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.Ball.Elementary

Contents

Description

Elementary operations on arbitrary precision dyadic balls

Synopsis

Ball operations (see also instances)

piBallP :: Precision -> MPBall #

Helpers for constructing ball functions

fromApproxWithLipschitz #

Arguments

:: (MPFloat -> MPFloat)

fDown: a version of f on MPFloat rounding *downwards*

-> (MPFloat -> MPFloat)

fUp: a version of f on MPFloat rounding *upwards*

-> 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 # 

Associated Types

type SqrtType MPBall :: * #

Methods

sqrt :: MPBall -> SqrtType MPBall #

CanExp MPBall # 

Associated Types

type ExpType MPBall :: * #

Methods

exp :: MPBall -> ExpType MPBall #

CanLog MPBall # 

Associated Types

type LogType MPBall :: * #

Methods

log :: MPBall -> LogType MPBall #

CanSinCos MPBall # 

Associated Types

type SinCosType MPBall :: * #

Methods

cos :: MPBall -> SinCosType MPBall #

sin :: MPBall -> SinCosType MPBall #

CanPow MPBall Rational # 
CanPow MPBall Dyadic # 
CanPow MPBall MPBall #