Copyright | (c) Michal Konecny |
---|---|
License | BSD3 |
Maintainer | mikkonecny@gmail.com |
Stability | experimental |
Portability | portable |
Safe Haskell | None |
Language | Haskell98 |
Arbitrary precision ball arithmetic
- module AERN2.Norm
- module AERN2.MP.Precision
- module AERN2.MP.Accuracy
- module AERN2.MP.UseMPFR.ErrorBound
- module AERN2.MP.Enclosure
- data MPBall = MPBall {}
- type CanBeMPBall t = ConvertibleExactly t MPBall
- mpBall :: CanBeMPBall t => t -> MPBall
- type CanBeMPBallP t = ConvertibleWithPrecision t MPBall
- mpBallP :: CanBeMPBallP t => Precision -> t -> MPBall
- reducePrecionIfInaccurate :: MPBall -> MPBall
- piBallP :: Precision -> MPBall
- byEndpointsMP :: (MPFloat -> MPFloat -> MPFloat) -> MPBall -> MPBall -> MPBall
- fromApproxWithLipschitz :: (MPFloat -> MPFloat) -> (MPFloat -> MPFloat) -> MPFloat -> MPBall -> MPBall
Auxiliary types
module AERN2.Norm
module AERN2.MP.Precision
module AERN2.MP.Accuracy
module AERN2.MP.UseMPFR.ErrorBound
module AERN2.MP.Enclosure
The Ball type
type CanBeMPBall t = ConvertibleExactly t MPBall Source #
mpBall :: CanBeMPBall t => t -> MPBall Source #
type CanBeMPBallP t = ConvertibleWithPrecision t MPBall Source #
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.
Ball construction/extraction functions
Ball operations (see also instances)
Helpers for constructing ball functions
byEndpointsMP :: (MPFloat -> MPFloat -> MPFloat) -> MPBall -> MPBall -> MPBall Source #
Computes an *increasing* ball fucntion f
from *exact* MPFR operations.
fromApproxWithLipschitz Source #
:: (MPFloat -> MPFloat) |
|
-> (MPFloat -> MPFloat) |
|
-> MPFloat |
|
-> MPBall -> MPBall |
|
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
.