Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary

Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary

Portability	portable
Stability	experimental
Maintainer	mik@konecny.aow.cz

Description

Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.

Implementation of elementary functions applied to polynomials.

Synopsis

enclSqrt :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclExp :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclPow :: (ERRealBase b, RealFrac b, Integral i, DomainBox box varid Int, Ord box) => Int -> Int -> (ERChebPoly box b, ERChebPoly box b) -> i -> (ERChebPoly box b, ERChebPoly box b)

enclLog :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclSine :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclCosine :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

sincosTaylorAux :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> Bool -> (ERChebPoly box b, ERChebPoly box b) -> Int -> Int -> ERInterval b -> ((ERChebPoly box b, ERChebPoly box b), Int, ERInterval b)

enclAtan :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

Documentation

enclSqrt

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	??
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise exponential of a square root enclosure.

enclExp

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	used to derive minimum approx Taylor degree
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise exponential of a polynomial enclosure.

enclPow

:: (ERRealBase b, RealFrac b, Integral i, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> (ERChebPoly box b, ERChebPoly box b)
-> i
-> (ERChebPoly box b, ERChebPoly box b)	lower (negated) and upper bound
Approximate the pointwise integer power of an enclosure.

enclLog

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	??
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise natural logarithm of an enclosure.

enclSine

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	how hard to try (determines Taylor degree and granularity)
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise sine of an enclosure. Assuming the polynomial range is [-pi2, pi2].

enclCosine

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	how hard to try (determines Taylor degree and granularity)
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise cosine of an enclosure. Assuming the polynomial range is [-pi2, pi2].

sincosTaylorAux

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> Bool	is sine ?
-> (ERChebPoly box b, ERChebPoly box b)
-> Int	how far to go in the Taylor series
-> Int	degree of the term now being constructed
-> ERInterval b	the coefficient of the term now being constructed
-> ((ERChebPoly box b, ERChebPoly box b), Int, ERInterval b)	Bounds for the series result and information about the first discarded term, from which some bound on the uniform error can be deduced.

enclAtan

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> EffortIndex	how far to go in the Euler's series
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise arcus tangens of an enclosure.

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