aern2-mp-0.1.2.0: Multi-precision floats via MPFR

Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

AERN2.MP.UseMPFR.Dyadic

Contents

Description

Arbitrary precision floating-point numbers with exact ring operations.

Currently, we use hmpfr when compiling with ghc 7.10 and higher and haskell-mpfr when compiling with ghc 7.8.

Synopsis

Dyadic numbers and their basic operations

data Dyadic Source #

Exact dyadic type based on MPFloat.

Instances

Eq Dyadic Source # 

Methods

(==) :: Dyadic -> Dyadic -> Bool #

(/=) :: Dyadic -> Dyadic -> Bool #

Num Dyadic Source # 
Ord Dyadic Source # 
Read Dyadic Source # 
Real Dyadic Source # 
Show Dyadic Source # 
Arbitrary Dyadic Source # 
Ring Dyadic Source # 
OrderedRing Dyadic Source # 
OrderedCertainlyRing Dyadic Source # 
CanRound Dyadic Source # 
HasIntegerBounds Dyadic Source # 
CanAbs Dyadic Source # 

Associated Types

type AbsType Dyadic :: * #

Methods

abs :: Dyadic -> AbsType Dyadic #

CanTestPosNeg Dyadic Source # 
CanTestInteger Dyadic Source # 
CanTestZero Dyadic Source # 
CanNeg Dyadic Source # 

Associated Types

type NegType Dyadic :: * #

HasNorm Dyadic Source # 
HasPrecision Dyadic Source # 
HasAccuracy Dyadic Source # 
Convertible Dyadic Double Source # 
CanDiv Int Dyadic Source # 

Associated Types

type DivTypeNoCN Int Dyadic :: * #

type DivType Int Dyadic :: * #

CanDiv Integer Dyadic Source # 
CanDiv Rational Dyadic Source # 
CanDiv Dyadic Int Source # 

Associated Types

type DivTypeNoCN Dyadic Int :: * #

type DivType Dyadic Int :: * #

CanDiv Dyadic Integer Source # 
CanDiv Dyadic Rational Source # 
CanMulAsymmetric Int Dyadic Source # 

