Add parentaxes, it, and gt fields to BSplineInterpolation

Storing parentaxes will allow us to do padding via OffsetArrays,
which has the major advantage of keeping the indices of the padded
array in-register with those of the original array. This should
simplify a lot of code.

src/b-splines/b-splines.jl

@@ -14,23 +14,27 @@ BSpline(::D) where {D<:Degree} = BSpline{D}()
 
 bsplinetype(::Type{BSpline{D}}) where {D<:Degree} = D
 
-struct BSplineInterpolation{T,N,TCoefs<:AbstractArray,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},pad} <: AbstractInterpolation{T,N,IT,GT}
+struct BSplineInterpolation{T,N,TCoefs<:AbstractArray,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},Axs<:Tuple{Vararg{AbstractUnitRange,N}}} <: AbstractInterpolation{T,N,IT,GT}
     coefs::TCoefs
+    parentaxes::Axs
+    it::IT
+    gt::GT
 end
-function BSplineInterpolation(::Type{TWeights}, A::AbstractArray{Tel,N}, ::IT, ::GT, ::Val{pad}) where {N,Tel,TWeights<:Real,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},pad}
-    isconcretetype(IT) || error("The b-spline type must be a leaf type (was $IT)")
-    isconcretetype(typeof(A)) || warn("For performance reasons, consider using an array of a concrete type (typeof(A) == $(typeof(A)))")
+function BSplineInterpolation(::Type{TWeights}, A::AbstractArray{Tel,N}, it::IT, gt::GT, axs) where {N,Tel,TWeights<:Real,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}
+    # String interpolation causes allocation, noinline avoids that unless they get called
+    @noinline err_concrete(IT) = error("The b-spline type must be a concrete type (was $IT)")
+    @noinline warn_concrete(A) = @warn("For performance reasons, consider using an array of a concrete type (typeof(A) == $(typeof(A)))")
 
-    c = zero(TWeights)
-    for _ in 2:N
-        c *= c
-    end
+    isconcretetype(IT) || err_concrete(IT)
+    isconcretetype(typeof(A)) || warn_concrete(A)
+
+    # Compute the output element type when positions have type TWeights
     if isempty(A)
-        T = Base.promote_op(*, typeof(c), eltype(A))
+        T = Base.promote_op(*, TWeights, eltype(A))
     else
-        T = typeof(c * first(A))
+        T = typeof(zero(TWeights) * first(A))
     end
-    BSplineInterpolation{T,N,typeof(A),IT,GT,pad}(A)
+    BSplineInterpolation{T,N,typeof(A),IT,GT,typeof(axs)}(A, fix_axis.(axs), it, gt)
 end
 
 # Utilities for working either with scalars or tuples/tuple-types
@@ -68,13 +72,17 @@ end
 @inline axes(itp::BSplineInterpolation{T,N,TCoefs,IT,GT,pad}) where {T,N,TCoefs,IT,GT,pad} =
     indices_removepad.(axes(itp.coefs), pad)
 
+fix_axis(r::Base.OneTo) = r
+fix_axis(r::Base.Slice) = r
+fix_axis(r::UnitRange) = Base.Slice(r)
+fix_axis(r::AbstractUnitRange) = fix_axis(UnitRange(r))
 function axes(itp::BSplineInterpolation{T,N,TCoefs,IT,GT,pad}, d) where {T,N,TCoefs,IT,GT,pad}
     d <= N ? indices_removepad(axes(itp.coefs, d), padextract(pad, d)) : axes(itp.coefs, d)
 end
 
 function interpolate(::Type{TWeights}, ::Type{TC}, A, it::IT, gt::GT) where {TWeights,TC,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}
-    Apad, Pad = prefilter(TWeights, TC, A, IT, GT)
-    BSplineInterpolation(TWeights, Apad, it, gt, Pad)
+    Apad = prefilter(TWeights, TC, A, it, gt)
+    BSplineInterpolation(TWeights, Apad, it, gt, axes(A))
 end
 function interpolate(A::AbstractArray, it::IT, gt::GT) where {IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}
     interpolate(tweight(A), tcoef(A), A, it, gt)
@@ -91,7 +99,12 @@ tcoef(A::AbstractArray{Float32}) = Float32
 tcoef(A::AbstractArray{Rational{Int}}) = Rational{Int}
 tcoef(A::AbstractArray{T}) where {T<:Integer} = typeof(float(zero(T)))
 
-interpolate!(::Type{TWeights}, A, it::IT, gt::GT) where {TWeights,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}} = BSplineInterpolation(TWeights, prefilter!(TWeights, A, IT, GT), it, gt, Val{0}())
+function interpolate!(::Type{TWeights}, A, it::IT, gt::GT) where {TWeights,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}
+    # Set the bounds of the interpolant inward, if necessary
+    axsA = axes(A)
+    axspad = padded_axes(axsA, it)
+    BSplineInterpolation(TWeights, prefilter!(TWeights, A, it, gt), it, gt, fix_axis.(padinset.(axsA, axspad)))
+end
 function interpolate!(A::AbstractArray, it::IT, gt::GT) where {IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}
     interpolate!(tweight(A), A, it, gt)
 end