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

AERN2.MP.Ball.Comparisons

Contents

Auxiliary types
Ball operations (see also instances)
Helpers for constructing ball functions
Orphan instances

Description

Comparisons of arbitrary precision dyadic balls

Synopsis

module AERN2.Norm
reducePrecionIfInaccurate :: MPBall -> MPBall
byEndpointsMP :: (MPFloat -> MPFloat -> MPFloat) -> MPBall -> MPBall -> MPBall

Auxiliary types

module AERN2.Norm

Ball operations (see also instances)

reducePrecionIfInaccurate :: MPBall -> MPBall #

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

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

Helpers for constructing ball functions

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

Computes an *increasing* ball fucntion f from *exact* MPFR operations.

Orphan instances

CanTestInteger MPBall #
Instance details Methods certainlyNotInteger :: MPBall -> Bool # certainlyInteger :: MPBall -> Bool # certainlyIntegerGetIt :: MPBall -> Maybe Integer #
CanTestZero MPBall #
Instance details Methods isCertainlyZero :: MPBall -> Bool # isCertainlyNonZero :: MPBall -> Bool #
CanTestPosNeg MPBall #
Instance details Methods isCertainlyPositive :: MPBall -> Bool # isCertainlyNonNegative :: MPBall -> Bool # isCertainlyNegative :: MPBall -> Bool # isCertainlyNonPositive :: MPBall -> Bool #
CanMinMaxAsymmetric Int MPBall #
Instance details Associated Types type MinMaxType Int MPBall :: Type # Methods min :: Int -> MPBall -> MinMaxType Int MPBall # max :: Int -> MPBall -> MinMaxType Int MPBall #
CanMinMaxAsymmetric Integer MPBall #
Instance details Associated Types type MinMaxType Integer MPBall :: Type # Methods min :: Integer -> MPBall -> MinMaxType Integer MPBall # max :: Integer -> MPBall -> MinMaxType Integer MPBall #
CanMinMaxAsymmetric Rational MPBall #
Instance details Associated Types type MinMaxType Rational MPBall :: Type # Methods min :: Rational -> MPBall -> MinMaxType Rational MPBall # max :: Rational -> MPBall -> MinMaxType Rational MPBall #
CanMinMaxAsymmetric Dyadic MPBall #
Instance details Associated Types type MinMaxType Dyadic MPBall :: Type # Methods min :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall # max :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall #
CanMinMaxAsymmetric MPBall Int #
Instance details Associated Types type MinMaxType MPBall Int :: Type # Methods min :: MPBall -> Int -> MinMaxType MPBall Int # max :: MPBall -> Int -> MinMaxType MPBall Int #
CanMinMaxAsymmetric MPBall Integer #
Instance details Associated Types type MinMaxType MPBall Integer :: Type # Methods min :: MPBall -> Integer -> MinMaxType MPBall Integer # max :: MPBall -> Integer -> MinMaxType MPBall Integer #
CanMinMaxAsymmetric MPBall Rational #
Instance details Associated Types type MinMaxType MPBall Rational :: Type # Methods min :: MPBall -> Rational -> MinMaxType MPBall Rational # max :: MPBall -> Rational -> MinMaxType MPBall Rational #
CanMinMaxAsymmetric MPBall Dyadic #
Instance details Associated Types type MinMaxType MPBall Dyadic :: Type # Methods min :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic # max :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic #
CanMinMaxAsymmetric MPBall MPBall #
Instance details Associated Types type MinMaxType MPBall MPBall :: Type # Methods min :: MPBall -> MPBall -> MinMaxType MPBall MPBall # max :: MPBall -> MPBall -> MinMaxType MPBall MPBall #
HasEqAsymmetric Int MPBall #
Instance details Associated Types type EqCompareType Int MPBall :: Type # Methods equalTo :: Int -> MPBall -> EqCompareType Int MPBall # notEqualTo :: Int -> MPBall -> EqCompareType Int MPBall #
HasEqAsymmetric Integer MPBall #
Instance details Associated Types type EqCompareType Integer MPBall :: Type # Methods equalTo :: Integer -> MPBall -> EqCompareType Integer MPBall # notEqualTo :: Integer -> MPBall -> EqCompareType Integer MPBall #
HasEqAsymmetric Rational MPBall #
Instance details Associated Types type EqCompareType Rational MPBall :: Type # Methods equalTo :: Rational -> MPBall -> EqCompareType Rational MPBall # notEqualTo :: Rational -> MPBall -> EqCompareType Rational MPBall #
HasEqAsymmetric Dyadic MPBall #
Instance details Associated Types type EqCompareType Dyadic MPBall :: Type # Methods equalTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall # notEqualTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall #
HasEqAsymmetric MPBall Int #
Instance details Associated Types type EqCompareType MPBall Int :: Type # Methods equalTo :: MPBall -> Int -> EqCompareType MPBall Int # notEqualTo :: MPBall -> Int -> EqCompareType MPBall Int #
HasEqAsymmetric MPBall Integer #
Instance details Associated Types type EqCompareType MPBall Integer :: Type # Methods equalTo :: MPBall -> Integer -> EqCompareType MPBall Integer # notEqualTo :: MPBall -> Integer -> EqCompareType MPBall Integer #
HasEqAsymmetric MPBall Rational #
Instance details Associated Types type EqCompareType MPBall Rational :: Type # Methods equalTo :: MPBall -> Rational -> EqCompareType MPBall Rational # notEqualTo :: MPBall -> Rational -> EqCompareType MPBall Rational #
HasEqAsymmetric MPBall Dyadic #
Instance details Associated Types type EqCompareType MPBall Dyadic :: Type # Methods equalTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic # notEqualTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic #
HasEqAsymmetric MPBall MPBall #