Associated Types

type MulType Int Dyadic :: * #

Methods

mul :: Int -> Dyadic -> MulType Int Dyadic #

CanMulAsymmetric Integer Dyadic Source # 

Associated Types

type MulType Integer Dyadic :: * #

CanMulAsymmetric Rational Dyadic Source # 

Associated Types

type MulType Rational Dyadic :: * #

CanMulAsymmetric Dyadic Int Source # 

Associated Types

type MulType Dyadic Int :: * #

Methods

mul :: Dyadic -> Int -> MulType Dyadic Int #

CanMulAsymmetric Dyadic Integer Source # 

Associated Types

type MulType Dyadic Integer :: * #

CanMulAsymmetric Dyadic Rational Source # 

Associated Types

type MulType Dyadic Rational :: * #

CanMulAsymmetric Dyadic Dyadic Source # 

Associated Types

type MulType Dyadic Dyadic :: * #

CanPow Dyadic Int Source # 

Associated Types

type PowTypeNoCN Dyadic Int :: * #

type PowType Dyadic Int :: * #

CanPow Dyadic Integer Source # 
CanAddAsymmetric Int Dyadic Source # 

Associated Types

type AddType Int Dyadic :: * #

Methods

add :: Int -> Dyadic -> AddType Int Dyadic #

CanAddAsymmetric Integer Dyadic Source # 

Associated Types

type AddType Integer Dyadic :: * #

CanAddAsymmetric Rational Dyadic Source # 

Associated Types

type AddType Rational Dyadic :: * #

CanAddAsymmetric Dyadic Int Source # 

Associated Types

type AddType Dyadic Int :: * #

Methods

add :: Dyadic -> Int -> AddType Dyadic Int #

CanAddAsymmetric Dyadic Integer Source # 

Associated Types

type AddType Dyadic Integer :: * #

CanAddAsymmetric Dyadic Rational Source # 

Associated Types

type AddType Dyadic Rational :: * #

CanAddAsymmetric Dyadic Dyadic Source # 

Associated Types

type AddType Dyadic Dyadic :: * #

CanSub Int Dyadic Source # 

Associated Types

type SubType Int Dyadic :: * #

Methods

sub :: Int -> Dyadic -> SubType Int Dyadic #

CanSub Integer Dyadic Source # 

Associated Types

type SubType Integer Dyadic :: * #

CanSub Rational Dyadic Source # 

Associated Types

type SubType Rational Dyadic :: * #

CanSub Dyadic Int Source # 

Associated Types

type SubType Dyadic Int :: * #

Methods

sub :: Dyadic -> Int -> SubType Dyadic Int #

CanSub Dyadic Integer Source # 

Associated Types

type SubType Dyadic Integer :: * #

CanSub Dyadic Rational Source # 

Associated Types

type SubType Dyadic Rational :: * #

CanSub Dyadic Dyadic Source # 

Associated Types

type SubType Dyadic Dyadic :: * #

CanMinMaxAsymmetric Int Dyadic Source # 

Associated Types

type MinMaxType Int Dyadic :: * #

CanMinMaxAsymmetric Integer Dyadic Source # 
CanMinMaxAsymmetric Rational Dyadic Source # 
CanMinMaxAsymmetric Dyadic Int Source # 

Associated Types

type MinMaxType Dyadic Int :: * #

CanMinMaxAsymmetric Dyadic Integer Source # 
CanMinMaxAsymmetric Dyadic Rational Source # 
CanMinMaxAsymmetric Dyadic Dyadic Source # 
HasOrderAsymmetric Int Dyadic Source # 
HasOrderAsymmetric Integer Dyadic Source # 
HasOrderAsymmetric Rational Dyadic Source # 
HasOrderAsymmetric Dyadic Int Source # 
HasOrderAsymmetric Dyadic Integer Source # 
HasOrderAsymmetric Dyadic Rational Source # 
HasOrderAsymmetric Dyadic Dyadic Source # 
HasEqAsymmetric Int Dyadic Source # 
HasEqAsymmetric Integer Dyadic Source # 
HasEqAsymmetric Rational Dyadic Source # 
HasEqAsymmetric Dyadic Int Source # 
HasEqAsymmetric Dyadic Integer Source # 
HasEqAsymmetric Dyadic Rational Source # 
HasEqAsymmetric Dyadic Dyadic Source # 
ConvertibleExactly Int Dyadic Source # 
ConvertibleExactly Integer Dyadic Source # 
ConvertibleExactly Rational Dyadic Source # 
ConvertibleExactly MPFloat Dyadic Source # 
ConvertibleExactly Dyadic Rational Source # 
ConvertibleExactly Dyadic MPFloat Source # 
ConvertibleExactly Dyadic Dyadic Source # 
ConvertibleExactly ErrorBound Dyadic # 
SuitableForCE es => CanEnsureCE es Dyadic Source # 

Associated Types

type EnsureCE es Dyadic :: * #

type EnsureNoCE es Dyadic :: * #

CanTestContains MPBall Dyadic Source # 

Methods

contains :: MPBall -> Dyadic -> Bool Source #

(CanDiv Dyadic b, CanEnsureCE es b, CanEnsureCE es (DivType Dyadic b), CanEnsureCE es (DivTypeNoCN Dyadic b), SuitableForCE es) => CanDiv Dyadic (CollectErrors es b) Source # 

Associated Types

type DivTypeNoCN Dyadic (CollectErrors es b) :: * #

type DivType Dyadic (CollectErrors es b) :: * #

(CanMulAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (MulType Dyadic b), SuitableForCE es) => CanMulAsymmetric Dyadic (CollectErrors es b) Source # 

Associated Types

type MulType Dyadic (CollectErrors es b) :: * #

Methods

mul :: Dyadic -> CollectErrors es b -> MulType Dyadic (CollectErrors es b) #

(CanPow Dyadic b, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN Dyadic b), CanEnsureCE es (PowType Dyadic b), SuitableForCE es) => CanPow Dyadic (CollectErrors es b) Source # 

Associated Types

type PowTypeNoCN Dyadic (CollectErrors es b) :: * #

type PowType Dyadic (CollectErrors es b) :: * #

(CanAddAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (AddType Dyadic b), SuitableForCE es) => CanAddAsymmetric Dyadic (CollectErrors es b) Source # 

Associated Types

type AddType Dyadic (CollectErrors es b) :: * #

Methods

add :: Dyadic -> CollectErrors es b -> AddType Dyadic (CollectErrors es b) #

(CanSub Dyadic b, CanEnsureCE es b, CanEnsureCE es (SubType Dyadic b), SuitableForCE es) => CanSub Dyadic (CollectErrors es b) Source # 

