Copyright	(c) Michal Konecny
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.Ball.Comparisons

Contents

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

Description

Comparisons of arbitrary precision dyadic balls

Synopsis

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

Auxiliary types

module AERN2.Norm

Ball operations (see also instances)

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.

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.

intersection and hull

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

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

Orphan instances

CanTestInteger MPBall Source #

Instance details

Methods

certainlyNotInteger :: MPBall -> Bool #

certainlyInteger :: MPBall -> Bool #

certainlyIntegerGetIt :: MPBall -> Maybe Integer #

CanTestZero MPBall Source #

Instance details

Methods

isCertainlyZero :: MPBall -> Bool #

isCertainlyNonZero :: MPBall -> Bool #

CanTestPosNeg MPBall Source #

Instance details

Methods

isCertainlyPositive :: MPBall -> Bool #

isCertainlyNonNegative :: MPBall -> Bool #

isCertainlyNegative :: MPBall -> Bool #

isCertainlyNonPositive :: MPBall -> Bool #

CanIntersectAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type IntersectionType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall MPBall = CN MPBall

Methods

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

CanUnionAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type UnionType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall MPBall = CN MPBall

Methods

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

HasEqAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type EqCompareType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall MPBall = Kleenean

Methods

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

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

HasEqAsymmetric MPBall Dyadic Source #

Instance details

Associated Types

type EqCompareType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Dyadic = Kleenean

Methods

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

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

HasEqAsymmetric MPBall Rational Source #

Instance details

Associated Types

type EqCompareType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Rational = Kleenean

Methods

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

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

HasEqAsymmetric MPBall Integer Source #

Instance details

Associated Types

type EqCompareType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Integer = Kleenean

Methods

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

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

HasEqAsymmetric MPBall Int Source #

Instance details

Associated Types

type EqCompareType MPBall Int
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Int = Kleenean

Methods

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

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

HasEqAsymmetric Dyadic MPBall Source #

Instance details

Associated Types

type EqCompareType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Dyadic MPBall = Kleenean

Methods

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

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

HasEqAsymmetric Rational MPBall Source #

Instance details

Associated Types

type EqCompareType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Rational MPBall = Kleenean

Methods

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

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

HasEqAsymmetric Integer MPBall Source #

Instance details

Associated Types

type EqCompareType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Integer MPBall = Kleenean

Methods

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

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

HasEqAsymmetric Int MPBall Source #

Instance details

Associated Types

type EqCompareType Int MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Int MPBall = Kleenean

Methods

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

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

CanMinMaxAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type MinMaxType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall MPBall = MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall Dyadic Source #

Instance details

Associated Types

type MinMaxType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Dyadic = MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall Rational Source #

Instance details

Associated Types

type MinMaxType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Rational = MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall Integer Source #

Instance details

Associated Types

type MinMaxType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Integer = MPBall

Methods

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

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

CanMinMaxAsymmetric MPBall Int Source #

Instance details

Associated Types

type MinMaxType MPBall Int
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Int = MPBall

Methods

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

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

CanMinMaxAsymmetric Dyadic MPBall Source #

Instance details

Associated Types

type MinMaxType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Dyadic MPBall = MPBall

Methods

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

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

CanMinMaxAsymmetric Rational MPBall Source #

Instance details

Associated Types

type MinMaxType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Rational MPBall = MPBall

Methods

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

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

CanMinMaxAsymmetric Integer MPBall Source #

Instance details

Associated Types

type MinMaxType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Integer MPBall = MPBall

Methods

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

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

CanMinMaxAsymmetric Int MPBall Source #

Instance details

Associated Types

type MinMaxType Int MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Int MPBall = MPBall

Methods

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

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

HasOrderAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type OrderCompareType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall MPBall = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Dyadic = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Rational = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Integer = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType MPBall Int
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Int = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Dyadic MPBall = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Rational MPBall = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Integer MPBall = Kleenean

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 Source #

Instance details

Associated Types

type OrderCompareType Int MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Int MPBall = Kleenean

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) Source #

Instance details

Associated Types

type IntersectionType MPBall (CollectErrors es b)
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType MPBall (CollectErrors es b) = CollectErrors es (IntersectionType MPBall b)

Methods

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

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

Instance details

Associated Types

type UnionType MPBall (CollectErrors es b)
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType MPBall (CollectErrors es b) = CollectErrors es (UnionType MPBall b)

Methods

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

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

Instance details

Associated Types

type EqCompareType MPBall (CollectErrors es b)
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall (CollectErrors es b) = CollectErrors es (EqCompareType MPBall 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) Source #

Instance details

Associated Types

type MinMaxType MPBall (CollectErrors es b)
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall (CollectErrors es b) = CollectErrors es (MinMaxType MPBall 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) Source #

Instance details

Associated Types

type OrderCompareType MPBall (CollectErrors es b)
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall (CollectErrors es b) = CollectErrors es (OrderCompareType MPBall 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 Source #

Instance details

Associated Types

type IntersectionType (CollectErrors es a) MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type IntersectionType (CollectErrors es a) MPBall = CollectErrors es (IntersectionType a MPBall)

Methods

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

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

Instance details

Associated Types

type UnionType (CollectErrors es a) MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type UnionType (CollectErrors es a) MPBall = CollectErrors es (UnionType a MPBall)

Methods

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

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

Instance details

Associated Types

type EqCompareType (CollectErrors es a) MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType (CollectErrors es a) MPBall = CollectErrors es (EqCompareType 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 Source #

Instance details

Associated Types

type MinMaxType (CollectErrors es a) MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType (CollectErrors es a) MPBall = CollectErrors es (MinMaxType 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 Source #

Instance details

Associated Types

type OrderCompareType (CollectErrors es a) MPBall
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType (CollectErrors es a) MPBall = CollectErrors es (OrderCompareType 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 #