Portability  nonportable (requires fenv.h) 

Stability  experimental 
Maintainer  mik@konecny.aow.cz 
This module bundles some of the most important functionality of the AERNRnToRm package. It is intended to be imported *qualified*.
AERNRnToRm provides
datatypes and abstractions for approximating functions
of type D > R^m
where D
is a bounded interval in R^n
with nonempty interior.
Abstractions are provided via 4 type classes:

ERUnitFnBase
: generalises polynomials with floating point coefficients. (Not exported here, used only internally.) 
ERFnApprox
: generalises functions enclosures on a certain unspecified domain. 
ERUnitFnApprox
(extendsERFnApprox
): generalises function graph enclosures on the domain[1,1]^n
. (Not exported here, used only internally.) 
ERFnDomApprox
(extendsERFnApprox
): generalises function enclosures over a specified and queriable domain box (instance of classDomainBox
).
At all levels, all field operations are supported as well as some elementary operations, namely exp, sin and cos. Log and sqrt are planned to be added soon.
Implementations of ERUnitFnBase
:
By using the Chebyshev basis on domain [1,1]^n
,
we gain simple and optimally rounding degree reduction
as well as relatively simple handling of rounding
in other operations.
Implementations of ERUnitFnApprox
:
Implementations of ERFnDomApprox
:

ERFnDomTranslApprox
: builds a basic implementation using an instance ofERUnitFnApprox
. 
ERFnTuple
: extends another implementation ofERFnDomApprox
to work with lists of functions simultaneously. 
ERFnDomEdgesApprox
: separately enclose a function on its domain box as well as on all the domain's hyperedges (including the corners) using another implementation ofERFnDomApprox
. 
ERFnPiecewise
: allows the domain box to be bisected to an arbitrary finite depth and uses another implementation ofERFnDomApprox
to approximate the function on each segment.
Documentation
module Data.Number.ER.RnToRm.Approx