aern2-mp-0.2.2.0: Multi-precision ball (interval) arithmetic
Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

AERN2.MP.Ball

Description

Arbitrary precision ball arithmetic

Synopsis

Auxiliary types

module AERN2.Norm

module AERN2.MP.Precision

module AERN2.MP.Accuracy

type CanBeErrorBound t = Convertible t ErrorBound Source #

data ErrorBound Source #

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

Instances

Instances details
Eq ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

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

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

Ord ErrorBound Source # 
Instance details

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 #

Show ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

showsPrec :: Int -> ErrorBound -> ShowS #

show :: ErrorBound -> String #

showList :: [ErrorBound] -> ShowS #

Generic ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type Rep ErrorBound :: Type -> Type #

Methods

from :: ErrorBound -> Rep ErrorBound x #

to :: Rep ErrorBound x -> ErrorBound #

Arbitrary ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

arbitrary :: Gen ErrorBound #

shrink :: ErrorBound -> [ErrorBound] #

NFData ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

rnf :: ErrorBound -> () #

HasAccuracy ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

getAccuracy :: ErrorBound -> Accuracy Source #

getFiniteAccuracy :: ErrorBound -> Accuracy Source #

CanDiv ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type DivType ErrorBound Integer #

Methods

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

CanMulAsymmetric Integer ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType Integer ErrorBound #

Methods

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

CanMulAsymmetric Rational ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType Rational ErrorBound #

Methods

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

CanMulAsymmetric MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType MPFloat ErrorBound #

Methods

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

CanMulAsymmetric ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound Integer #

Methods

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

CanMulAsymmetric ErrorBound Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound Rational #

Methods

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

CanMulAsymmetric ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound MPFloat #

Methods

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

CanMulAsymmetric ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MulType ErrorBound ErrorBound #

Methods

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

CanAddAsymmetric MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType MPFloat ErrorBound #

Methods

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

CanAddAsymmetric ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType ErrorBound MPFloat #

Methods

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

CanAddAsymmetric ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type AddType ErrorBound ErrorBound #

Methods

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

CanMinMaxAsymmetric ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type MinMaxType ErrorBound ErrorBound #

Methods

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

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

HasEqAsymmetric Int ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType Int ErrorBound #

Methods

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

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

HasEqAsymmetric Integer ErrorBound Source # 
Instance details

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 Rational ErrorBound Source # 
Instance details

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 ErrorBound Int Source # 
Instance details

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 ErrorBound Integer Source # 
Instance details

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 Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Associated Types

type EqCompareType ErrorBound Rational #

Methods

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

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

HasOrderAsymmetric Int ErrorBound Source # 
Instance details

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 #

HasOrderAsymmetric Integer ErrorBound Source # 
Instance details

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 Rational ErrorBound Source # 
Instance details

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 MPFloat ErrorBound Source # 
Instance details

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 ErrorBound Int Source # 
Instance details

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 ErrorBound Integer Source # 
Instance details

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 Rational Source # 
Instance details

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 MPFloat Source # 
Instance details

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 ErrorBound Source # 
Instance details

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 #

ConvertibleExactly ErrorBound Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult Rational #

ConvertibleExactly ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPFloat #

ConvertibleExactly ErrorBound Dyadic Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult Dyadic #

ConvertibleExactly ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult ErrorBound #

ConvertibleExactly ErrorBound MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPBall #

Convertible Int ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Int -> ConvertResult ErrorBound #

Convertible Integer ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Integer -> ConvertResult ErrorBound #

Convertible Rational ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: Rational -> ConvertResult ErrorBound #

Convertible MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

Methods

safeConvert :: MPFloat -> ConvertResult ErrorBound #

Convertible MPBall ErrorBound Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvert :: MPBall -> ConvertResult ErrorBound #