Instance details Associated Types type EqCompareType MPBall MPBall :: Type # Methods equalTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall # notEqualTo :: MPBall -> MPBall -> EqCompareType MPBall MPBall #
HasOrderAsymmetric Int MPBall #
Instance details Associated Types type OrderCompareType Int MPBall :: Type # 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 #
Instance details Associated Types type OrderCompareType Integer MPBall :: Type # 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 #
Instance details Associated Types type OrderCompareType Rational MPBall :: Type # 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 #
Instance details Associated Types type OrderCompareType Dyadic MPBall :: Type # 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 #
Instance details Associated Types type OrderCompareType MPBall Int :: Type # 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 #
Instance details Associated Types type OrderCompareType MPBall Integer :: Type # 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 #
Instance details Associated Types type OrderCompareType MPBall Rational :: Type # 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 #
Instance details Associated Types type OrderCompareType MPBall Dyadic :: Type # 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 #
Instance details Associated Types type OrderCompareType MPBall MPBall :: Type # 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 #
CanUnionAsymmetric MPBall MPBall #
Instance details Associated Types type UnionType MPBall MPBall :: Type # Methods union :: MPBall -> MPBall -> UnionType MPBall MPBall #
CanIntersectAsymmetric MPBall MPBall #
Instance details Associated Types type IntersectionType MPBall MPBall :: Type # Methods intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall #
(CanMinMaxAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (MinMaxType MPBall b), SuitableForCE es) => CanMinMaxAsymmetric MPBall (CollectErrors es b) #
Instance details Associated Types type MinMaxType MPBall (CollectErrors es b) :: Type # Methods min :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) # max :: MPBall -> CollectErrors es b -> MinMaxType MPBall (CollectErrors es b) #
(HasEqAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (EqCompareType MPBall b), IsBool (EnsureCE es (EqCompareType MPBall b)), SuitableForCE es) => HasEqAsymmetric MPBall (CollectErrors es b) #
Instance details Associated Types type EqCompareType MPBall (CollectErrors es b) :: Type # Methods equalTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) # notEqualTo :: MPBall -> CollectErrors es b -> EqCompareType MPBall (CollectErrors es b) #
(HasOrderAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType MPBall b), IsBool (EnsureCE es (OrderCompareType MPBall b)), SuitableForCE es) => HasOrderAsymmetric MPBall (CollectErrors es b) #
Instance details Associated Types type OrderCompareType MPBall (CollectErrors es b) :: Type # 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) #
(CanUnionAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (UnionType MPBall b), SuitableForCE es) => CanUnionAsymmetric MPBall (CollectErrors es b) #
Instance details Associated Types type UnionType MPBall (CollectErrors es b) :: Type # Methods union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b) #
(CanIntersectAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (IntersectionType MPBall b), SuitableForCE es) => CanIntersectAsymmetric MPBall (CollectErrors es b) #
Instance details Associated Types type IntersectionType MPBall (CollectErrors es b) :: Type # Methods intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b) #
(CanMinMaxAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (MinMaxType a MPBall), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall #
Instance details Associated Types type MinMaxType (CollectErrors es a) MPBall :: Type # Methods min :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall # max :: CollectErrors es a -> MPBall -> MinMaxType (CollectErrors es a) MPBall #
(HasEqAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (EqCompareType a MPBall), IsBool (EnsureCE es (EqCompareType a MPBall)), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) MPBall #
Instance details Associated Types type EqCompareType (CollectErrors es a) MPBall :: Type # Methods equalTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall # notEqualTo :: CollectErrors es a -> MPBall -> EqCompareType (CollectErrors es a) MPBall #
(HasOrderAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a MPBall), IsBool (EnsureCE es (OrderCompareType a MPBall)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) MPBall #
Instance details Associated Types type OrderCompareType (CollectErrors es a) MPBall :: Type # 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 #
(CanUnionAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (UnionType a MPBall), SuitableForCE es) => CanUnionAsymmetric (CollectErrors es a) MPBall #
Instance details Associated Types type UnionType (CollectErrors es a) MPBall :: Type # Methods union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall #
(CanIntersectAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (IntersectionType a MPBall), SuitableForCE es) => CanIntersectAsymmetric (CollectErrors es a) MPBall #
Instance details Associated Types type IntersectionType (CollectErrors es a) MPBall :: Type # Methods intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall #