBall -> SubType MPBall 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

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 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 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 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 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 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 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 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

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

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 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 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 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 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 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 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 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

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

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 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 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 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 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 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 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 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

ConvertibleExactly Int MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Int -> ConvertResult MPBall

ConvertibleExactly Integer MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Integer -> 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 MPBall MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: MPBall -> ConvertResult MPBall

Convertible MPBall ErrorBound

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvert :: MPBall -> ConvertResult ErrorBound

ConvertibleWithPrecision Int MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Int -> ConvertResult MPBall

ConvertibleWithPrecision Integer MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Integer -> ConvertResult MPBall

ConvertibleWithPrecision Rational MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Rational -> ConvertResult MPBall

ConvertibleWithPrecision Dyadic MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall

CanUnionAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType MPBall MPBall

Methods

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

CanIntersectAsymmetric MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType MPBall MPBall

Methods

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

CanTestContains MPBall Int

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Int -> Bool

CanTestContains MPBall Integer

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Integer -> Bool

CanTestContains MPBall Rational

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Rational -> Bool

CanTestContains MPBall Dyadic

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Dyadic -> Bool

CanTestContains MPBall MPBall

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> MPBall -> Bool

CanBeErrorBound t => CanPlusMinus MPBall t

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType MPBall t

Methods

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

(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)

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)

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)

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)

(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)))

(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)

(HasEqAsymmetric MPBall b, IsBool (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)

(HasOrderAsymmetric MPBall b, IsBool (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 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)

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 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)

(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)

(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)

(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))

Ring (CN MPBall)

Defined in AERN2.MP.Ball

OrderedRing (CN MPBall)

Defined in AERN2.MP.Ball

OrderedCertainlyRing (CN MPBall)

Defined in AERN2.MP.Ball

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

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

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

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

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

(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

(HasEqAsymmetric a MPBall, IsBool (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

(HasOrderAsymmetric a MPBall, IsBool (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

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

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: (c, e) -> ConvertResult MPBall

ConvertibleWithPrecision (Rational, Rational) MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult 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

(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

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 => Ring (WithCurrentPrec p (CN MPBall))

Defined in AERN2.MP.WithCurrentPrec

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

Defined in AERN2.MP.WithCurrentPrec

type Rep MPBall

Defined in AERN2.MP.Ball.Type

type Rep MPBall = D1 ('MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.2.8.0-7EdW5MADRpY8tQ5ayaur95" '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

Defined in AERN2.MP.Ball.Elementary

type SqrtType 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 AbsType MPBall

Defined in AERN2.MP.Ball.Type

type AbsType MPBall = MPBall

type NegType MPBall

Defined in AERN2.MP.Ball.Type

type NegType MPBall = MPBall

type Approximate MPBall

Defined in AERN2.MP.Ball.Type

type Approximate MPBall = (MPFloat, Bool)

type IntervalEndpoint MPBall

Defined in AERN2.MP.Ball.Type

type IntervalEndpoint MPBall = MPFloat

type CentreType MPBall

Defined in AERN2.MP.Ball.Type

type CentreType MPBall = Dyadic

type DivType Int MPBall

Defined in AERN2.MP.Ball.Field

type DivType Int MPBall = MPBall

type DivType Integer MPBall

Defined in AERN2.MP.Ball.Field

type DivType Integer MPBall = MPBall

type DivType Rational MPBall

Defined in AERN2.MP.Ball.Field

type DivType Rational MPBall = MPBall

type DivType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type DivType Dyadic MPBall = MPBall

type DivType MPBall Int

Defined in AERN2.MP.Ball.Field

type DivType MPBall Int = MPBall

type DivType MPBall Integer

Defined in AERN2.MP.Ball.Field

type DivType MPBall Integer = MPBall

type DivType MPBall Rational

Defined in AERN2.MP.Ball.Field

type DivType MPBall Rational = MPBall

type DivType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type DivType MPBall Dyadic = MPBall

type DivType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type DivType MPBall MPBall = MPBall

type PPowType Int MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Int MPBall = PowType Int MPBall

type PPowType Integer MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Integer MPBall = PowType Integer MPBall

type PPowType Rational MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType Rational MPBall = PowType Rational MPBall

type PPowType MPBall Int

Defined in AERN2.MP.Ball.Field

type PPowType MPBall Int = PowType MPBall Int

type PPowType MPBall Integer

Defined in AERN2.MP.Ball.Field

type PPowType MPBall Integer = PowType MPBall Integer

type PPowType MPBall Rational

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall Rational = PowType MPBall Rational

type PPowType MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall Dyadic = PowType MPBall Dyadic

type PPowType MPBall MPBall

Defined in AERN2.MP.Ball.Elementary

type PPowType MPBall MPBall = PowType MPBall MPBall

type PowType Int MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Int MPBall = MPBall

type PowType Integer MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Integer MPBall = MPBall

type PowType Rational MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType Rational MPBall = MPBall

type PowType MPBall Int

Defined in AERN2.MP.Ball.Field

type PowType MPBall Int = MPBall

type PowType MPBall Integer

Defined in AERN2.MP.Ball.Field

type PowType MPBall Integer = MPBall

type PowType MPBall Rational

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Rational = MPBall

type PowType MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Dyadic = MPBall

type PowType MPBall MPBall

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall MPBall = MPBall

type ModType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type ModType MPBall MPBall = MPBall

type DivIType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type DivIType MPBall MPBall = Integer

