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

AERN2.MP.UseMPFR.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 #

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

Instances

Eq ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods (==) :: ErrorBound -> ErrorBound -> Bool # (/=) :: ErrorBound -> ErrorBound -> Bool #
Ord ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods showsPrec :: Int -> ErrorBound -> ShowS # show :: ErrorBound -> String # showList :: [ErrorBound] -> ShowS #
Arbitrary ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods arbitrary :: Gen ErrorBound # shrink :: ErrorBound -> [ErrorBound] #
HasAccuracy ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods getAccuracy :: ErrorBound -> Accuracy #
Convertible Int ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvert :: Int -> ConvertResult ErrorBound #
Convertible Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvert :: Integer -> ConvertResult ErrorBound #
Convertible Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvert :: Rational -> ConvertResult ErrorBound #
Convertible MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvert :: MPFloat -> ConvertResult ErrorBound #
Convertible MPBall ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Conversions Methods safeConvert :: MPBall -> ConvertResult ErrorBound #
CanDiv ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type DivTypeNoCN ErrorBound Integer :: * # type DivType ErrorBound Integer :: * # Methods divideNoCN :: ErrorBound -> Integer -> DivTypeNoCN ErrorBound Integer # divide :: ErrorBound -> Integer -> DivType ErrorBound Integer #
CanMulAsymmetric Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType Integer ErrorBound :: * # Methods mul :: Integer -> ErrorBound -> MulType Integer ErrorBound #
CanMulAsymmetric Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType Rational ErrorBound :: * # Methods mul :: Rational -> ErrorBound -> MulType Rational ErrorBound #
CanMulAsymmetric MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType MPFloat ErrorBound :: * # Methods mul :: MPFloat -> ErrorBound -> MulType MPFloat ErrorBound #
CanMulAsymmetric ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType ErrorBound Integer :: * # Methods mul :: ErrorBound -> Integer -> MulType ErrorBound Integer #
CanMulAsymmetric ErrorBound Rational #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType ErrorBound Rational :: * # Methods mul :: ErrorBound -> Rational -> MulType ErrorBound Rational #
CanMulAsymmetric ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType ErrorBound MPFloat :: * # Methods mul :: ErrorBound -> MPFloat -> MulType ErrorBound MPFloat #
CanMulAsymmetric ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MulType ErrorBound ErrorBound :: * # Methods mul :: ErrorBound -> ErrorBound -> MulType ErrorBound ErrorBound #
CanAddAsymmetric MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type AddType MPFloat ErrorBound :: * # Methods add :: MPFloat -> ErrorBound -> AddType MPFloat ErrorBound #
CanAddAsymmetric ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type AddType ErrorBound MPFloat :: * # Methods add :: ErrorBound -> MPFloat -> AddType ErrorBound MPFloat #
CanAddAsymmetric ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type AddType ErrorBound ErrorBound :: * # Methods add :: ErrorBound -> ErrorBound -> AddType ErrorBound ErrorBound #
CanMinMaxAsymmetric ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type MinMaxType ErrorBound ErrorBound :: * # Methods min :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound # max :: ErrorBound -> ErrorBound -> MinMaxType ErrorBound ErrorBound #
HasEqAsymmetric Int ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType Int ErrorBound :: * # Methods equalTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound # notEqualTo :: Int -> ErrorBound -> EqCompareType Int ErrorBound #
HasEqAsymmetric Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType Integer ErrorBound :: * # Methods equalTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound # notEqualTo :: Integer -> ErrorBound -> EqCompareType Integer ErrorBound #
HasEqAsymmetric Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType Rational ErrorBound :: * # Methods equalTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound # notEqualTo :: Rational -> ErrorBound -> EqCompareType Rational ErrorBound #
HasEqAsymmetric ErrorBound Int #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType ErrorBound Int :: * # Methods equalTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int # notEqualTo :: ErrorBound -> Int -> EqCompareType ErrorBound Int #
HasEqAsymmetric ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType ErrorBound Integer :: * # Methods equalTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer # notEqualTo :: ErrorBound -> Integer -> EqCompareType ErrorBound Integer #
HasEqAsymmetric ErrorBound Rational #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Associated Types type EqCompareType ErrorBound Rational :: * # Methods equalTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational # notEqualTo :: ErrorBound -> Rational -> EqCompareType ErrorBound Rational #
HasOrderAsymmetric Int ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.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 #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult Rational #
ConvertibleExactly ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult MPFloat #
ConvertibleExactly ErrorBound Dyadic #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult Dyadic #
ConvertibleExactly ErrorBound MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Conversions Methods safeConvertExactly :: ErrorBound -> ConvertResult MPBall #
type DivType ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type DivType ErrorBound Integer = ErrorBound
type DivTypeNoCN ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type DivTypeNoCN ErrorBound Integer = ErrorBound
type MulType Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType Integer ErrorBound = ErrorBound
type MulType Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType Rational ErrorBound = ErrorBound
type MulType MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType MPFloat ErrorBound = ErrorBound
type MulType ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType ErrorBound Integer = ErrorBound
type MulType ErrorBound Rational #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType ErrorBound Rational = ErrorBound
type MulType ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType ErrorBound MPFloat = ErrorBound
type MulType ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MulType ErrorBound ErrorBound = ErrorBound
type AddType MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type AddType MPFloat ErrorBound = ErrorBound
type AddType ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type AddType ErrorBound MPFloat = ErrorBound
type AddType ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type AddType ErrorBound ErrorBound = ErrorBound
type MinMaxType ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type MinMaxType ErrorBound ErrorBound = ErrorBound
type EqCompareType Int ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType Int ErrorBound = Bool
type EqCompareType Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType Integer ErrorBound = Bool
type EqCompareType Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType Rational ErrorBound = Bool
type EqCompareType ErrorBound Int #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType ErrorBound Int = Bool
type EqCompareType ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType ErrorBound Integer = Bool
type EqCompareType ErrorBound Rational #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type EqCompareType ErrorBound Rational = Bool
type OrderCompareType Int ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType Int ErrorBound = Bool
type OrderCompareType Integer ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType Integer ErrorBound = Bool
type OrderCompareType Rational ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType Rational ErrorBound = Bool
type OrderCompareType MPFloat ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType MPFloat ErrorBound = Bool
type OrderCompareType ErrorBound Int #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType ErrorBound Int = Bool
type OrderCompareType ErrorBound Integer #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType ErrorBound Integer = Bool
type OrderCompareType ErrorBound Rational #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType ErrorBound Rational = Bool
type OrderCompareType ErrorBound MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType ErrorBound MPFloat = Bool
type OrderCompareType ErrorBound ErrorBound #
Instance details Defined in AERN2.MP.UseMPFR.ErrorBound type OrderCompareType ErrorBound ErrorBound = Bool

type CanBeErrorBound t = Convertible t ErrorBound #

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

absMP :: MPFloat -> ErrorBound #

subMP :: MPFloat -> MPFloat -> ErrorBound #