type Rep ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type Rep ErrorBound = D1 ('MetaData "ErrorBound" "AERN2.MP.ErrorBound" "aern2-mp-0.2.2.0-DTtN6apnExTAMCmcKkOJZI" 'True) (C1 ('MetaCons "ErrorBound" 'PrefixI 'True) (S1 ('MetaSel ('Just "er2mp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat)))
type DivType ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type DivType ErrorBound Integer = ErrorBound
type MulType Integer ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType Integer ErrorBound = ErrorBound
type MulType Rational ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType Rational ErrorBound = ErrorBound
type MulType MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType MPFloat ErrorBound = ErrorBound
type MulType ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound Integer = ErrorBound
type MulType ErrorBound Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound Rational = ErrorBound
type MulType ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound MPFloat = ErrorBound
type MulType ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MulType ErrorBound ErrorBound = ErrorBound
type AddType MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type AddType MPFloat ErrorBound = ErrorBound
type AddType ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type AddType ErrorBound MPFloat = ErrorBound
type AddType ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type AddType ErrorBound ErrorBound = ErrorBound
type MinMaxType ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type MinMaxType ErrorBound ErrorBound = ErrorBound
type EqCompareType Int ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType Int ErrorBound = Bool
type EqCompareType Integer ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType Integer ErrorBound = Bool
type EqCompareType Rational ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType Rational ErrorBound = Bool
type EqCompareType ErrorBound Int Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Int = Bool
type EqCompareType ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Integer = Bool
type EqCompareType ErrorBound Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type EqCompareType ErrorBound Rational = Bool
type OrderCompareType Int ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType Int ErrorBound = Bool
type OrderCompareType Integer ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType Integer ErrorBound = Bool
type OrderCompareType Rational ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType Rational ErrorBound = Bool
type OrderCompareType MPFloat ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType MPFloat ErrorBound = Bool
type OrderCompareType ErrorBound Int Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Int = Bool
type OrderCompareType ErrorBound Integer Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Integer = Bool
type OrderCompareType ErrorBound Rational Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound Rational = Bool
type OrderCompareType ErrorBound MPFloat Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound MPFloat = Bool
type OrderCompareType ErrorBound ErrorBound Source # 
Instance details

Defined in AERN2.MP.ErrorBound

type OrderCompareType ErrorBound ErrorBound = Bool

errorBound :: CanBeErrorBound t => t -> ErrorBound Source #

module AERN2.MP.Enclosure

The Ball type

data MPBall Source #

Constructors

MPBall 

Fields

Instances

Instances details
Eq MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.PreludeOps

Methods

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

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

Floating MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.PreludeOps

Methods

pi :: MPBall #

exp :: MPBall -> MPBall #

log :: MPBall -> MPBall #

sqrt :: MPBall -> MPBall #

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

logBase :: MPBall -> MPBall -> MPBall #

sin :: MPBall -> MPBall #

cos :: MPBall -> MPBall #

tan :: MPBall -> MPBall #

asin :: MPBall -> MPBall #

acos :: MPBall -> MPBall #

atan :: MPBall -> MPBall #

sinh :: MPBall -> MPBall #

cosh :: MPBall -> MPBall #

tanh :: MPBall -> MPBall #

asinh :: MPBall -> MPBall #

acosh :: MPBall -> MPBall #

atanh :: MPBall -> MPBall #

log1p :: MPBall -> MPBall #

expm1 :: MPBall -> MPBall #

log1pexp :: MPBall -> MPBall #

log1mexp :: MPBall -> MPBall #

Fractional MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.PreludeOps

Methods

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

recip :: MPBall -> MPBall #

fromRational :: Rational -> MPBall #

Num MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.PreludeOps

Methods

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

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

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

negate :: MPBall -> MPBall #

abs :: MPBall -> MPBall #

signum :: MPBall -> MPBall #

fromInteger :: Integer -> MPBall #

Ord MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.PreludeOps

Methods

compare :: MPBall -> MPBall -> Ordering #

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

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

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

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

max :: MPBall -> MPBall -> MPBall #

min :: MPBall -> MPBall -> MPBall #

Show MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

showsPrec :: Int -> MPBall -> ShowS #

show :: MPBall -> String #

showList :: [MPBall] -> ShowS #

Generic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type Rep MPBall :: Type -> Type #

Methods

from :: MPBall -> Rep MPBall x #

to :: Rep MPBall x -> MPBall #

Arbitrary MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Tests

Methods

arbitrary :: Gen MPBall #

shrink :: MPBall -> [MPBall] #

NFData MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

rnf :: MPBall -> () #

CanSqrt MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type SqrtType MPBall #

Methods

sqrt :: MPBall -> SqrtType MPBall #

CanExp MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type ExpType MPBall #

Methods

exp :: MPBall -> ExpType MPBall #

CanLog MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type LogType MPBall #

Methods

log :: MPBall -> LogType MPBall #

CanSinCos MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type SinCosType MPBall #