Associated Types

type SubType Dyadic (CollectErrors es b) :: * #

Methods

sub :: Dyadic -> CollectErrors es b -> SubType Dyadic (CollectErrors es b) #

(CanMinMaxAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Dyadic b), SuitableForCE es) => CanMinMaxAsymmetric Dyadic (CollectErrors es b) Source # 

Associated Types

type MinMaxType Dyadic (CollectErrors es b) :: * #

(HasOrderAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Dyadic b), IsBool (EnsureCE es (OrderCompareType Dyadic b)), SuitableForCE es) => HasOrderAsymmetric Dyadic (CollectErrors es b) Source # 
(HasEqAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (EqCompareType Dyadic b), IsBool (EnsureCE es (EqCompareType Dyadic b)), SuitableForCE es) => HasEqAsymmetric Dyadic (CollectErrors es b) Source # 
(ConvertibleExactly Dyadic t, Monoid es) => ConvertibleExactly Dyadic (CollectErrors es t) Source # 
Ring (CN Dyadic) Source # 
OrderedRing (CN Dyadic) Source # 
OrderedCertainlyRing (CN Dyadic) Source # 
(CanDiv a Dyadic, CanEnsureCE es a, CanEnsureCE es (DivType a Dyadic), CanEnsureCE es (DivTypeNoCN a Dyadic), SuitableForCE es) => CanDiv (CollectErrors es a) Dyadic Source # 

Associated Types

type DivTypeNoCN (CollectErrors es a) Dyadic :: * #

type DivType (CollectErrors es a) Dyadic :: * #

(CanMulAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (MulType a Dyadic), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Dyadic Source # 

Associated Types

type MulType (CollectErrors es a) Dyadic :: * #

Methods

mul :: CollectErrors es a -> Dyadic -> MulType (CollectErrors es a) Dyadic #

(CanPow a Dyadic, CanEnsureCE es a, CanEnsureCE es (PowType a Dyadic), CanEnsureCE es (PowTypeNoCN a Dyadic), SuitableForCE es) => CanPow (CollectErrors es a) Dyadic Source # 

Associated Types

type PowTypeNoCN (CollectErrors es a) Dyadic :: * #

type PowType (CollectErrors es a) Dyadic :: * #

(CanAddAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (AddType a Dyadic), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) Dyadic Source # 

Associated Types

type AddType (CollectErrors es a) Dyadic :: * #

Methods

add :: CollectErrors es a -> Dyadic -> AddType (CollectErrors es a) Dyadic #

(CanSub a Dyadic, CanEnsureCE es a, CanEnsureCE es (SubType a Dyadic), SuitableForCE es) => CanSub (CollectErrors es a) Dyadic Source # 

Associated Types

type SubType (CollectErrors es a) Dyadic :: * #

Methods

sub :: CollectErrors es a -> Dyadic -> SubType (CollectErrors es a) Dyadic #

(CanMinMaxAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Dyadic), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Dyadic Source # 

