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

AERN2.MP.ErrorBound

Description

Fixed precision non-negative up-rounded floating-point numbers.

Currently using a fixed-precision MPFloat.

Synopsis

data ErrorBound
type CanBeErrorBound t = Convertible t ErrorBound
errorBound :: CanBeErrorBound t => t -> ErrorBound
absMP :: MPFloat -> ErrorBound
subMP :: MPFloat -> MPFloat -> ErrorBound

Documentation

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

type CanBeErrorBound t = Convertible t ErrorBound Source #

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

absMP :: MPFloat -> ErrorBound Source #

subMP :: MPFloat -> MPFloat -> ErrorBound Source #