aern2-mp-0.2.2.0: Multi-precision ball (interval) arithmetic
Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

AERN2.MP.Ball.Elementary

Description

Elementary operations on arbitrary precision dyadic balls

Synopsis

Ball operations (see also instances)

Helpers for constructing ball functions

fromApproxWithLipschitz Source #

Arguments

:: (MPFloat -> BoundsCEDU MPFloat)

fCEDU: a version of f on MPFloat returning rigorous bounds

-> MPFloat

lip a Lipschitz constant for f, lip > 0

-> MPBall -> MPBall

f on MPBall rounding *outwards*

Computes a real function f from correctly rounded MPFR-approximations and a number lip which is a Lipschitz constant for f, i.e. |f(x) - f(y)| <= lip * |x - y| for all x,y.

Orphan instances

CanSqrt MPBall Source # 
Instance details

Associated Types

type SqrtType MPBall #

Methods

sqrt :: MPBall -> SqrtType MPBall #

CanExp MPBall Source # 
Instance details

Associated Types

type ExpType MPBall #

Methods

exp :: MPBall -> ExpType MPBall #

CanLog MPBall Source # 
Instance details

Associated Types

type LogType MPBall #

Methods

log :: MPBall -> LogType MPBall #

CanSinCos MPBall Source # 
Instance details

Associated Types

type SinCosType MPBall #

CanPow Int MPBall Source # 
Instance details

Associated Types

type PowType Int MPBall #

Methods

pow :: Int -> MPBall -> PowType Int MPBall #

CanPow Integer MPBall Source # 
Instance details

Associated Types

type PowType Integer MPBall #

CanPow Rational MPBall Source # 
Instance details

Associated Types

type PowType Rational MPBall #

CanPow MPBall Rational Source # 
Instance details

Associated Types

type PowType MPBall Rational #

CanPow MPBall Dyadic Source # 
Instance details

Associated Types

type PowType MPBall Dyadic #

CanPow MPBall MPBall Source # 
Instance details

Associated Types

type PowType MPBall MPBall #