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

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

Implementation of elementary functions applied to polynomials.

Documentation

enclSqrt

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> Int

maximum polynomial degree

-> Int

maximum term count

-> EffortIndex

for calls to other ER functions

-> Int

how many times to iterate

-> (ERChebPoly box b, ERChebPoly box b)

-> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise square root of a polynomial enclosure.

enclExp

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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

Arguments

:: (Integral i, ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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

Arguments

:: (ERRealBase 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

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> 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.