Methods

cos :: MPBall -> SinCosType MPBall #

sin :: MPBall -> SinCosType MPBall #

Field MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedField MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedCertainlyField MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

HasIntegerBounds MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

integerBounds :: MPBall -> (Integer, Integer) #

Ring MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedRing MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedCertainlyRing MPBall Source # 
Instance details

Defined in AERN2.MP.Ball

CanAbs MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type AbsType MPBall #

Methods

abs :: MPBall -> AbsType MPBall #

CanTestNaN MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

isNaN :: MPBall -> Bool #

CanTestFinite MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

isInfinite :: MPBall -> Bool #

isFinite :: MPBall -> Bool #

CanTestInteger MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Methods

certainlyNotInteger :: MPBall -> Bool #

certainlyInteger :: MPBall -> Bool #

certainlyIntegerGetIt :: MPBall -> Maybe Integer #

CanTestZero MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyZero :: MPBall -> Bool #

isCertainlyNonZero :: MPBall -> Bool #

CanTestPosNeg MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Methods

isCertainlyPositive :: MPBall -> Bool #

isCertainlyNonNegative :: MPBall -> Bool #

isCertainlyNegative :: MPBall -> Bool #

isCertainlyNonPositive :: MPBall -> Bool #

CanNeg MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type NegType MPBall #

Methods

negate :: MPBall -> NegType MPBall #

CanGiveUpIfVeryInaccurate MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

giveUpIfVeryInaccurate :: CN MPBall -> CN MPBall #

CanSetPrecision MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

setPrecision :: Precision -> MPBall -> MPBall Source #

HasPrecision MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

getPrecision :: MPBall -> Precision Source #

HasNorm MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

getNormLog :: MPBall -> NormLog Source #

HasApproximate MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type Approximate MPBall Source #

Methods

getApproximate :: Accuracy -> MPBall -> Approximate MPBall Source #

ShowWithAccuracy MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

showWithAccuracy :: Accuracy -> MPBall -> String Source #

HasAccuracy MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

getAccuracy :: MPBall -> Accuracy Source #

getFiniteAccuracy :: MPBall -> Accuracy Source #

IsInterval MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type IntervalEndpoint MPBall Source #

Methods

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

fromEndpoints :: IntervalEndpoint MPBall -> IntervalEndpoint MPBall -> MPBall Source #

IsBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Associated Types

type CentreType MPBall Source #

Methods

centre :: MPBall -> CentreType MPBall Source #

centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound) Source #

centreAsBall :: MPBall -> MPBall Source #

radius :: MPBall -> ErrorBound Source #

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

makeExactCentre :: MPBall -> MPBall Source #

CanNormalize MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

normalize :: MPBall -> MPBall Source #

CanPow Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Int MPBall #

Methods

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

CanPow Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Integer MPBall #

Methods

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

CanPow Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType Rational MPBall #

Methods

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

CanPow MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall Int #

Methods

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

CanPow MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall Integer #

Methods

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

CanPow MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall Rational #

Methods

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

CanPow MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall Dyadic #

Methods

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

CanPow MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall MPBall #

Methods

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

CanDiv Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Int MPBall #

Methods

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

CanDiv Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Integer MPBall #

Methods

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

CanDiv Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Rational MPBall #

Methods

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

CanDiv Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Dyadic MPBall #

Methods

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

CanDiv MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Int #

Methods

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

CanDiv MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Integer #

Methods

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

CanDiv MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Rational #

Methods

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

CanDiv MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Dyadic #

Methods

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

CanDiv MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall MPBall #

Methods

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

CanDivIMod MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivIType MPBall MPBall #

type ModType MPBall MPBall #

Methods

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

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

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

CanMulAsymmetric Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Int MPBall #

Methods

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

CanMulAsymmetric Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Integer MPBall #

Methods

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

CanMulAsymmetric Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Rational MPBall #

Methods

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

CanMulAsymmetric Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Dyadic MPBall #

Methods

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

CanMulAsymmetric MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Int #

Methods

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

CanMulAsymmetric MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Integer #

Methods

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

CanMulAsymmetric MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Rational #

Methods

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

CanMulAsymmetric MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Dyadic #

Methods

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

CanMulAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall MPBall #

Methods

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

CanAddAsymmetric Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Int MPBall #

Methods

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

CanAddAsymmetric Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Integer MPBall #