Associated Types

type MinMaxType (CollectErrors es a) Dyadic :: * #

(HasOrderAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Dyadic), IsBool (EnsureCE es (OrderCompareType a Dyadic)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Dyadic Source # 
(HasEqAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (EqCompareType a Dyadic), IsBool (EnsureCE es (EqCompareType a Dyadic)), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) Dyadic Source # 
type AbsType Dyadic Source # 
type NegType Dyadic Source # 
type DivType Int Dyadic Source # 
type DivType Integer Dyadic Source # 
type DivType Rational Dyadic Source # 
type DivType Dyadic Int Source # 
type DivType Dyadic Integer Source # 
type DivType Dyadic Rational Source # 
type DivType Dyadic Dyadic # 
type DivType Dyadic MPBall # 
type DivType MPBall Dyadic # 
type DivTypeNoCN Int Dyadic Source # 
type DivTypeNoCN Integer Dyadic Source # 
type DivTypeNoCN Rational Dyadic Source # 
type DivTypeNoCN Dyadic Int Source # 
type DivTypeNoCN Dyadic Integer Source # 
type DivTypeNoCN Dyadic Rational Source # 
type DivTypeNoCN Dyadic Dyadic # 
type DivTypeNoCN Dyadic MPBall # 
type DivTypeNoCN MPBall Dyadic # 
type MulType Int Dyadic Source # 
type MulType Integer Dyadic Source # 
type MulType Rational Dyadic Source # 
type MulType Dyadic Int Source # 
type MulType Dyadic Integer Source # 
type MulType Dyadic Rational Source # 
type MulType Dyadic Dyadic Source # 
type MulType Dyadic MPBall # 
type MulType MPBall Dyadic # 
type PowType Dyadic Int Source # 
type PowType Dyadic Integer Source # 
type PowType MPBall Dyadic # 
type PowTypeNoCN Dyadic Int Source # 
type PowTypeNoCN Dyadic Integer Source # 
type PowTypeNoCN MPBall Dyadic # 
type AddType Int Dyadic Source # 
type AddType Integer Dyadic Source # 
type AddType Rational Dyadic Source # 
type AddType Dyadic Int Source # 
type AddType Dyadic Integer Source # 
type AddType Dyadic Rational Source # 
type AddType Dyadic Dyadic Source # 
type AddType Dyadic MPBall # 
type AddType MPBall Dyadic # 
type SubType Int Dyadic Source # 
type SubType Integer Dyadic Source # 
type SubType Rational Dyadic Source # 
type SubType Dyadic Int Source # 
type SubType Dyadic Integer Source # 
type SubType Dyadic Rational Source # 
type SubType Dyadic Dyadic Source # 
type SubType Dyadic MPBall # 
type SubType MPBall Dyadic # 
type MinMaxType Int Dyadic Source # 
type MinMaxType Integer Dyadic Source # 
type MinMaxType Rational Dyadic Source # 
type MinMaxType Dyadic Int Source # 
type MinMaxType Dyadic Integer Source # 
type MinMaxType Dyadic Rational Source # 
type MinMaxType Dyadic Dyadic Source # 
type MinMaxType Dyadic MPBall # 
type MinMaxType MPBall Dyadic # 
type OrderCompareType Int Dyadic Source # 
type OrderCompareType Integer Dyadic Source # 
type OrderCompareType Rational Dyadic Source # 
type OrderCompareType Dyadic Int Source # 
type OrderCompareType Dyadic Integer Source # 
type OrderCompareType Dyadic Rational Source # 
type OrderCompareType Dyadic Dyadic Source # 
type OrderCompareType Dyadic MPBall # 
type OrderCompareType MPBall Dyadic # 
type EqCompareType Int Dyadic Source # 
type EqCompareType Integer Dyadic Source # 
type EqCompareType Rational Dyadic Source # 
type EqCompareType Dyadic Int Source # 
type EqCompareType Dyadic Integer Source # 
type EqCompareType Dyadic Rational Source # 
type EqCompareType Dyadic Dyadic Source # 
type EqCompareType Dyadic MPBall # 
type EqCompareType MPBall Dyadic # 
type EnsureNoCE es Dyadic Source # 
type EnsureCE es Dyadic Source # 
type DivType Dyadic (CollectErrors es b) Source # 
type DivTypeNoCN Dyadic (CollectErrors es b) Source # 
type MulType Dyadic (CollectErrors es b) Source # 
type PowType Dyadic (CollectErrors es b) Source # 
type PowTypeNoCN Dyadic (CollectErrors es b) Source # 
type AddType Dyadic (CollectErrors es b) Source # 
type SubType Dyadic (CollectErrors es b) Source # 
type MinMaxType Dyadic (CollectErrors es b) Source # 
type OrderCompareType Dyadic (CollectErrors es b) Source # 
type EqCompareType Dyadic (CollectErrors es b) Source # 
type DivType (CollectErrors es a) Dyadic Source # 
type DivTypeNoCN (CollectErrors es a) Dyadic Source # 
type MulType (CollectErrors es a) Dyadic Source # 
type PowType (CollectErrors es a) Dyadic Source # 
type PowTypeNoCN (CollectErrors es a) Dyadic Source # 
type AddType (CollectErrors es a) Dyadic Source # 
type SubType (CollectErrors es a) Dyadic Source # 
type MinMaxType (CollectErrors es a) Dyadic Source # 
type OrderCompareType (CollectErrors es a) Dyadic Source # 
type EqCompareType (CollectErrors es a) Dyadic Source # 

Dyadic constructors

tests

tDyadic :: T Dyadic Source #

A runtime representative of type Dyadic. Used for specialising polymorphic tests to concrete types.