type MulType Int MPBall

Defined in AERN2.MP.Ball.Field

type MulType Int MPBall = MPBall

type MulType Integer MPBall

Defined in AERN2.MP.Ball.Field

type MulType Integer MPBall = MPBall

type MulType Rational MPBall

Defined in AERN2.MP.Ball.Field

type MulType Rational MPBall = MPBall

type MulType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type MulType Dyadic MPBall = MPBall

type MulType MPBall Int

Defined in AERN2.MP.Ball.Field

type MulType MPBall Int = MPBall

type MulType MPBall Integer

Defined in AERN2.MP.Ball.Field

type MulType MPBall Integer = MPBall

type MulType MPBall Rational

Defined in AERN2.MP.Ball.Field

type MulType MPBall Rational = MPBall

type MulType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type MulType MPBall Dyadic = MPBall

type MulType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type MulType MPBall MPBall = MPBall

type AddType Int MPBall

Defined in AERN2.MP.Ball.Field

type AddType Int MPBall = MPBall

type AddType Integer MPBall

Defined in AERN2.MP.Ball.Field

type AddType Integer MPBall = MPBall

type AddType Rational MPBall

Defined in AERN2.MP.Ball.Field

type AddType Rational MPBall = MPBall

type AddType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type AddType Dyadic MPBall = MPBall

type AddType MPBall Int

Defined in AERN2.MP.Ball.Field

type AddType MPBall Int = MPBall

type AddType MPBall Integer

Defined in AERN2.MP.Ball.Field

type AddType MPBall Integer = MPBall

type AddType MPBall Rational

Defined in AERN2.MP.Ball.Field

type AddType MPBall Rational = MPBall

type AddType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type AddType MPBall Dyadic = MPBall

type AddType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type AddType MPBall MPBall = MPBall

type SubType Int MPBall

Defined in AERN2.MP.Ball.Field

type SubType Int MPBall = AddType Int (NegType MPBall)

type SubType Integer MPBall

Defined in AERN2.MP.Ball.Field

type SubType Integer MPBall = AddType Integer (NegType MPBall)

type SubType Rational MPBall

Defined in AERN2.MP.Ball.Field

type SubType Rational MPBall = AddType Rational (NegType MPBall)

type SubType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)

type SubType MPBall Int

Defined in AERN2.MP.Ball.Field

type SubType MPBall Int = AddType MPBall (NegType Int)

type SubType MPBall Integer

Defined in AERN2.MP.Ball.Field

type SubType MPBall Integer = AddType MPBall (NegType Integer)

type SubType MPBall Rational

Defined in AERN2.MP.Ball.Field

type SubType MPBall Rational = AddType MPBall (NegType Rational)

type SubType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)

type SubType MPBall MPBall

Defined in AERN2.MP.Ball.Field

type SubType MPBall MPBall = AddType MPBall (NegType MPBall)

type MinMaxType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Int MPBall = MPBall

type MinMaxType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Integer MPBall = MPBall

type MinMaxType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Rational MPBall = MPBall

type MinMaxType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Dyadic MPBall = MPBall

type MinMaxType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Int = MPBall

type MinMaxType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Integer = MPBall

type MinMaxType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Rational = MPBall

type MinMaxType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Dyadic = MPBall

type MinMaxType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall MPBall = MPBall

type EqCompareType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Int MPBall = Kleenean

type EqCompareType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Integer MPBall = Kleenean

type EqCompareType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Rational MPBall = Kleenean

type EqCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Dyadic MPBall = Kleenean

type EqCompareType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Int = Kleenean

type EqCompareType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Integer = Kleenean

type EqCompareType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Rational = Kleenean

type EqCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Dyadic = Kleenean

type EqCompareType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall MPBall = Kleenean

type OrderCompareType Int MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Int MPBall = Kleenean

type OrderCompareType Integer MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Integer MPBall = Kleenean

type OrderCompareType Rational MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Rational MPBall = Kleenean

type OrderCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Dyadic MPBall = Kleenean

type OrderCompareType MPBall Int

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Int = Kleenean

type OrderCompareType MPBall Integer

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Integer = Kleenean

type OrderCompareType MPBall Rational

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Rational = Kleenean

type OrderCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Dyadic = Kleenean

type OrderCompareType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall MPBall = Kleenean

type UnionType MPBall MPBall

Defined in AERN2.MP.Ball.Comparisons

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

Defined in AERN2.MP.Ball.Field

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

Defined in AERN2.MP.Ball.Field

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

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 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 MinMaxType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

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

Defined in AERN2.MP.Ball.Comparisons

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

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 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 Rational (CN MPBall -> CN MPBall)

Defined in AERN2.MP.Ball.Limit

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

type UnionType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

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

type IntersectionType MPBall (CollectErrors es b)

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType MPBall (CollectErrors es b) = CollectErrors es (IntersectionType 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 DivType (CN a) MPBall

Defined in AERN2.MP.Ball.Field

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

Defined in AERN2.MP.Ball.Field

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

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType (CN MPBall) t = CN 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 EqCompareType (CollectErrors es a) MPBall

Defined in AERN2.MP.Ball.Comparisons

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

Defined in AERN2.MP.Ball.Comparisons

type UnionType (CollectErrors es a) MPBall = CollectErrors es (UnionType 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 CanBeMPBall t = ConvertibleExactly t MPBall

mpBall :: CanBeMPBall t => t -> MPBall

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

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall

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

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

reducePrecionIfInaccurate :: MPBall -> MPBall

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

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

Ball construction/extraction functions

fromMPFloatEndpoints :: MPFloat -> MPFloat -> MPBall

mpBallEndpoints :: MPBall -> (MPBall, MPBall)

fromMPBallEndpoints :: MPBall -> MPBall -> MPBall