Methods

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

CanAddAsymmetric Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Rational MPBall #

Methods

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

CanAddAsymmetric Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Dyadic MPBall #

Methods

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

CanAddAsymmetric MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Int #

Methods

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

CanAddAsymmetric MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Integer #

Methods

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

CanAddAsymmetric MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Rational #

Methods

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

CanAddAsymmetric MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Dyadic #

Methods

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

CanAddAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall MPBall #

Methods

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

CanSub Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Int MPBall #

Methods

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

CanSub Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Integer MPBall #

Methods

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

CanSub Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Rational MPBall #

Methods

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

CanSub Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Dyadic MPBall #

Methods

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

CanSub MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Int #

Methods

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

CanSub MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Integer #

Methods

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

CanSub MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Rational #

Methods

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

CanSub MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Dyadic #

Methods

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

CanSub MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall MPBall #

Methods

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

CanMinMaxAsymmetric Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Int MPBall #

Methods

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

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

CanMinMaxAsymmetric Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Integer MPBall #

Methods

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

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

CanMinMaxAsymmetric Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Rational MPBall #

Methods

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

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

CanMinMaxAsymmetric Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType Dyadic MPBall #

Methods

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

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

CanMinMaxAsymmetric MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Int #

Methods

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

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

CanMinMaxAsymmetric MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Integer #

Methods

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

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

CanMinMaxAsymmetric MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Rational #

Methods

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

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

CanMinMaxAsymmetric MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall Dyadic #

Methods

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

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

CanMinMaxAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall MPBall #

Methods

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

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

HasEqAsymmetric Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Int MPBall #

Methods

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

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

HasEqAsymmetric Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Integer MPBall #

Methods

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

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

HasEqAsymmetric Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Rational MPBall #

Methods

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

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

HasEqAsymmetric Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType Dyadic MPBall #

Methods

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

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

HasEqAsymmetric MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Int #

Methods

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

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

HasEqAsymmetric MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Integer #

Methods

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

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

HasEqAsymmetric MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Rational #

Methods

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

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

HasEqAsymmetric MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall Dyadic #

Methods

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

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

HasEqAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall MPBall #

Methods

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

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

HasOrderAsymmetric Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Int MPBall #

Methods

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

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

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

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

HasOrderAsymmetric Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Integer MPBall #

Methods

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

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

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

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

HasOrderAsymmetric Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Rational MPBall #

Methods

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

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

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

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

HasOrderAsymmetric Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType Dyadic MPBall #

Methods

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

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

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

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

HasOrderAsymmetric MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Int #

Methods

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

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

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

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

HasOrderAsymmetric MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Integer #

Methods

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

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

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

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

HasOrderAsymmetric MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Rational #

Methods

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

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

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

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

HasOrderAsymmetric MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall Dyadic #

Methods

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

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

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

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

HasOrderAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall MPBall #

Methods

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

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

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

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

ConvertibleExactly Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Int -> ConvertResult MPBall #

ConvertibleExactly Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Integer -> ConvertResult MPBall #

ConvertibleExactly Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Dyadic -> ConvertResult MPBall #

ConvertibleExactly ErrorBound MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: ErrorBound -> ConvertResult MPBall #

ConvertibleExactly MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: MPBall -> ConvertResult MPBall #

Convertible MPBall ErrorBound Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvert :: MPBall -> ConvertResult ErrorBound #

ConvertibleWithPrecision Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Int -> ConvertResult MPBall Source #

ConvertibleWithPrecision Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Integer -> ConvertResult MPBall Source #

ConvertibleWithPrecision Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Rational -> ConvertResult MPBall Source #

ConvertibleWithPrecision Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall Source #

CanUnionAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType MPBall MPBall Source #

Methods

union :: MPBall -> MPBall -> UnionType MPBall MPBall Source #

CanIntersectAsymmetric MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType MPBall MPBall Source #

Methods

intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall Source #

CanTestContains MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Int -> Bool Source #

CanTestContains MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Integer -> Bool Source #

CanTestContains MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Rational -> Bool Source #

CanTestContains MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Dyadic -> Bool Source #

CanTestContains MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> MPBall -> Bool Source #

CanBeErrorBound t => CanPlusMinus MPBall t Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType MPBall t Source #

Methods

plusMinus :: MPBall -> t -> PlusMinusType MPBall t Source #

CanPow MPBall b => CanPow MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType MPBall (CN b) #

