Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.Ball.Elementary

Contents

Ball operations (see also instances)
Helpers for constructing ball functions
Orphan instances

Description

Elementary operations on arbitrary precision dyadic balls

Synopsis

piBallP :: Precision -> MPBall
fromApproxWithLipschitz :: (MPFloat -> BoundsCEDU MPFloat) -> MPFloat -> MPBall -> MPBall

Ball operations (see also instances)

piBallP :: Precision -> MPBall Source #

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 # Methods cos :: MPBall -> SinCosType MPBall # sin :: MPBall -> SinCosType MPBall #
CanPow Int MPBall Source #
Instance details Associated Types type PowType Int MPBall # type PPowType Int MPBall # Methods pow :: Int -> MPBall -> PowType Int MPBall # ppow :: Int -> MPBall -> PPowType Int MPBall #
CanPow Integer MPBall Source #
Instance details Associated Types type PowType Integer MPBall # type PPowType Integer MPBall # Methods pow :: Integer -> MPBall -> PowType Integer MPBall # ppow :: Integer -> MPBall -> PPowType Integer MPBall #
CanPow Rational MPBall Source #
Instance details Associated Types type PowType Rational MPBall # type PPowType Rational MPBall # Methods pow :: Rational -> MPBall -> PowType Rational MPBall # ppow :: Rational -> MPBall -> PPowType Rational MPBall #
CanPow MPBall Rational Source #
Instance details Associated Types type PowType MPBall Rational # type PPowType MPBall Rational # Methods pow :: MPBall -> Rational -> PowType MPBall Rational # ppow :: MPBall -> Rational -> PPowType MPBall Rational #
CanPow MPBall Dyadic Source #
Instance details Associated Types type PowType MPBall Dyadic # type PPowType MPBall Dyadic # Methods pow :: MPBall -> Dyadic -> PowType MPBall Dyadic # ppow :: MPBall -> Dyadic -> PPowType MPBall Dyadic #
CanPow MPBall MPBall Source #
Instance details Associated Types type PowType MPBall MPBall # type PPowType MPBall MPBall # Methods pow :: MPBall -> MPBall -> PowType MPBall MPBall # ppow :: MPBall -> MPBall -> PPowType MPBall MPBall #