AERN2.MP.Ball.Comparisons

Comparisons of arbitrary precision dyadic balls

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

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

intersection and hull

intersectCNMPBall :: CN MPBall -> CN MPBall -> CN MPBall

hullMPBall :: MPBall -> MPBall -> MPBall

Orphan instances

CanTestInteger MPBall

Methods

certainlyNotInteger :: MPBall -> Bool

certainlyInteger :: MPBall -> Bool

certainlyIntegerGetIt :: MPBall -> Maybe Integer

CanTestZero MPBall

Methods

isCertainlyZero :: MPBall -> Bool

isCertainlyNonZero :: MPBall -> Bool

CanTestPosNeg MPBall

Methods

isCertainlyPositive :: MPBall -> Bool

isCertainlyNonNegative :: MPBall -> Bool

isCertainlyNegative :: MPBall -> Bool

isCertainlyNonPositive :: MPBall -> Bool

CanIntersectAsymmetric MPBall MPBall

Associated Types

type IntersectionType MPBall MPBall

Methods

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

CanUnionAsymmetric MPBall MPBall

Associated Types

type UnionType MPBall MPBall

Methods

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

HasEqAsymmetric MPBall MPBall

Associated Types

type EqCompareType MPBall MPBall

Methods

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

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

HasEqAsymmetric MPBall Dyadic

Associated Types

type EqCompareType MPBall Dyadic

Methods

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

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

HasEqAsymmetric MPBall Rational

Associated Types

type EqCompareType MPBall Rational

Methods

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

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

HasEqAsymmetric MPBall Integer

Associated Types

type EqCompareType MPBall Integer

Methods

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

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

HasEqAsymmetric MPBall Int

Associated Types

type EqCompareType MPBall Int

Methods

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

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

HasEqAsymmetric Dyadic MPBall

Associated Types

type EqCompareType Dyadic MPBall

Methods

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

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

HasEqAsymmetric Rational MPBall

Associated Types

type EqCompareType Rational MPBall

Methods

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

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

HasEqAsymmetric Integer MPBall

Associated Types

type EqCompareType Integer MPBall

Methods

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

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

HasEqAsymmetric Int MPBall

Associated Types

type EqCompareType Int MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall MPBall

Associated Types

type MinMaxType MPBall MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall Dyadic

Associated Types

type MinMaxType MPBall Dyadic

Methods

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

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

CanMinMaxAsymmetric MPBall Rational

Associated Types

type MinMaxType MPBall Rational

Methods

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

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

CanMinMaxAsymmetric MPBall Integer

Associated Types

type MinMaxType MPBall Integer

Methods

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

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

CanMinMaxAsymmetric MPBall Int

Associated Types

type MinMaxType MPBall Int

Methods

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

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

CanMinMaxAsymmetric Dyadic MPBall

Associated Types

type MinMaxType Dyadic MPBall

Methods

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

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

CanMinMaxAsymmetric Rational MPBall

Associated Types

type MinMaxType Rational MPBall

Methods

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

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

CanMinMaxAsymmetric Integer MPBall

Associated Types

type MinMaxType Integer MPBall

Methods

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

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

CanMinMaxAsymmetric Int MPBall

Associated Types

type MinMaxType Int MPBall

Methods

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

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

HasOrderAsymmetric MPBall MPBall

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

HasOrderAsymmetric MPBall Dyadic

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 Rational

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 Integer

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 Int

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 Dyadic MPBall

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 Rational MPBall

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 Integer MPBall

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 Int MPBall

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

(CanIntersectAsymmetric MPBall b, CanBeErrors es) => CanIntersectAsymmetric MPBall (CollectErrors es b)

Associated Types

type IntersectionType MPBall (CollectErrors es b)

Methods

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

(CanUnionAsymmetric MPBall b, CanBeErrors es) => CanUnionAsymmetric MPBall (CollectErrors es b)

Associated Types

type UnionType MPBall (CollectErrors es b)

Methods

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

(HasEqAsymmetric MPBall b, IsBool (EqCompareType MPBall b), CanTestCertainly (EqCompareType MPBall b), CanBeErrors es) => HasEqAsymmetric MPBall (CollectErrors es b)

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)

(CanMinMaxAsymmetric MPBall b, CanBeErrors es) => CanMinMaxAsymmetric MPBall (CollectErrors es b)

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)

(HasOrderAsymmetric MPBall b, IsBool (OrderCompareType MPBall b), CanTestCertainly (OrderCompareType MPBall b), CanBeErrors es) => HasOrderAsymmetric MPBall (CollectErrors es b)

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)

(CanIntersectAsymmetric a MPBall, CanBeErrors es) => CanIntersectAsymmetric (CollectErrors es a) MPBall

Associated Types

type IntersectionType (CollectErrors es a) MPBall

Methods

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

(CanUnionAsymmetric a MPBall, CanBeErrors es) => CanUnionAsymmetric (CollectErrors es a) MPBall

Associated Types

type UnionType (CollectErrors es a) MPBall

Methods

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

(HasEqAsymmetric a MPBall, IsBool (EqCompareType a MPBall), CanTestCertainly (EqCompareType a MPBall), CanBeErrors es) => HasEqAsymmetric (CollectErrors es a) MPBall

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

(CanMinMaxAsymmetric a MPBall, CanBeErrors es) => CanMinMaxAsymmetric (CollectErrors es a) MPBall

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

(HasOrderAsymmetric a MPBall, IsBool (OrderCompareType a MPBall), CanTestCertainly (OrderCompareType a MPBall), CanBeErrors es) => HasOrderAsymmetric (CollectErrors es a) MPBall

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