Methods

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

(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall (CN b) #

Methods

divide :: MPBall -> CN b -> DivType MPBall (CN b) #

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall (CN b) #

Methods

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

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall (CN b) #

Methods

add :: MPBall -> CN b -> AddType MPBall (CN b) #

CanSub MPBall b => CanSub MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall (CN b) #

Methods

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

(CanMinMaxAsymmetric MPBall b, CanBeErrors es) => CanMinMaxAsymmetric MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType MPBall (CollectErrors es b) #

Methods

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

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

(HasEqAsymmetric MPBall b, IsBool (EqCompareType MPBall b), CanBeErrors es) => HasEqAsymmetric MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType MPBall (CollectErrors es b) #

Methods

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

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

(HasOrderAsymmetric MPBall b, IsBool (OrderCompareType MPBall b), CanBeErrors es) => HasOrderAsymmetric MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType MPBall (CollectErrors es b) #

Methods

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

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

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

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

HasLimits Int (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Int (CN MPBall -> CN MPBall) Source #

Methods

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

HasLimits Integer (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Integer (CN MPBall -> CN MPBall) Source #

Methods

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

HasLimits Rational (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

Associated Types

type LimitType Rational (CN MPBall -> CN MPBall) Source #

Methods

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

(CanUnionAsymmetric MPBall b, CanBeErrors es) => CanUnionAsymmetric MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType MPBall (CollectErrors es b) Source #

Methods

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

(CanIntersectAsymmetric MPBall b, CanBeErrors es) => CanIntersectAsymmetric MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType MPBall (CollectErrors es b) Source #

Methods

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

(HasLimits ix (CN MPBall -> CN MPBall), LimitType ix (CN MPBall -> CN MPBall) ~ (CN MPBall -> CN MPBall), HasCurrentPrecision p) => HasLimits ix (WithCurrentPrec (CN MPBall) p) Source # 
Instance details

Defined in AERN2.MP.WithCurrentPrec

Associated Types

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

Methods

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

Field (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedField (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedCertainlyField (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

Ring (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedRing (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

OrderedCertainlyRing (CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball

CanPow a MPBall => CanPow (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type PowType (CN a) MPBall #

Methods

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

CanDiv a MPBall => CanDiv (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType (CN a) MPBall #

Methods

divide :: CN a -> MPBall -> DivType (CN a) MPBall #

CanMulAsymmetric a MPBall => CanMulAsymmetric (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType (CN a) MPBall #

Methods

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

CanAddAsymmetric a MPBall => CanAddAsymmetric (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType (CN a) MPBall #

Methods

add :: CN a -> MPBall -> AddType (CN a) MPBall #

CanSub a MPBall => CanSub (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType (CN a) MPBall #

Methods

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

CanBeErrorBound t => CanPlusMinus (CN MPBall) t Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType (CN MPBall) t Source #

Methods

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

(CanMinMaxAsymmetric a MPBall, CanBeErrors es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type MinMaxType (CollectErrors es a) MPBall #

Methods

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

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

(HasEqAsymmetric a MPBall, IsBool (EqCompareType a MPBall), CanBeErrors es) => HasEqAsymmetric (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type EqCompareType (CollectErrors es a) MPBall #

Methods

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

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

(HasOrderAsymmetric a MPBall, IsBool (OrderCompareType a MPBall), CanBeErrors es) => HasOrderAsymmetric (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type OrderCompareType (CollectErrors es a) MPBall #

Methods

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

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

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

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

(ConvertibleExactly c Dyadic, ConvertibleExactly e Dyadic, Show c, Show e, Typeable c, Typeable e) => ConvertibleExactly (c, e) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

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

ConvertibleWithPrecision (Rational, Rational) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult MPBall Source #

(CanUnionAsymmetric a MPBall, CanBeErrors es) => CanUnionAsymmetric (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type UnionType (CollectErrors es a) MPBall Source #

Methods

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

(CanIntersectAsymmetric a MPBall, CanBeErrors es) => CanIntersectAsymmetric (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

Associated Types

type IntersectionType (CollectErrors es a) MPBall Source #

Methods

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

HasCurrentPrecision p => Floating (WithCurrentPrec (CN MPBall) p) Source # 
Instance details

Defined in AERN2.MP.WithCurrentPrec

Methods

pi :: WithCurrentPrec (CN MPBall) p #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

type Rep MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type Rep MPBall = D1 ('MetaData "MPBall" "AERN2.MP.Ball.Type" "aern2-mp-0.2.2.0-DTtN6apnExTAMCmcKkOJZI" 'False) (C1 ('MetaCons "MPBall" 'PrefixI 'True) (S1 ('MetaSel ('Just "ball_value") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 MPFloat) :*: S1 ('MetaSel ('Just "ball_error") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ErrorBound)))
type SqrtType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type SqrtType MPBall = MPBall
type ExpType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type ExpType MPBall = MPBall
type LogType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type LogType MPBall = MPBall
type SinCosType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type SinCosType MPBall = MPBall
type AbsType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type AbsType MPBall = MPBall
type NegType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type NegType MPBall = MPBall
type Approximate MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type Approximate MPBall = (MPFloat, Bool)
type IntervalEndpoint MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type IntervalEndpoint MPBall = MPFloat
type CentreType MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Type

type CentreType MPBall = Dyadic
type PowType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType Int MPBall = MPBall
type PowType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType Integer MPBall = MPBall
type PowType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType Rational MPBall = MPBall
type PowType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type PowType MPBall Int = MPBall
type PowType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type PowType MPBall Integer = MPBall
type PowType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Rational = MPBall
type PowType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Dyadic = MPBall
type PowType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall MPBall = MPBall
type DivType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType Int MPBall = MPBall
type DivType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType Integer MPBall = MPBall
type DivType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType Rational MPBall = MPBall
type DivType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType Dyadic MPBall = MPBall
type DivType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall Int = MPBall
type DivType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall Integer = MPBall
type DivType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall Rational = MPBall
type DivType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall Dyadic = MPBall
type DivType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall MPBall = MPBall
type ModType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type ModType MPBall MPBall = MPBall
type DivIType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivIType MPBall MPBall = Integer
type MulType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType Int MPBall = MPBall
type MulType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType Integer MPBall = MPBall
type MulType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType Rational MPBall = MPBall
type MulType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType Dyadic MPBall = MPBall
type MulType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall Int = MPBall
type MulType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall Integer = MPBall
type MulType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall Rational = MPBall
type MulType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall Dyadic = MPBall
type MulType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall MPBall = MPBall
type AddType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType Int MPBall = MPBall
type AddType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType Integer MPBall = MPBall
type AddType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType Rational MPBall = MPBall
type AddType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType Dyadic MPBall = MPBall
type AddType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall Int = MPBall
type AddType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall Integer = MPBall
type AddType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall Rational = MPBall
type AddType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall Dyadic = MPBall
type AddType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall MPBall = MPBall
type SubType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType Int MPBall = AddType Int (NegType MPBall)
type SubType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType Integer MPBall = AddType Integer (NegType MPBall)
type SubType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType Rational MPBall = AddType Rational (NegType MPBall)
type SubType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall Int = AddType MPBall (NegType Int)
type SubType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall Integer = AddType MPBall (NegType Integer)
type SubType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall Rational = AddType MPBall (NegType Rational)
type SubType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type SubType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall MPBall = AddType MPBall (NegType MPBall)
type MinMaxType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Int MPBall = MPBall
type MinMaxType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Integer MPBall = MPBall
type MinMaxType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Rational MPBall = MPBall
type MinMaxType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Int = MPBall
type MinMaxType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Integer = MPBall
type MinMaxType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Rational = MPBall
type MinMaxType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Dyadic = MPBall
type MinMaxType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall MPBall = MPBall
type EqCompareType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Int MPBall = Kleenean
type EqCompareType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Integer MPBall = Kleenean
type EqCompareType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Rational MPBall = Kleenean
type EqCompareType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Dyadic MPBall = Kleenean
type EqCompareType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Int = Kleenean
type EqCompareType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Integer = Kleenean
type EqCompareType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Rational = Kleenean
type EqCompareType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Dyadic = Kleenean
type EqCompareType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall MPBall = Kleenean
type OrderCompareType Int MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Int MPBall = Kleenean
type OrderCompareType Integer MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Integer MPBall = Kleenean
type OrderCompareType Rational MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Rational MPBall = Kleenean
type OrderCompareType Dyadic MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Dyadic MPBall = Kleenean
type OrderCompareType MPBall Int Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Int = Kleenean
type OrderCompareType MPBall Integer Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Integer = Kleenean
type OrderCompareType MPBall Rational Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Rational = Kleenean
type OrderCompareType MPBall Dyadic Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Dyadic = Kleenean
type OrderCompareType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall MPBall = Kleenean
type UnionType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type UnionType MPBall MPBall = CN MPBall
type IntersectionType MPBall MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType MPBall MPBall = CN MPBall
type PlusMinusType MPBall t Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType MPBall t = MPBall
type PowType MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type PowType MPBall (CN b) = CN (PowType MPBall b)
type DivType MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType MPBall (CN b) = CN (DivType MPBall b)
type MulType MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType MPBall (CN b) = CN (MulType MPBall b)
type AddType MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType MPBall (CN b) = CN (AddType MPBall b)
type SubType MPBall (CN b) Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType MPBall (CN b) = CN (SubType MPBall b)
type MinMaxType MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall (CollectErrors es b) = CollectErrors es (MinMaxType MPBall b)
type EqCompareType MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall (CollectErrors es b) = CollectErrors es (EqCompareType MPBall b)
type OrderCompareType MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall (CollectErrors es b) = CollectErrors es (OrderCompareType MPBall b)
type LimitType Int (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

type LimitType Int (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type LimitType Integer (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

type LimitType Integer (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type LimitType Rational (CN MPBall -> CN MPBall) Source # 
Instance details

Defined in AERN2.MP.Ball.Limit

type LimitType Rational (CN MPBall -> CN MPBall) = CN MPBall -> CN MPBall
type UnionType MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type UnionType MPBall (CollectErrors es b) = CollectErrors es (UnionType MPBall b)
type IntersectionType MPBall (CollectErrors es b) Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type IntersectionType MPBall (CollectErrors es b) = CollectErrors es (IntersectionType MPBall b)
type LimitType ix (WithCurrentPrec (CN MPBall) p) Source # 
Instance details

Defined in AERN2.MP.WithCurrentPrec

type LimitType ix (WithCurrentPrec (CN MPBall) p) = WithCurrentPrec (CN MPBall) p
type PowType (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type PowType (CN a) MPBall = CN (PowType a MPBall)
type DivType (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type DivType (CN a) MPBall = CN (DivType a MPBall)
type MulType (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type MulType (CN a) MPBall = CN (MulType a MPBall)
type AddType (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type AddType (CN a) MPBall = CN (AddType a MPBall)
type SubType (CN a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Field

type SubType (CN a) MPBall = CN (SubType a MPBall)
type PlusMinusType (CN MPBall) t Source # 
Instance details

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType (CN MPBall) t = CN MPBall
type MinMaxType (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType (CollectErrors es a) MPBall = CollectErrors es (MinMaxType a MPBall)
type EqCompareType (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType (CollectErrors es a) MPBall = CollectErrors es (EqCompareType a MPBall)
type OrderCompareType (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType (CollectErrors es a) MPBall = CollectErrors es (OrderCompareType a MPBall)
type UnionType (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

type UnionType (CollectErrors es a) MPBall = CollectErrors es (UnionType a MPBall)
type IntersectionType (CollectErrors es a) MPBall Source # 
Instance details

Defined in AERN2.MP.Ball.Comparisons

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

type CanBeMPBall t = ConvertibleExactly t MPBall Source #

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

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

type CanBeMPBallP t = ConvertibleWithPrecision t MPBall Source #

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

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

reducePrecionIfInaccurate :: MPBall -> MPBall Source #

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

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

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 Source #

intersectCNMPBall :: CN MPBall -> CN MPBall -> CN MPBall Source #

hullMPBall :: MPBall -> MPBall -> MPBall Source #

Helpers for constructing ball functions

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

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

fromApproxWithLipschitz Source #

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

Field MPBall Source # 
Instance details

OrderedField MPBall Source # 
Instance details

OrderedCertainlyField MPBall Source # 
Instance details

Ring MPBall Source # 
Instance details

OrderedRing MPBall Source # 
Instance details

OrderedCertainlyRing MPBall Source # 
Instance details

Field (CN MPBall) Source # 
Instance details

OrderedField (CN MPBall) Source # 
Instance details

OrderedCertainlyField (CN MPBall) Source # 
Instance details

Ring (CN MPBall) Source # 
Instance details

OrderedRing (CN MPBall) Source # 
Instance details

OrderedCertainlyRing (CN MPBall) Source # 
Instance details